(19)
(11)EP 2 153 561 B1

(12)EUROPEAN PATENT SPECIFICATION

(45)Mention of the grant of the patent:
09.01.2019 Bulletin 2019/02

(21)Application number: 08795885.6

(22)Date of filing:  05.06.2008
(51)International Patent Classification (IPC): 
H04J 11/00(2006.01)
H04L 1/00(2006.01)
H04L 27/34(2006.01)
(86)International application number:
PCT/US2008/065994
(87)International publication number:
WO 2008/151308 (11.12.2008 Gazette  2008/50)

(54)

METHOD AND APPARATUS FOR SIGNALING WITH CAPACITY OPTIMIZED CONSTELLATIONS

VERFAHREN UND VORRICHTUNG ZUR SIGNALISIERUNG MIT KAPAZITÄTSOPTIMIERTEN KONSTELLATIONEN

PROCÉDÉ ET APPAREIL DE SIGNALISATION DE CONSTELLATIONS OPTIMISANT LA CAPACITÉ


(84)Designated Contracting States:
AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HR HU IE IS IT LI LT LU LV MC MT NL NO PL PT RO SE SI SK TR

(30)Priority: 05.06.2007 US 933319 P

(43)Date of publication of application:
17.02.2010 Bulletin 2010/07

(73)Proprietor: Constellation Designs, Inc.
Pacific Palisades, CA 90272 (US)

(72)Inventors:
  • Barsoum, Maged F.
    San Jose, CA 95120 (US)
  • Jones, Christopher Richard
    Pacific Palisades, CA 90272 (US)

(74)Representative: Derry, Paul Stefan 
Venner Shipley LLP 200 Aldersgate
London EC1A 4HD
London EC1A 4HD (GB)


(56)References cited: : 
US-A1- 2004 022 179
US-A1- 2007 116 161
US-A1- 2006 155 843
US-B1- 6 603 801
  
  • RICCARDO DE GAUDENZI ET AL: "Performance analysis of turbo-coded APSK modulations over Nonlinear Satellite Channels", IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, IEEE SERVICE CENTER, PISCATAWAY, NJ, US, vol. 5, no. 9, 6 September 2006 (2006-09-06), pages 2396-2407, XP002457811, ISSN: 1536-1276, DOI: 10.1109/TWC.2006.1687763
  • DIRK SOMMER ET AL: "Signal Shaping by Non-Uniform QAM for AWGN Channels and Applications Using Turbo Coding", PROC. ITG CONF. SOURCE AND CHANNEL CODING, 31 January 2000 (2000-01-31), pages 81-86, XP055110228,
  • RICCARDO DE GAUDENZI ET AL: "Turbo-coded APSK modulations design for satellite broadband communications", INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING, JOHN WILEY & SONS, CHICHESTER, GB, vol. 24, no. 4, 1 July 2006 (2006-07-01), pages 261-281, XP008134566, ISSN: 1542-0973, DOI: 10.1002/SAT.841 [retrieved on 2006-05-19]
  • FEI ZESONG ET AL: "Shaping gain by non-uniform qam constellation i with binary turbo coded modulation", PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS, 2003. PIMRC 2003. 14TH IEEE PROCEEDINGS ON SEPT. 7-10, 2003, IEEE, PISCATAWAY, NJ, USA, vol. 2, 7 September 2003 (2003-09-07), pages 1863-1867, XP010678797, ISBN: 978-0-7803-7822-3
  • MAGED F BARSOUM ET AL: "Constellation Design via Capacity Maximization", INFORMATION THEORY, 2007. ISIT 2007. IEEE INTERNATIONAL SYMPOSIUM ON, IEEE, PISCATAWAY, NJ, USA, 24 June 2007 (2007-06-24), pages 1821-1825, XP031440978, ISBN: 978-1-4244-1397-3
  
Note: Within nine months from the publication of the mention of the grant of the European patent, any person may give notice to the European Patent Office of opposition to the European patent granted. Notice of opposition shall be filed in a written reasoned statement. It shall not be deemed to have been filed until the opposition fee has been paid. (Art. 99(1) European Patent Convention).


Description

BACKGROUND



[0001] The present invention generally relates to bandwidth and/or power efficient digital transmission systems and more specifically to the use of unequally spaced constellations having increased capacity.

[0002] The term "constellation" is used to describe the possible symbols that can be transmitted by a typical digital communication system. A receiver attempts to detect the symbols that were transmitted by mapping a received signal to the constellation. The minimum distance (dmin) between constellation points is indicative of the capacity of a constellation at high signal-to-noise ratios (SNRs). Therefore, constellations used in many communication systems are designed to maximize dmin. Increasing the dimensionality of a constellation allows larger minimum distance for constant constellation energy per dimension. Therefore, a number of multi-dimensional constellations with good minimum distance properties have been designed.

[0003] Communication systems have a theoretical maximum capacity, which is known as the Shannon limit. Many communication systems attempt to use codes to increase the capacity of a communication channel. Significant coding gains have been achieved using coding techniques such as turbo codes and LDPC codes. The coding gains achievable using any coding technique are limited by the constellation of the communication system. The Shannon limit can be thought of as being based upon a theoretical constellation known as a Gaussian distribution, which is an infinite constellation where symbols at the center of the constellation are transmitted more frequently than symbols at the edge of the constellation. Practical constellations are finite and transmit symbols with equal likelihoods, and therefore have capacities that are less than the Gaussian capacity. The capacity of a constellation is thought to represent a limit on the gains that can be achieved using coding when using that constellation..

[0004] Prior attempts have been made to develop unequally spaced constellations. For example, a system has been proposed that uses unequally spaced constellations that are optimized to minimize the error rate of an uncoded system. Another proposed system uses a constellation with equiprobable but unequally spaced symbols in an attempts to mimic a Gaussian distribution.

[0005] Other approaches increases the dimensionality of a constellation or select a new symbol to be transmitted taking into consideration previously transmitted symbols. However, these constellation were still designed based on a minimum distance criteria..

[0006] The use of non-uniform QAM constellation for capacity improvement has been disclosed in the following document: D. Sommer and G. P. Fettweis, "Signal shaping by non-uniform QAM for AWGN channels and applications using turbo coding", Proc. 2000 ITG Conf. Source and Channel Coding, pp. 81-86. The optimizing of APSK constellations has been disclosed in the following document: R. De Gaudenzi, A. Guillen i Fabregas and A. Martinez, "Performance analysis of turbo-coded APSK modulations over nonlinear satellite channels," in IEEE Transactions on Wireless Communications, vol. 5, no. 9, pp. 2396-2407, September 2006.

SUMMARY OF THE INVENTION



[0007] The invention is defined and limited by the scope of appended claims 1-17. In the following description, any embodiment(s) referred to and not falling within the scope of the appended claims, is (are) merely example(s) useful to the understanding of the invention.

[0008] Systems and methods are described for constructing a modulation such that the constrained capacity between a transmitter and a receiver approaches the Gaussian channel capacity limit first described by Shannon [ref Shannon 1948]. Traditional communications systems employ modulations that leave a significant gap to Shannon Gaussian capacity. The modulations of the present invention reduce, and in some cases, nearly eliminate this gap. The invention does not require specially designed coding mechanisms that tend to transmit some points of a modulation more frequently than others but rather provides a method for locating points (in a one or multiple dimensional space) in order to maximize capacity between the input and output of a bit or symbol mapper and demapper respectively. Practical application of the method allows systems to transmit data at a given rate for less power or to transmit data at a higher rate for the same amount of power.

[0009] One embodiment of the invention includes a transmitter configured to transmit signals to a receiver via a communication channel, wherein the transmitter, includes a coder configured to receive user bits and output encoded bits at an expanded output encoded bit rate, a mapper configured to map encoded bits to symbols in a symbol constellation, a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper. In addition, the receiver includes a demodulator configured to demodulate the received signal via the communication channel, a demapper configured to estimate likelihoods from the demodulated signal, a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper. Furthermore, the symbol constellation is a capacity optimized geometrically spaced symbol constellation that provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes dmin.

[0010] A further embodiment of the invention includes encoding the bits of user information using a coding scheme, mapping the encoded bits of user information to a symbol constellation, wherein the symbol constellation is a capacity optimized geometrically spaced symbol constellation that provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes dmin, modulating the symbols in accordance with a modulation scheme, transmitting the modulated signal via the communication channel, receiving a modulated signal, demodulating the modulated signal in accordance with the modulation scheme, demapping the demodulated signal using the geometrically shaped signal constellation to produce likelihoods, and decoding the likelihoods to obtain an estimate of the decoded bits.

[0011] Another embodiment of the invention includes selecting an appropriate constellation size and a desired capacity per dimension, estimating an initial SNR at which the system is likely to operate, and iteratively optimizing the location of the points of the constellation to maximize a capacity measure until a predetermined improvement in the SNR performance of the constellation relative to a constellation that maximizes dmin has been achieved.

[0012] A still further embodiment of the invention includes selecting an appropriate constellation size and a desired capacity per dimension, estimating an initial SNR at which the system is likely to operate, and iteratively optimizing the location of the points of the constellation to maximize a capacity measure until a predetermined improvement in the SNR performance of the constellation relative to a constellation that maximizes dmin has been achieved.

[0013] Still another embodiment of the invention includes selecting an appropriate constellation size and a desired SNR, and optimizing the location of the points of the constellation to maximize a capacity measure of the constellation.

[0014] A yet further embodiment of the invention includes obtaining a geometrically shaped PAM constellation with a constellation size that is the square root of said given constellation size, where the geometrically shaped PAM constellation has a capacity greater than that of a PAM constellation that maximizes dmin, creating an orthogonalized PAM constellation using the geometrically shaped PAM constellation, and combining the geometrically shaped PAM constellation and the orthogonalized PAM constellation to produce a geometrically shaped QAM constellation.

[0015] Another further embodiment of the invention includes transmitting information over a channel using a geometrically shaped symbol constellation, and modifying the location of points within the geometrically shaped symbol constellation to change the target user data rate.

BRIEF DESCRIPTION OF DRAWINGS



[0016] 

FIG. 1 is a conceptual illustration of a communication system in accordance with an embodiment of the invention.

FIG. 2 is a conceptual illustration of a transmitter in accordance with an embodiment of the invention.

FIG. 3 is a conceptual illustration of a receiver in accordance with an embodiment of the invention.

FIG. 4a is a conceptual illustration of the joint capacity of a channel.

FIG. 4b is a conceptual illustration of the parallel decoding capacity of a channel.

FIG. 5 is a flow chart showing a process for obtaining a constellation optimized for capacity for use in a communication system having a fixed code rate and modulation scheme in accordance with an embodiment of the invention.

FIG. 6a is a chart showing a comparison of Gaussian capacity and PD capacity for traditional PAM-2,4,8,16,32.

FIG. 6b is a chart showing a comparison between Gaussian capacity and joint capacity for traditional PAM-2,4,8,16,32.

FIG. 7 is a chart showing the SNR gap to Gaussian capacity for the PD capacity and joint capacity of traditional PAM-2,4,8,16,32 constellations.

FIG. 8a is a chart comparing the SNR gap to Gaussian capacity of the PD capacity for traditional and optimized PAM-2,4,8,16,32 constellations.

FIG. 8b is a chart comparing the SNR gap to Gaussian capacity of the joint capacity for traditional and optimized PAM-2,4,8,16,32 constellations.

FIG. 9 is a chart showing Frame Error Rate performance of traditional and PD capacity optimized PAM-32 constellations in simulations involving several different length LDPC codes.

FIGS. 10a - 10d are locus plots showing the location of constellation points of a PAM-4 constellation optimized for PD capacity and joint capacity versus user bit rate per dimension and versus SNR.

FIGS. 11a and 11b are design tables of PD capacity and joint capacity optimized PAM-4 constellations in accordance with embodiments of the invention.

FIGS. 12a - 12d are locus plots showing the location of constellation points of a PAM-8 constellation optimized for PD capacity and joint capacity versus user bit rate per dimension and versus SNR.

FIGS. 13a and 13b are design tables of PD capacity and joint capacity optimized PAM-8 constellations in accordance with embodiments of the invention.

FIGS. 14a - 14d are locus plots showing the location of constellation points of a PAM- 16 constellation optimized for PD capacity and joint capacity versus user bit rate per dimension and versus SNR.

FIGS. 15a and 15b are design tables of PD capacity and joint capacity optimized PAM-16 constellations in accordance with embodiments of the invention.

FIGS. 16a - 16d are locus plots showing the location of constellation points of a PAM-32 constellation optimized for PD capacity and joint capacity versus user bit rate per dimension and versus SNR.

FIGS. 17a and 17b are design tables of PD capacity and joint capacity optimized PAM-32 constellations in accordance with embodiments of the invention.

FIG. 18 is a chart showing the SNR gap to Gaussian capacity for traditional and capacity optimized PSK constellations.

FIG. 19 is a chart showing the location of constellation points of PD capacity optimized PSK-32 constellations.

FIG. 20 is a series of PSK-32 constellations optimized for PD capacity at different SNRs.

FIG. 21 illustrates a QAM-64 constructed from orthogonal Cartesian product of two PD optimized PAM-8 constellations in accordance with an embodiment of the invention.

FIGS. 22a and 22b are locus plots showing the location of constellation points of a PAM-4 constellation optimized for PD capacity over a fading channel versus user bit rate per dimension and versus SNR.

FIGS. 23a and 23b are locus plots showing the location of constellation points of a PAM-8 constellation optimized for PD capacity over a fading channel versus user bit rate per dimension and versus SNR.

FIGS. 24a and 24b are locus plots showing the location of constellation points of a PAM-16 constellation optimized for PD capacity over a fading channel versus user bit rate per dimension and versus SNR.


DETAILED DESCRIPTION OF THE INVENTION



[0017] Turning now to the drawings, communication systems in accordance with embodiments of the invention are described that use signal constellations, which have unequally spaced (i.e. 'geometrically' shaped) points. In several embodiments, the locations of geometrically shaped points are designed to provide a given capacity measure at a reduced signal-to-noise ratio (SNR) compared to the SNR required by.a constellation that maximizes dmin. In many embodiments, the constellations are selected to provide increased capacity at a predetermined range of channel signal-to-noise ratios (SNR). Capacity measures that can be used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

[0018] In many embodiments, the communication systems utilize capacity approaching codes including, but not limited to, LDPC and Turbo codes. As is discussed further below, direct optimization of the constellation points of a communication system utilizing a capacity approaching channel code, can yield different constellations depending on the SNR for which they are optimized. Therefore, the same constellation is unlikely to achieve the same coding gains applied across all code rates; that is, the same constellation will not enable the best possible performance across all rates. In many instances, a constellation at one code rate can achieve gains that cannot be achieved at another code rate. Processes for selecting capacity optimized constellations to achieve increased coding gains based upon a specific coding rate in accordance with embodiments of the invention are described below. In a number of embodiments, the communication systems can adapt location of points in a constellation in response to channel conditions, changes in code rate and/or to change the target user data rate.

COMMUNICATION SYSTEMS



[0019] A communication system in accordance with an embodiment of the invention is shown in FIG. 1. The communication system 10 includes a source 12 that provides user bits to a transmitter 14. The transmitter transmits symbols over a channel to a receiver 16 using a predetermined modulation scheme. The receiver uses knowledge of the modulation scheme, to decode the signal received from the transmitter. The decoded bits are provided to a sink device that is connected to the receiver.

[0020] A transmitter in accordance with an embodiment of the invention is shown in FIG. 2. The transmitter 14 includes a coder 20 that receives user bits from a source and encodes the bits in accordance with a predetermined coding scheme. In a number of embodiments, a capacity approaching code such as a turbo code or a LDPC code is used. In other embodiments, other coding schemes can be used to providing a coding gain within the communication system. A mapper 22 is connected to the coder. The mapper maps the bits output by the coder to a symbol within a geometrically distributed signal constellation stored within the mapper. The mapper provides the symbols to a modulator 24, which modulates the symbols for transmission via the channel.

[0021] A receiver in accordance with an embodiment of the invention is illustrated in FIG. 3. The receiver 16 includes a demodulator 30 that demodulates a signal received via the channel to obtain symbol or bit likelihoods. The demapper uses knowledge of the geometrically shaped symbol constellation used by the transmitter to determine these likelihoods. The demapper 32 provides the likelihoods to a decoder 34 that decodes the encoded bit stream to provide a sequence of received bits to a sink.

GEOMETRICALLY SHAPED CONSTELLATIONS



[0022] Transmitters and receivers in accordance with embodiments of the invention utilize geometrically shaped symbol constellations. In several embodiments, a geometrically shaped symbol constellation is used that optimizes the capacity of the constellation. Various geometrically shaped symbol constellations that can be used in accordance with embodiments of the invention, techniques for deriving geometrically shaped symbol constellations are described below.

SELECTION OF A GEOMETRICALLY SHAPED CONSTELLATIONS



[0023] Selection of a geometrically shaped constellation for use in a communication system in accordance with an embodiment of the invention can depend upon a variety of factors including whether the code rate is fixed. In many embodiments, a geometrically shaped constellation is used to replace a conventional constellation (i.e. a constellation maximized for dmin) in the mapper of transmitters and the demapper of receivers within a communication system. Upgrading a communication system involves selection of a constellation and in many instances the upgrade can be achieved via a simple firmware upgrade. In other embodiments, a geometrically shaped constellation is selected in conjunction with a code rate to meet specific performance requirements, which can for example include such factors as a specified bit rate, a maximum transmit power. Processes for selecting a geometric constellation when upgrading existing communication systems and when designing new communication systems are discussed further below.

UPGRADING EXISTING COMMUNICATION SYSTEMS



[0024] A geometrically shaped constellation that provides a capacity, which is greater than the capacity of a constellation maximized for dmin, can be used in place of a conventional constellation in a communication system in accordance with embodiments of the invention. In many instances, the substitution of the geometrically shaped constellation can be achieved by a firmware or software upgrade of the transmitters and receivers within the communication system. Not all geometrically shaped constellations have greater capacity than that of a constellation maximized for dmin. One approach to selecting a geometrically shaped constellation having a greater capacity than that of a constellation maximized for dmin is to optimize the shape of the constellation with respect to a measure of the capacity of the constellation for a given SNR. Capacity measures that can be used in the optimization process can include, but are not limited to, joint capacity or parallel decoding capacity.

JOINT CAPACITY AND PARALLEL DECODING CAPACITY



[0025] A constellation can be parameterized by the total number of constellation points, M, and the number of real dimensions, Ndim. In systems where there are no belief propagation iterations between the decoder and the constellation demapper, the constellation demapper can be thought of as part of the channel. A diagram conceptually illustrating the portions of a communication system that can be considered part of the channel for the purpose of determining PD capacity is shown in FIG. 4a. The portions of the communication system that are considered part of the channel are indicated by the ghost line 40. The capacity of the channel defined as such is the parallel decoding (PD) capacity, given by:

where Xi is the ith bit of the /-bits transmitted symbol, and Y is the received symbol, and I(A;B) denotes the mutual information between random variables A and B.

[0026] Expressed another way, the PD capacity of a channel can be viewed in terms of the mutual information between the output bits of the encoder (such as an LDPC encoder) at the transmitter and the likelihoods computed by the demapper at the receiver. The PD capacity is influenced by both the placement of points within the constellation and by the labeling assignments.

[0027] With belief propagation iterations between the demapper and the decoder, the demapper can no longer be viewed as part of the channel, and the joint capacity of the constellation becomes the tightest known bound on the system performance. A diagram conceptually illustrating the portions of a communication system that are considered part of the channel for the purpose of determining the joint capacity of a constellation is shown in FIG. 4b. The portions of the communication system that are considered part of the channel are indicated by the ghost line 42. The joint capacity of the channel is given by:



[0028] Joint capacity is a description of the achievable capacity between the input of the mapper on the transmit side of the link and the output of the channel (including for example AWGN and Fading channels). Practical systems must often 'demap' channel observations prior to decoding. In general, the step causes some loss of capacity. In fact it can be proven that CGCJOINTCPD. That is, CJOINT upper bounds the capacity achievable by CPD. The methods of the present invention are motivated by considering the fact that practical limits to a given communication system capacity are limited by CJOINT and CPD. In several embodiments of the invention, geometrically shaped constellations are selected that maximize these measures.

SELECTING A CONSTELLATION HAVING AN OPTIMAL CAPACITY



[0029] Geometrically shaped constellations in accordance with embodiments of the invention can be designed to optimize capacity measures including, but not limited to PD capacity or joint capacity. A process for selecting the points, and the labeling, of a geometrically shaped constellation for use in a communication system having a fixed code rate in accordance with an embodiment of the invention is shown in FIG. 5. The process 50 commences with the selection (52) of an appropriate constellation size M and a desired capacity per dimension η. In the illustrated embodiment, the process involves a check (52) to ensure that the constellation size can support the desired capacity. In the event that the constellation size could support the desired capacity, then the process iteratively optimizes the M-ary constellation for the specified capacity. Optimizing a constellation for a specified capacity often involves an iterative process, because the optimal constellation depends upon the SNR at which the communication system operates. The SNR for the optimal constellation to give a required capacity is not known a priori. Throughout the description of the present invention SNR is defined as the ratio of the average constellation energy per dimension to the average noise energy per dimension. In most cases the capacity can be set to equal the target user bit rate per symbol per dimension. In some cases adding some implementation margin on top of the target user bit rate could result in a practical system that can provide the required user rate at a lower rate. The margin is code dependent. The following procedure could be used to determine the target capacity that includes some margin on top of the user rate. First, the code (e.g. LDPC or Turbo) can be simulated in conjunction with a conventional equally spaced constellation. Second, from the simulation results the actual SNR of operation at the required error rate can be found. Third, the capacity of the conventional constellation at that SNR can be computed. Finally, a geometrically shaped constellation can be optimized for that capacity.

[0030] In the illustrated embodiment, the iterative optimization loop involves selecting an initial estimate of the SNR at which the system is likely to operate (i.e. SNRin). In several embodiments the initial estimate is the SNR required using a conventional constellation. In other embodiments, other techniques can be used for selecting the initial SNR. An M-ary constellation is then obtained by optimizing (56) the constellation to maximize a selected capacity measure at the initial SNRin estimate. Various techniques for obtaining an optimized constellation for a given SNR estimate are discussed below.

[0031] The SNR at which the optimized M-ary constellation provides the desired capacity per dimension η (SNRout) is determined (57). A determination (58) is made as to whether the SNRout and SNRin have converged. In the illustrated embodiment convergence is indicated by SNRout equaling SNRin. In a number of embodiments, convergence can be determined based upon the difference between SNRout and SNRin being less than a predetermined threshold. When SNRout and SNRin have not converged, the process performs another iteration selecting SNRout as the new SNRin (55). When SNRout and SNRin have converged, the capacity measure of the constellation has been optimized. As is explained in more detail below, capacity optimized constellation at low SNRs are geometrically shaped constellations that can achieve significantly higher performance gains (measured as reduction in minimum required SNR) than constellations that maximize dmin.

[0032] The process illustrated in FIG. 5 can maximize PD capacity or joint capacity of an M-ary constellation for a given SNR. Although the process illustrated in FIG. 5 shows selecting an M-ary constellation optimized for capacity, a similar process could be used that terminates upon generation of an M-ary constellation where the SNR gap to Gaussian capacity at a given capacity is a predetermined margin lower than the SNR gap of a conventional constellation, for example 0.5 db. Alternatively, other processes that identify M-ary constellations having capacity greater than the capacity of a conventional constellation can be used in accordance with embodiments of the invention. A geometrically shaped constellation in accordance with embodiments of the invention can achieve greater capacity than the capacity of a constellation that maximizes dmin without having the optimal capacity for the SNR range within which the communication system operates.

[0033] We note that constellations designed to maximize joint capacity may also be particularly well suited to codes with symbols over GF(q), or with multi-stage decoding.. Conversely constellations optimized for PD capacity could be better suited to the more common case of codes with symbols over GF(2)

OPTIMIZING THE CAPACITY OF AN M-ARY CONSTELLATION AT A GIVEN SNR



[0034] Processes for obtaining a capacity optimized constellation often involve determining the optimum location for the points of an M-ary constellation at a given SNR. An optimization process, such as the optimization process 56 shown in FIG. 5, typically involves unconstrained or constrained non-linear optimization. Possible objective functions to be maximized are the Joint or PD capacity functions. These functions may be targeted to channels including but not limited to Additive White Gaussian Noise (AWGN) or Rayleigh fading channels. The optimization process gives the location of each constellation point identified by its symbol labeling. In the case where the objective is joint capacity, point bit labelings are irrelevant meaning that changing the bit labelings doesn't change the joint capacity as long as the set of point locations remains unchanged..

[0035] The optimization process typically finds the constellation that gives the largest PD capacity or joint capacity at a given SNR. The optimization process itself often involves an iterative numerical process that among other things considers several constellations and selects the constellation that gives the highest capacity at a given SNR. In other embodiments, the constellation that requires the least SNR to give a required PD capacity or joint capacity can also be found. This requires running the optimization process iteratively as shown in FIG. 5.

[0036] Optimization constraints on the constellation point locations may include, but are not limited to, lower and upper bounds on point location, peak to average power of the resulting constellation, and zero mean in the resulting constellation. It can be easily shown that a globally optimal constellation will have zero mean (no DC component). Explicit inclusion of a zero mean constraint helps the optimization routine to converge more rapidly. Except for cases where exhaustive search of all combinations of point locations and labelings is possible it will not necessarily always be the case that solutions are provably globally optimal. In cases where exhaustive search is possible, the solution provided by the non-linear optimizer is in fact globally optimal.

[0037] The processes described above provide examples of the manner in which a geometrically shaped constellation having an increased capacity relative to a conventional capacity can be obtained for use in a communication system having a fixed code rate and modulation scheme. The actual gains achievable using constellations that are optimized for capacity compared to conventional constellations that maximize dmin are considered below.

GAINS ACHIEVED BY OPTIMIZED GEOMETRICALLY SPACED CONSTELLATIONS



[0038] The ultimate theoretical capacity achievable by any communication method is thought to be the Gaussian capacity, CG which is defined as:



[0039] Where signal-to-noise (SNR) is the ratio of expected signal power to expected noise power. The gap that remains between the capacity of a constellation and CG can be considered a measure of the quality of a given constellation design.

[0040] The gap in capacity between a conventional modulation scheme in combination with a theoretically optimal coder can be observed with reference to FIGS. 6a and 6b. FIG. 6a includes a chart 60 showing a comparison between Gaussian capacity and the PD capacity of conventional PAM-2, 4, 8, 16, and 32 constellations that maximize dmin, Gaps 62 exist between the plot of Gaussian capacity and the PD capacity of the various PAM constellations. FIG. 6b includes a chart 64 showing a comparison between Gaussian capacity and the joint capacity of conventional PAM-2, 4, 8, 16, and 32 constellations that maximize dmin, Gaps 66 exist between the plot of Gaussian capacity and the joint capacity of the various PAM constellations. These gaps in capacity represent the extent to which conventional PAM constellations fall short of obtaining the ultimate theoretical capacity i.e. the Gaussian capacity..

[0041] In order to gain a better view of the differences between the curves shown in FIGS. 6a and 6b at points close to the Gaussian capacity, the SNR gap to Gaussian capacity for different values of capacity for each constellation are plotted in FIG. 7. It is interesting to note from the chart 70 in FIG. 7 that (unlike the joint capacity) at the same SNR, the PD capacity does not necessarily increase with the number of constellation points. As is discussed further below, this is not the case with PAM constellations optimized for PD capacity.

[0042] FIGS. 8a and 8b summarize performance of constellations for PAM-4, 8, 16, and 32 optimized for PD capacity and joint capacity (it should be noted that BPSK is the optimal PAM-2 constellation at all code rates). The constellations are optimized for PD capacity and joint capacity for different target user bits per dimension (i.e. code rates). The optimized constellations are different depending on the target user bits per dimension, and also depending on whether they have been designed to maximize the PD capacity or the joint capacity. All the PD optimized PAM constellations are labeled using a gray labeling which is not always the binary reflective gray labeling. It should be noted that not all gray labels achieve the maximum possible PD capacity even given the freedom to place the constellation points anywhere on the real line. FIG. 8a shows the SNR gap for each constellation optimized for PD capacity. FIG. 8b shows the SNR gap to Gaussian capacity for each constellation optimized for joint capacity. Again, it should be emphasized that each '+' on the plot represents a different constellation.

[0043] Referring to FIG. 8a, the coding gain achieved using a constellation optimized for PD capacity can be appreciated by comparing the SNR gap at a user bit rate per dimension of 2.5 bits for PAM-32. A user bit rate per dimension of 2.5 bits for a system transmitting 5 bits per symbol constitutes a code rate of 1/2. At that code rate the constellation optimized for PD capacity provides an additional coding gain of approximately 1.5 dB when compared to the conventional PAM-32 constellation.

[0044] The SNR gains that can be achieved using constellations that are optimized for PD capacity can be verified through simulation. The results of a simulation conducted using a rate 1/2 LDPC code in conjunction with a conventional PAM-32 constellation and in conjunction with a PAM-32 constellation optimized for PD capacity are illustrated in FIG. 9. A chart 90 includes plots of Frame Error Rate performance of the different constellations with respect to SNR and using different length codes (i.e. k=4,096 and k=16,384). Irrespective of the code that is used, the constellation optimized for PD capacity achieves a gain of approximately 1.3 dB, which closely approaches the gain predicted from FIG. 8a.

CAPACITY OPTIMIZED PAM CONSTELLATIONS



[0045] Using the processes outlined above, locus plots of PAM constellations optimized for capacity can be generated that show the location of points within PAM constellations versus SNR. Locus plots of PAM-4, 8, 16, and 32 constellations optimized for PD capacity and joint capacity and corresponding design tables at various typical user bit rates per dimension are illustrated in FIGS. 10a - 17b. The locus plots and design tables show PAM-4,8,16,32 constellation point locations and labelings from low to high SNR corresponding to a range of low to high spectral efficiency.

[0046] In FIG.10a, a locus plot 100 shows the location of the points of PAM-4 constellations optimized for Joint capacity plotted against achieved capacity. A similar locus plot 105 showing the location of the points of Joint capacity optimized PAM-4 constellations plotted against SNR is included in FIG. 10b. In FIG. 10c. the location of points for PAM-4 optimized for PD capacity is plotted against achievable capacity and in FIG. 10d the location of points for PAM-4 for PD capacity is plotted against SNR. At low SNRs, the PD capacity optimized PAM-4 constellations have only 2 unique points, while the Joint optimized constellations have 3. As SNR is increased, each optimization eventually provides 4 unique points. This phenomenon is explicitly described in FIG. 11a and FIG. 11b where vertical slices of FIGS. 10ab and 10cd are captured in tables describing some PAM-4 constellations designs of interest. The SNR slices selected represent designs that achieve capacities = {0.5, 0.75, 1.0, 1.25, 1.5} bits per symbol (bps). Given that PAM-4 can provide at most log2(4) = 2 bps, these design points represent systems with information code rates R = {1/4, 3/8, 1/2, 5/8, 3/4} respectively.

[0047] FIGS. 12ab and 12cd present locus plots of PD capacity and joint capacity optimized PAM-8 constellation points versus achievable capacity and SNR. FIGS. 13a and 13b provide slices from these plots at SNRs corresponding to achievable capacities η = {0.5, 1.0, 1.5, 2.0, 2.5} bps. Each of these slices correspond to systems with code rate R = η bps / log2(8), resulting in R ={1/6, 1/3, 1/2, 2/3, 5/6}. As an example of the relative performance of the constellations in these tables, consider FIG. 13b which shows a PD capacity optimized PAM-8 constellation optimized for SNR = 9.00 dB, or 1.5 bps. We next examine the plot provided in FIG. 8a and see that the gap of the optimized constellation to the ultimate, Gaussian, capacity (CG) is approximately 0.5 dB. At the same spectral efficiency, the gap of the traditional PAM-8 constellation is approximately 1.0 dB. The advantage of the optimized constellation is 0.5dB for the same rate (in this case R=1/2). This gain can be obtained by only changing the mapper and demapper in the communication system and leaving all other blocks the same.

[0048] Similar information is presented in FIGS. 14abcd, and 15ab which provide loci plots and design tables for PAM-16 PD capacity and joint capacity optimized constellations. Likewise FIGS. 16abcd, 17ab provide loci plots and design tables for PAM-32 PD capacity and joint capacity optimized constellations.

CAPACITY OPTIMIZED PSK CONSTELLATIONS



[0049] Traditional phase shift keyed (PSK) constellations are already quite optimal. This can be seen in the chart 180 comparing the SNR gaps of tradition PSK with capacity optimized PSK constellations shown in FIG. 18 where the gap between PD capacity and Gaussian capacity is plotted for traditional PSK-4,8,16,32 and for PD capacaity optimized PSK-4,8,16,32.

[0050] The locus plot of PD optimized PSK-32 points across SNR is shown in FIG. 19, which actually characterizes all PSKs with spectral efficiency η ≤ 5 . This can be seen in FIG. 20. Note that at low SNR (0.4 dB) the optimal PSK-32 design is the same as traditional PSK-4, at SNR = 8.4 dB optimal PSK-32 is the same as traditional PSK-8, at SNR = 14.8 dB optimal PSK-32 is the same as traditional PSK-16, and finally at SNRs greater than 20.4 dB optimized PSK-32 is the same as traditional PSK-32. There are SNRs between these discrete points (for instance SNR = 2 and 15. dB) for which optimized PSK-32 provides superior PD capacity when compared to traditional PSK constellations.

[0051] We note now that the locus of points for PD optimized PSK-32 in FIG. 19 in conjunction with the gap to Gaussian capacity curve for optimized PSK-32 in FIG. 18 implies a potential design methodology. Specifically, the designer could achieve performance equivalent or better than that enabled by traditional PSK-4,8,16 by using only the optimized PSK-32 in conjunction with a single tuning parameter that controlled where the constellation points should be selected from on the locus of FIG. 19. Such an approach would couple a highly rate adaptive channel code that could vary its rate, for instance, rate 4/5 to achieve and overall (code plus optimized PSK-32 modulation) spectral efficiency of 4 bits per symbol, down to 1/5 to achieve an overall spectral efficiency of 1 bit per symbol. Such an adaptive modulation and coding system could essentially perform on the optimal continuum represented by the rightmost contour of FIG. 18.

ADAPTIVE RATE DESIGN



[0052] In the previous example spectrally adaptive use of PSK-32 was described. Techniques similar to this can be applied for other capacity optimized constellations across the link between a transmitter and receiver. For instance, in the case where a system implements quality of service it is possible to instruct a transmitter to increase or decrease spectral efficiency on demand. In the context of the current invention a capacity optimized constellation designed precisely for the target spectral efficiency can be loaded into the transmit mapper in conjunction with a code rate selection that meets the end user rate goal. When such a modulation / code rate change occurred a message could propagated to the receiver so that the receiver, in anticipation of the change, could select a demapper / decoder configuration in order to match the new transmit-side configuration.

[0053] Conversely, the receiver could implement a quality of performance based optimized constellation / code rate pair control mechanism. Such an approach would include some form of receiver quality measure. This could be the receiver's estimate of SNR or bit error rate. Take for example the case where bit error rate was above some acceptable threshold. In this case, via a backchannel, the receiver could request that the transmitter lower the spectral efficiency of the link by swapping to an alternate capacity optimized constellation / code rate pair in the coder and mapper modules and then signaling the receiver to swap in the complementary pairing in the demapper / decoder modules.

GEOMETRICALLY SHAPED QAM CONSTELLATIONS



[0054] Quadrature amplitude modulation (QAM) constellations can be constructed by orthogonalizing PAM constellations into QAM inphase and quadrature components. Constellations constructed in this way can be attractive in many applications because they have low-complexity demappers.

[0055] In FIG. 21 we provide an example of a Quadrature Amplitude Modulation constellation constructed from a Pulse Amplitude Modulation constellation. The illustrated embodiment was constructed using a PAM-8 constellation optimized for PD capacity at user bit rate per dimension of 1.5 bits (corresponds to an SNR of 9.0 dB) (see FIG. 13b). The label-point pairs in this PAM-8 constellation are {(000, -1.72), (001, -0.81), (010, 1.72), (011,-0.62), (100, 0.62), (101, 0.02), (110, 0.81), (111, -0.02)}. Examination of FIG. 21 shows that the QAM constellation construction is achieved by replicating a complete set of PAM-8 points in the quadrature dimension for each of the 8 PAM-8 points in the in-phase dimension. Labeling is achieved by assigning the PAM-8 labels to the LSB range on the in-phase dimension and to the MSB range on the quadrature dimension. The resulting 8x8 outer product forms a highly structured QAM-64 for which very low-complexity de-mappers can be constructed. Due to the orthogonality of the in-phase and quadrature components the capacity characteristics of the resulting QAM-64 constellation are identical to that of the PAM-8 constellation on a per-dimension basis.

N-DIMENSIONAL CONSTELLATION OPTIMIZATION



[0056] Rather than designing constellations in 1-D (PAM for instance) and then extending to 2-D (QAM), it is possible to take direct advantage in the optimization step of the additional degree of freedom presented by an extra spatial dimension. In general it is possible to design N-dimensional constellations and associated labelings. The complexity of the optimization step grows exponentially in the number of dimensions as does the complexity of the resulting receiver de-mapper. Such constructions constitute embodiments of the invention and simply require more 'run-time' to produce.

CAPACITY. OPTIMIZED CONSTELALTIONS FOR FADING CHANNELS



[0057] Similar processes to those outlined above can be used to design capacity optimized constellations for fading channels in accordance with embodiments of the invention. The processes are essentially the same with the exception that the manner in which capacity is calculated is modified to account for the fading channel. A fading channel can be described using the following equation:

where X is the transmitted signal, N is an additive white Gaussian noise signal and a(t) is the fading distribution, which is a function of time.

[0058] In the case of a fading channel, the instantaneous SNR at the receiver changes according to a fading distribution. The fading distribution is Rayleigh and has the property that the average SNR of the system remains the same as in the case of the AWGN channel, E[X2]/E[N2]. Therefore, the capacity of the fading channel can be computed by taking the expectation of AWGN capacity, at a given average SNR, over the Rayleigh fading distribution of a that drives the distribution of the instantaneous SNR.

[0059] Many fading channels follow a Rayleigh distribution. FIGS. 22a - 24b are locus plots of PAM-4, 8, and 16 constellations that have been optimized for PD capacity on a Rayleigh fading channel. Locus plots versus user bit rate per dimension and versus SNR are provided. Similar processes can be used to obtain capacity optimized constellations that are optimized using other capacity measures, such as joint capacity, and/or using different modulation schemes.


Claims

1. A digital communication system (10), comprising:

a transmitter (14) configured to transmit signals via a communication channel (15);

wherein the transmitter (14), comprises:

a coder (20) configured to receive user bits and output encoded bits at an expanded output encoded bit rate;

a mapper (22) configured to map encoded bits to symbols in a modulated symbol constellation; and

a modulator (24) configured to generate a modulated signal for transmission via the communication channel using symbols generated by the mapper.

wherein the transmitter is characterized in that the symbol constellation is an unequally spaced symbol constellation obtained by optimizing locations and labeling of constellation points to maximize parallel decode capacity at a given signal-to-noise ratio so that the symbol constellation provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.


 
2. The communication system (10) of claim 1, further comprising:

a receiver (16) configured to receive signals via a communication channel (15),

wherein the receiver comprises:

a demodulator (30) configured to demodulate a signal received via the communication channel;

a demapper (32) configured to estimate likelihoods from the demodulated signal using the symbol constellation; and

a decoder (34) that is configured to estimate decoded bits from the likelihoods generated by the demapper (32).


 
3. A digital communication system (10), comprising:

a receiver (16) configured to receive signals via a communication channel (15); the receiver comprising:

a demodulator (30) configured to demodulate a signal received via the communication channel;

a demapper (32) configured to estimate likelihoods from the demodulated signal using a symbol constellation;

a decoder (34) that is configured to estimate decoded bits from the likelihoods generated by the demapper (32); and

wherein the receiver is characterized in that the symbol constellation is an unequally spaced symbol constellation obtained by optimizing locations and labeling of constellation points to maximize parallel decode capacity at a given signal-to-noise ratio so that the symbol constellation provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.


 
4. The communication system (10) of any preceding claim, wherein the unequally spaced symbol constellation is optimized subject to optimization constraints including any one of:

lower and upper bounds on point location;

peak to average power of the resulting constellation; and

mean in the resulting constellation.


 
5. The communication system (10) of any preceding claim, wherein the channel is an Additive White Gaussian Noise, AWGN, channel.
 
6. The communication system (10) of any preceding claim, wherein the channel is a fading channel.
 
7. The communication system (10) of any preceding claim , wherein the constellations points of the unequally spaced symbol constellation are variable depending on the user rate.
 
8. The communication system (10) of any preceding claim, wherein the constellation points were obtained by optimizing the locations and the labeling of the constellation points to maximize parallel decode capacity measure at a given signal-to-noise ratio in such a way that the obtained constellation points have a greater capacity than the capacity of a constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.
 
9. The communication system (10) of any preceding claim wherein the constellation points provide an SNR gap to Gaussian capacity at a given capacity that is a predetermined margin lower than the signal-to-noise ratio gap to Gaussian capacity of a signal constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.
 
10. The communication system (10) of claim 9, wherein the predetermined margin is 0.5 dB.
 
11. The communication system (10) of any preceding claim, wherein the symbol constellation comprises a ring of constellation points that are unevenly spaced around the ring.
 
12. The communication system (10) of claims 11, wherein the symbol constellation is a non-uniform PSK constellation.
 
13. The communication system (10) of any preceding claim, configured to utilize an LDPC code.
 
14. The communication system (10) of any of claims 2 or 3 wherein there are no belief propagation iterations between the decoder and the constellation demapper.
 
15. The communication system (10) of any preceding claim, wherein the constellation is selected in conjunction with a code rate to meet a maximum transmit power requirement.
 
16. A method performed in digital communication system (10), the method comprising:

a transmitter (14) transmitting signals via a communication channel (15) by;
a coder (20) receiving user bits and outputing encoded bits at an expanded output encoded bit rate;
a mapper (22) mapping encoded bits to symbols in a modulated symbol constellation; and
a modulator (24) generating a modulated signal for transmission via the communication channel using symbols generated by the mapper,

wherein the method is characterized in that the symbol constellation is an unequally spaced symbol constellation obtained by optimizing locations and labeling of constellation points to maximize parallel decode capacity at a given signal-to-noise ratio so that the symbol constellation provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.


 
17. A method performed in a digital communication system (10), the method comprising:

a receiver (16) receiving signals via a communication channel (15) by:

a demodulator (30) demodulating a signal received via the communication channel;

a demapper (32) estimating likelihoods from the demodulated signal using a symbol constellation; and

a decoder (34) estimating decoded bits from the likelihoods generated by the demapper (32),

wherein the method is characterized in that the symbol constellation is an unequally spaced symbol constellation obtained by optimizing locations and labeling of constellation points to maximize parallel decode capacity at a given signal-to-noise ratio so that the symbol constellation provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes the minimum distance, dmin, between the constellation points of the symbol constellation.


 


Ansprüche

1. Digitales Kommunikationssystem (10), umfassend:

einen Sender (14), der dazu konfiguriert ist, Signale über einen Kommunikationskanal (15) zu übertragen; wobei der Sender (14) Folgendes umfasst:

einen Codierer (20), der dazu konfiguriert ist, Benutzerbits zu empfangen und codierte Bits mit einer erweiterten Ausgangscodierbitrate auszugeben;

einen Mapper (22), der dazu konfiguriert ist, die codierten Bits Symbolen in einer modulierten Symbolkonstellation zuzuordnen; und

einen Modulator (24), der dazu konfiguriert ist, ein moduliertes Signal zur Übertragung über den Kommunikationskanal unter Verwendung der durch den Mapper generierten Symbole zu generieren,

wobei der Sender dadurch gekennzeichnet ist, dass die Symbolkonstellation eine ungleichmäßig beabstandete Symbolkonstellation ist, die durch Optimieren von Stellen und Markierungen von Konstellationspunkten erlangt wird, um eine parallele Decodierkapazität bei einem gegebenen Signal-Rausch-Verhältnis zu maximieren, sodass die Symbolkonstellation eine gegebene Kapazität bei einem reduzierten Signal-Rausch-Verhältnis im Vergleich zu einer Signalkonstellation, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert, bereitstellt.


 
2. Kommunikationssystem (10) nach Anspruch 1, ferner umfassend:
einen Empfänger (16), der dazu konfiguriert ist, Signale über einen Kommunikationskanal (15) zu empfangen, wobei der Empfänger Folgendes umfasst:

einen Demodulator (30), der dazu konfiguriert ist, ein über den Kommunikationskanal empfangenes Signal zu demodulieren;

einen Demapper (32), der dazu konfiguriert ist, Wahrscheinlichkeiten aus dem demodulierten Signal unter Verwendung der Symbolkonstellation zu schätzen; und

einen Decodierer (34), der dazu konfiguriert ist, die decodierten Bits aus den durch den Demapper (32) generierten Wahrscheinlichkeiten zu schätzen.


 
3. Digitales Kommunikationssystem (10), umfassend:

einen Empfänger (16), der dazu konfiguriert ist, Signale über einen Kommunikationskanal (15) zu empfangen, wobei der Empfänger Folgendes umfasst:

einen Demodulator (30), der dazu konfiguriert ist, ein über den Kommunikationskanal empfangenes Signal zu demodulieren;

einen Demapper (32), der dazu konfiguriert ist, Wahrscheinlichkeiten aus dem demodulierten Signal unter Verwendung einer Symbolkonstellation zu schätzen;

einen Decodierer (34), der dazu konfiguriert ist, die decodierten Bits aus den durch den Demapper (32) generierten Wahrscheinlichkeiten zu schätzen; und

wobei der Empfänger dadurch gekennzeichnet ist, dass die Symbolkonstellation eine ungleichmäßig beabstandete Symbolkonstellation ist, die durch Optimieren von Stellen und Markierungen von Konstellationspunkten erlangt wird, um eine parallele Decodierkapazität bei einem gegebenen Signal-Rausch-Verhältnis zu maximieren, sodass die Symbolkonstellation eine gegebene Kapazität bei einem reduzierten Signal-Rausch-Verhältnis im Vergleich zu einer Signalkonstellation, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert, bereitstellt.


 
4. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die ungleichmäßig beabstandete Symbolkonstellation optimiert ist, vorbehaltlich Optimierungseinschränkungen, die eines der folgenden beinhalten:

untere und obere Begrenzung an der Punktstelle;

Spitzenleistung zu Durchschnittsleistung der resultierenden Konstellation; und

Mittelwert in der resultierenden Konstellation.


 
5. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei der Kanal ein Kanal des additiven weißen Gaußschen Rauschens (AWGN) ist.
 
6. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei der Kanal ein Fading-Kanal ist.
 
7. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die Konstellationspunkte der ungleichmäßig beabstandeten Symbolkonstellation abhängig von der Benutzerrate variabel sind.
 
8. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die Konstellationspunkte durch Optimieren der Stellen und der Markierung von Konstellationspunkten erlangt wurden, um ein paralleles Decodierkapazitätsmaß bei einem gegebenen Signal-Rausch-Verhältnis in einer Weise zu maximieren, dass die erlangten Konstellationspunkte eine größere Kapazität aufweisen als die Kapazität einer Konstellation, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert.
 
9. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die Konstellationspunkte eine SNR-Lücke zur Gaußschen Kapazität bei einer gegebenen Kapazität bereitstellen, die eine vorbestimmte Toleranz geringer als die Signal-Rausch-Verhältnislücke zur Gaußschen Kapazität einer Signalkonstellation ist, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert.
 
10. Kommunikationssystem (10) nach Anspruch 9, wobei die vorbestimmte Toleranz 0,5 dB ist.
 
11. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die Symbolkonstellation einen Ring von Konstellationspunkten umfasst, die ungleichmäßig um den Ring beabstandet sind.
 
12. Kommunikationssystem (10) nach Anspruch 11, wobei die Symbolkonstellation eine nicht einheitliche PSK-Konstellation ist.
 
13. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, dazu konfiguriert, einen LDPC-Code zu nutzen.
 
14. Kommunikationssystem (10) nach einem der Ansprüche 2 oder 3, wobei es keine Glaubenspropagationswiederholungen zwischen dem Decodierer und dem Konstellationsdemapper gibt.
 
15. Kommunikationssystem (10) nach einem der vorstehenden Ansprüche, wobei die Konstellation in Verbindung mit einer Coderate ausgewählt ist, um eine maximale Übertragungsleistungsanforderung zu erfüllen.
 
16. Verfahren, durchgeführt in einem digitalen Kommunikationssystem (10), wobei das Verfahren Folgendes umfasst:

einen Sender (14), der Signale über einen Kommunikationskanal (15) überträgt, durch:

einen Codierer (20), der Benutzerbits empfängt und codierte Bits mit einer erweiterten Ausgangscodierbitrate ausgibt;

einen Mapper (22), der die codierten Bits Symbolen in einer modulierten Symbolkonstellation zuordnet; und

einen Modulator (24), der ein moduliertes Signal zur Übertragung über den Kommunikationskanal unter Verwendung der durch den Mapper generierten Symbole generiert,

wobei das Verfahren dadurch gekennzeichnet ist, dass die Symbolkonstellation eine ungleichmäßig beabstandete Symbolkonstellation ist, die durch Optimieren von Stellen und Markierungen von Konstellationspunkten erlangt wird, um eine parallele Decodierkapazität bei einem gegebenen Signal-Rausch-Verhältnis zu maximieren, sodass die Symbolkonstellation eine gegebene Kapazität bei einem reduzierten Signal-Rausch-Verhältnis im Vergleich zu einer Signalkonstellation, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert, bereitstellt.


 
17. Verfahren, durchgeführt in einem digitalen Kommunikationssystem (10), wobei das Verfahren Folgendes umfasst:

einen Empfänger (16), der Signale über einen Kommunikationskanal (15) empfängt, durch:

einen Demodulator (30), der ein über den Kommunikationskanal empfangenes Signal demoduliert;

einen Demapper (32), der Wahrscheinlichkeiten aus dem demodulierten Signal unter Verwendung einer Symbolkonstellation schätzt; und

einen Decodierer (34), der die decodierten Bits aus den durch den Demapper (32) generierten Wahrscheinlichkeiten schätzt;

wobei das Verfahren dadurch gekennzeichnet ist, dass die Symbolkonstellation eine ungleichmäßig beabstandete Symbolkonstellation ist, die durch Optimieren von Stellen und Markierungen von Konstellationspunkten erlangt wird, um eine parallele Decodierkapazität bei einem gegebenen Signal-Rausch-Verhältnis zu maximieren, sodass die Symbolkonstellation eine gegebene Kapazität bei einem reduzierten Signal-Rausch-Verhältnis im Vergleich zu einer Signalkonstellation, die den Mindestabstand, dmin, zwischen den Konstellationspunkten der Symbolkonstellation maximiert, bereitstellt.


 


Revendications

1. Système de communication numérique (10), comprenant :

un transmetteur (14) configuré pour transmettre des signaux par l'intermédiaire d'un canal de communication (15) ;

dans lequel le transmetteur (14) comprend :

un codeur (20) configuré pour recevoir des bits utilisateur et des bits codés de sortie à une vitesse de bits codés de sortie accrue ;

un mappeur (22) configuré pour faire correspondre les bits codés à des symboles dans une constellation à symboles modulée ; et

un modulateur (24) configuré pour générer un signal modulé pour la transmission par l'intermédiaire du canal de communication à l'aide de symboles générés par le mappeur.

le transmetteur étant caractérisé en ce que la constellation à symboles est une constellation à symboles inégalement espacée obtenue par l'optimisation des emplacements et l'étiquetage des points de constellation pour maximiser la capacité de décodage parallèle à un rapport signal sur bruit donné de sorte que la constellation à symboles fournit une capacité donnée à un rapport signal sur bruit réduit en comparaison avec une constellation de signaux qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.


 
2. Système de communication (10) selon la revendication 1, comprenant en outre :

un récepteur (16) configuré pour recevoir des signaux par l'intermédiaire d'un canal de communication (15),

dans lequel le récepteur comprend :

un démodulateur (30) configuré pour démoduler un signal reçu par l'intermédiaire du canal de communication ;

un démappeur (32) configuré pour estimer les probabilités à partir du signal démodulé à l'aide de la constellation à symboles ; et

un décodeur (34) qui est configuré pour estimer les bits décodés à partir des probabilités générées par le démappeur (32) .


 
3. Système de communication numérique (10), comprenant :

un récepteur (16) configuré pour recevoir des signaux par l'intermédiaire d'un canal de communication (15) ; le récepteur comprenant :

un démodulateur (30) configuré pour démoduler un signal reçu par l'intermédiaire du canal de communication ;

un démappeur (32) configuré pour estimer les probabilités à partir du signal démodulé à l'aide d'une constellation à symboles ;

un décodeur (34) qui est configuré pour estimer des bits décodés à partir des probabilités générées par le démappeur (32) ; et

dans lequel le récepteur est caractérisé en ce que la constellation à symboles est une constellation à symboles inégalement espacée obtenue par l'optimisation des emplacements et l'étiquetage des points de constellation pour maximiser la capacité de décodage parallèle à un rapport signal sur bruit donné de sorte que la constellation à symboles fournit une capacité donnée à un rapport signal sur bruit réduit en comparaison avec une constellation de signal qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.


 
4. Système de communication (10) selon une quelconque revendication précédente, dans lequel la constellation à symboles inégalement espacée est optimisée en étant sujette aux contraintes d'optimisation comprenant l'un quelconque parmi :

des limites supérieures et inférieures sur l'emplacement des points ;

un pic pour la puissance moyenne de la constellation résultante ; et

une moyenne dans la constellation résultante.


 
5. Système de communication (10) selon une quelconque revendication précédente, dans lequel le canal est un canal à bruit blanc gaussien additif (AWGN).
 
6. Système de communication (10) selon une quelconque revendication précédente, dans lequel le canal est un canal à évanouissement.
 
7. Système de communication (10) selon une quelconque revendication précédente, dans lequel les points de constellation de la constellation à symboles inégalement espacée sont variables en fonction de la vitesse utilisateur.
 
8. Système de communication (10) selon une quelconque revendication précédente, dans lequel les points de constellation ont été obtenus par l'optimisation des emplacements et l'étiquetage des points de constellation pour maximiser la mesure de capacité de décodage parallèle à un rapport signal sur bruit donné de sorte que les points de constellation obtenus présentent une meilleure capacité que la capacité d'une constellation qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.
 
9. Système de communication (10) selon une quelconque revendication précédente, dans lequel les points de constellation fournissent un écart SNR à la capacité gaussienne à une capacité donnée qui est une marge prédéterminée inférieure à l'écart de rapport signal sur bruit à la capacité gaussienne d'une constellation de signal qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.
 
10. Système de communication (10) selon la revendication 9, dans lequel la marge prédéterminée est de 0,5 dB.
 
11. Système de communication (10) selon une quelconque revendication précédente, dans lequel la constellation à symboles comprend une bague de points de constellation qui sont espacés de manière inégale autour de la bague.
 
12. Système de communication (10) selon la revendication 11, dans lequel la constellation à symboles est une constellation PSK non uniforme.
 
13. Système de communication (10) selon une quelconque revendication précédente, configuré pour utiliser un code LDPC.
 
14. Système de communication (10) selon l'une quelconque des revendications 2 ou 3, dans lequel il n'existe pas d'itération de propagation de croyance entre le décodeur et le démappeur de constellation.
 
15. Système de communication (10) selon une quelconque revendication précédente, dans lequel la constellation est choisie en conjonction avec une vitesse de code pour satisfaire à une exigence d'énergie de transmission maximale.
 
16. Procédé effectué dans le système de communication numérique (10), le procédé comprenant :

un transmetteur (14) transmettant les signaux par l'intermédiaire d'un canal de communication (15) par ;
un codeur (20) recevant les bits utilisateur et les bits codés de sortie à une vitesse de bits codés de sortie accrue ;
un mappeur (22) faisant correspondre les bits codés à des symboles dans une constellation à symboles modulée ; et
un modulateur (24) générant un signal modulé pour la transmission par l'intermédiaire du canal de communication à l'aide de symboles générés par le mappeur,

le procédé étant caractérisé en ce que la constellation à symboles est une constellation à symboles inégalement espacée obtenue par l'optimisation des emplacements et l'étiquetage des points de constellation pour maximiser la capacité de décodage parallèle à un rapport signal sur bruit donné de sorte que la constellation à symboles fournit une capacité donnée à un rapport signal sur bruit réduit en comparaison avec une constellation de signal qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.


 
17. Procédé effectué dans un système de communication numérique (10), le procédé comprenant :

un récepteur (16) recevant des signaux par l'intermédiaire d'un canal de communication (15) par :

un démodulateur (30) démodulant un signal reçu par l'intermédiaire du canal de communication ;

un démappeur (32) estimant les probabilités à partir du signal démodulé à l'aide d'une constellation à symboles ; et

un décodeur (34) estimant des bits décodés à partir des probabilités générées par le démappeur (32),

le procédé étant caractérisé en ce que la constellation à symboles est une constellation à symboles inégalement espacée obtenue par l'optimisation des emplacements et l'étiquetage des points de constellation pour maximiser la capacité de décodage parallèle à une rapport signal sur bruit donné de sorte que la constellation à symboles fournit une capacité donnée à un rapport signal sur bruit réduit en comparaison avec une constellation de signal qui maximise la distance minimale, dmin, entre les points de constellation de la constellation à symboles.


 




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Cited references

REFERENCES CITED IN THE DESCRIPTION



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Non-patent literature cited in the description