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The Mutual information of LDGM codes
[article]
2017
arXiv
pre-print
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We provide matching upper and lower bounds on the mutual information in noisy reconstruction of parity check codes and thereby prove a long-standing conjecture by Montanari [IEEE Transactions on Information ...
Besides extending a prior concentration result of Abbe and Montanari [Theory of Computing 2015] to the case of odd check degrees, we precisely determine the conjectured formula for code ensembles of arbitrary ...
This paper aims to break the first ground by proving a precise formula for the mutual information of LDGM codes which was previously conjectured by Montanari [34] . 1.1. Optimal codes on graphs. ...
arXiv:1707.04413v2
fatcat:4utmot2r3rhsphjmucu4m7ujxy
Asymptotic BER EXIT chart analysis for high rate codes based on the parallel concatenation of analog RCM and digital LDGM codes
2019
EURASIP Journal on Wireless Communications and Networking
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This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN ...
The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. ...
The corresponding mutual information trajectory at EXIT chart and mutual information trajectory of a RCM-LDGM code when transmitting a non-uniform source with entropy H(p 0 ) = 0.72 over an AWGN channel ...
doi:10.1186/s13638-018-1330-z
fatcat:rohd5xrtd5gahod7wmfcbay2ti
Capacity Approaching Low-Rate LDGM Codes
2011
IEEE Transactions on Communications
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We study the ability of low-rate Serially-Concatenated Low Density Generator Matrix (SCLDGM) codes to approach theoretical limits. ...
Although two layer SCLDGM codes approach capacity for medium rates (0.25 < < 0.9), they do not perform adequately for lower rates. ...
Correspondingly, 2 0 and 2 1 1 are the number of edges carrying the mutual informations → 2 and 1 → 2 . ...
doi:10.1109/tcomm.2010.112310.090086
fatcat:6icttptfvrbepfonwxggr2g2bq
Interleave-division multiple access (IDMA) using low-rate layered LDGM codes
2010
Wireless Communications and Mobile Computing
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We study the behavior of the soft interference cancellation (SIC) detector employed in IDMA systems and design the channel codes using EXtrinsic Information Transfer (EXIT) evolution, aiming at optimizing ...
We propose the use of low-rate layered serially concatenated low-density generator matrix (SCLDGM) codes in interleavedivision multiple access (IDMA) systems to approach the multiuser capacity. ...
ACKNOWLEDGMENTS This work has been supported by Xunta de Galicia, Ministerio de Educación y Ciencia of Spain, and FEDER funds of the European Union under grants number 09TIC008105PR, TEC2007-68020-C04- ...
doi:10.1002/wcm.1055
fatcat:mlrfetgk4ndaxbqyebnlk6j2nq
Lower bounds on the rate-distortion function of LDGM codes
2007
2007 IEEE Information Theory Workshop
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We analyze the performance of low-density generator matrix (LDGM) codes for lossy source coding. ...
We illustrate this method for the ensemble of check-regular lowdensity generator matrix (LDGM) codes by deriving an explicit lower bound on its rate-distortion performance as a function of the check degree ...
Gallager-style bound A classical approach to analyzing the performance of LDPC codes for channel coding, originally due to Gallager [7] , is based decomposing the mutual information between the channel ...
doi:10.1109/itw.2007.4313151
fatcat:am33aaygubgetptw7ngnpohw6u
Systematic Convolutional Low Density Generator Matrix Code
[article]
2020
arXiv
pre-print
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down to any target as required by increasing the density of the uncoupled LDGM codes. ...
As a universal construction, the main advantage of the SC-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered ...
The mutual information between the input and the output is given by I(p) = (1 − p)I 0 (p) + pI 1 (p), (3) where I 0 (p) = y∈Y P Y |X (y|0) log P Y |X (y|0) P Y (y) , (4) I 1 (p) = y∈Y P Y |X (y|1) log ...
arXiv:2001.02854v1
fatcat:omdiglj4vnazlpqdt5y4alxvqq
Analysis of LDGM and compound codes for lossy compression and binning
[article]
2006
arXiv
pre-print
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We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary symmetric source, showing that they quickly approach the rate-distortion function as the degree increases ...
Moreover, this compound construction can be used to generate nested codes that are simultaneously good as source and channel codes, and are hence well-suited to source/channel coding with side information ...
The ensemble of LDGM codes that we study in m n γ t G Fig. 1 . Factor graph representation of an LDGM code with n checks (each associated with a source bit), and m information bits. ...
arXiv:cs/0602046v1
fatcat:tlsvfw6vwrhq3lcunnkcu2emje
Design of systematic GIRA codes for CPM
2014
2014 8th International Symposium on Turbo Codes and Iterative Information Processing (ISTC)
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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. ...
serially concatenated turbo schemes that works for both systematic generalized irregular repeat accumulate (GIRA) and low density generator matrix (LDGM) codes concatenated with a continuous phase modulation ...
Figure 4 shows how I ℓ cpm,acc varies as function of the apriori mutual information I cn,acc . ...
doi:10.1109/istc.2014.6955075
dblp:conf/istc/BenaddiPBGL14
fatcat:zjik5kafp5cebidgct6flahzeu
Design of Nested LDGM-LDPC Codes for Compress-and-Forward in Relay Channel
[article]
2010
arXiv
pre-print
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Firstly a practical coding scheme was proposed to achieve the cut-set bound on the capacity of the system, employing LDPC and Nested LDGM-LDPC codes at the source and relay respectively. ...
Then, the degree distribution of LDGM and LDPC codes was optimized with a given rate bound, which ensured that the iterative belief propagation (BP) decoding algorithm at the destination was convergent ...
I qs , I sq represent the average mutual information (MI) in every q-tos, s-to-q message at a certain iteration respectively. ...
arXiv:1003.3765v1
fatcat:ochvl2agj5ac3o72kayphpu7ve
Low-density constructions can achieve the Wyner-Ziv and Gelfand-Pinsker bounds
2006
2006 IEEE International Symposium on Information Theory
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We describe and analyze sparse graphical code constructions for the problems of source coding with decoder side information (the Wyner-Ziv problem), and channel coding with encoder side information (the ...
Our approach relies on a combination of low-density parity check (LDPC) codes and low-density generator matrix (LDGM) codes, and produces sparse constructions that are simultaneously good as both source ...
We use I(·; ·), H(·), and D (·||·) to denote mutual information, entropy, and relative entropy (Kullback-Leibler distance), respectively. ...
doi:10.1109/isit.2006.261716
dblp:conf/isit/MartinianW06
fatcat:63rkhg2n6ja6xaxn5ab5mvvi64
Distributed joint source-channel code design for GMAC using irregular LDPC codes
2014
EURASIP Journal on Wireless Communications and Networking
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The degree profile defining the LDPC code is optimized for the joint source probabilities using extrinsic information transfer (EXIT) analysis and linear programming. ...
A key issue addressed is the Gaussian modeling of log-likelihood ratios (LLRs) generated by nodes representing the joint source probabilities in the combined factor graph of the two LDPC codes, referred ...
Acknowledgements This work has been supported by the National Science and Engineering Research Council (NSERC) of Canada. ...
doi:10.1186/1687-1499-2014-3
fatcat:5plrbj37grbevlcirkh63c6osm
Comparison Between the Joint and Successive Decoding Schemes for the Binary CEO Problem
[article]
2020
arXiv
pre-print
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We utilize the logarithmic loss as the criterion for measuring and comparing the total distortion of the decoding techniques. ...
On the other hand the successive decoding method has lower complexity; therefore, it is efficient for the cases with higher number of links. ...
A compound LDGM-LDPC code performs a binary quantization by employing an LDGM code at the first step of encoding. ...
arXiv:2004.05386v1
fatcat:irhwfdvbbbenbmflc4rxwdabwy
Rate Compatible Modulation for Correlated Information Sources
2021
IEEE Access
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At the receiver, if the superimposed LDGM MAC symbols present mutual reinforcement (are all 1 or -1) it is easy to estimate the LDGM symbols of each user. ...
Finally, a parallel RCM-LDGM code of rate K/N , with N = M + I, consists of a parallel concatenation of an RCM code of rate K/M with the I non-systematic coded binary symbols of a systematic LDGM code. ...
His research interests are in the area of information processing and wireless communications with a focus on error correcting codes, joint source-channel coding, analog coding, and coded modulations. ...
doi:10.1109/access.2021.3073972
fatcat:uzrst5pbu5blplv5n7tg6zynsu
Lossy Source Compression Using Low-Density Generator Matrix Codes: Analysis and Algorithms
2010
IEEE Transactions on Information Theory
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We study the use of low-density generator matrix (LDGM) codes for lossy compression of the Bernoulli symmetric source. ...
First, we establish rigorous upper bounds on the average distortion achieved by check-regular ensemble of LDGM codes under optimal minimum distance source encoding. ...
ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their careful reading and constructive suggestions. ...
doi:10.1109/tit.2009.2039160
fatcat:kkxpq2sz6bdllm2l6pf2r37kdu
Low-density constructions can achieve the Wyner-Ziv and Gelfand-Pinsker bounds
[article]
2006
arXiv
pre-print
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The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We describe and analyze sparse graphical code constructions for the problems of source coding with decoder side information (the Wyner-Ziv problem), and channel coding with encoder side information (the ...
Our approach relies on a combination of low-density parity check (LDPC) codes and low-density generator matrix (LDGM) codes, and produces sparse constructions that are simultaneously good as both source ...
We use I(·; ·), H(·), and D (·||·) to denote mutual information, entropy, and relative entropy (Kullback-Leibler distance), respectively. ...
arXiv:cs/0605091v1
fatcat:bdnyeugewngprbq2rd2425vz5m
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