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The Mutual information of LDGM codes [article]

Jan van den Brand, Nor Jaafari
2017 arXiv   pre-print
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

Imanol Granada, Pedro M. Crespo, Javier Garcia-Frías
2019 EURASIP Journal on Wireless Communications and Networking  
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

Francisco J. Vazquez-Araujo, Miguel Gonzalez-Lopez, Luis Castedo, Javier Garcia-Frias
2011 IEEE Transactions on Communications  
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

Francisco J. Vázquez-Araújo, Miguel González-López, Luis Castedo, Javier Garcia-Frias
2010 Wireless Communications and Mobile Computing  
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

A. G. Dimakis, M. J. Wainwright, K. Ramchandran
2007 2007 IEEE Information Theory Workshop  
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]

Suihua Cai, Wenchao Lin, Xinyuanmeng Yao, Baodian Wei, Xiao Ma
2020 arXiv   pre-print
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]

Emin Martinian, Martin J. Wainwright
2006 arXiv   pre-print
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

Tarik Benaddi, Charly Poulliat, Marie-Laure Boucheret, Benjamin Gadat, Guy Lesthievent
2014 2014 8th International Symposium on Turbo Codes and Iterative Information Processing (ISTC)  
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]

Zheng Bingbing, Jiang Lingge, He Chen, Wang Qingchuan
2010 arXiv   pre-print
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

Emin Martinian, Martin Wainwright
2006 2006 IEEE International Symposium on Information Theory  
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

Iqbal Shahid, Pradeepa Yahampath
2014 EURASIP Journal on Wireless Communications and Networking  
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]

Mahdi Nangir, Jafar Pourrostam, Javad Musevi Niya, Behzad Mozaffari Tazehkand
2020 arXiv   pre-print
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

Imanol Granada, Pedro M. Crespo, Mariano E. Burich, Javier Garcia-Frias
2021 IEEE Access  
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

Martin J. Wainwright, Elitza Maneva, Emin Martinian
2010 IEEE Transactions on Information Theory  
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]

Emin Martinian, Martin J. Wainwright
2006 arXiv   pre-print
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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