Symbol Message Passing Decoding of Nonbinary Spatially-Coupled Low-Density Parity-Check Codes

The performance of a decoding algorithm, called symbol message passing (SMP), is analyzed for nonbinary spatially coupled low-density parity-check (LDPC) codes. The SMP algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary LDPC codes. The analysis is performed via density evolution over the q-ary symmetric channel, with q being the field order used for the code construction.

[1]  Alexandre Graell i Amat,et al.  One and Two Bit Message Passing for SC-LDPC Codes With Higher-Order Modulation , 2019, Journal of Lightwave Technology.

[2]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[3]  D. Declercq,et al.  Fast Decoding Algorithm for LDPC over GF(2q) , 2003 .

[4]  Alexandre Graell i Amat,et al.  Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes , 2019, 2019 IEEE Global Communications Conference (GLOBECOM).

[5]  Stephan ten Brink,et al.  Extrinsic information transfer functions: model and erasure channel properties , 2004, IEEE Transactions on Information Theory.

[6]  Fabian Steiner,et al.  Protograph-Based LDPC Code Design for Ternary Message Passing Decoding , 2018, ArXiv.

[7]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[8]  Troels Pedersen,et al.  Analysis and Design of Binary Message Passing Decoders , 2012, IEEE Transactions on Communications.

[9]  Kamil Sh. Zigangirov,et al.  Time-varying periodic convolutional codes with low-density parity-check matrix , 1999, IEEE Trans. Inf. Theory.

[10]  David Declercq,et al.  Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ , 2007, IEEE Transactions on Communications.

[11]  Gerhard Bauch,et al.  Decoding of Non-Binary LDPC Codes using the Information Bottleneck Method , 2019, ICC 2019 - 2019 IEEE International Conference on Communications (ICC).

[12]  Michael Lentmaier,et al.  Spatially Coupled LDPC Codes Constructed From Protographs , 2014, IEEE Transactions on Information Theory.

[13]  David Declercq,et al.  Finite Alphabet Iterative Decoders—Part I: Decoding Beyond Belief Propagation on the Binary Symmetric Channel , 2013, IEEE Transactions on Communications.

[14]  Fan Zhang,et al.  Analysis of Verification-Based Decoding on the q -ary Symmetric Channel for Large q , 2008, IEEE Trans. Inf. Theory.

[15]  Lara Dolecek,et al.  Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs , 2014, IEEE Transactions on Information Theory.

[16]  Alexandre Graell i Amat,et al.  Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel , 2016, IEEE Transactions on Information Theory.

[17]  Michael Mitzenmacher,et al.  Verification-based decoding for packet-based low-density parity-check codes , 2005, IEEE Transactions on Information Theory.

[18]  K. Yamaguchi,et al.  Density Evolution for GF(q) LDPC Codes Via Simplified Message-passing Sets , 2007, 2007 Information Theory and Applications Workshop.

[19]  Michael Lentmaier,et al.  Iterative Decoding Threshold Analysis for LDPC Convolutional Codes , 2010, IEEE Transactions on Information Theory.

[20]  Paul H. Siegel,et al.  Windowed Decoding of Protograph-Based LDPC Convolutional Codes Over Erasure Channels , 2010, IEEE Transactions on Information Theory.

[21]  Rüdiger L. Urbanke,et al.  Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC , 2010, IEEE Transactions on Information Theory.

[22]  Wei Wang,et al.  Low-density parity-check codes with rates very close to the capacity of the q-ary symmetric channel for large q , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[23]  John J. Metzner Majority-logic-like decoding of vector symbols , 1996, IEEE Trans. Commun..

[24]  Rüdiger L. Urbanke,et al.  Spatially coupled ensembles universally achieve capacity under belief propagation , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.