Construction and Decoding of Rate-Compatible Globally Coupled LDPC Codes

This paper presents a family of rate-compatible (RC) globally coupled low-density parity-check (GC-LDPC) codes, which is constructed by combining algebraic construction method and graph extension. Specifically, the highest rate code is constructed using the algebraic method and the codes of lower rates are formed by successively extending the graph of the higher rate codes. The proposed rate-compatible codes provide more flexibility in code rate and guarantee the structural property of algebraic construction. It is confirmed, by numerical simulations over the AWGN channel, that the proposed codes have better performances than their counterpart GC-LDPC codes formed by the classical method and exhibit an approximately uniform gap to the capacity over a wide range of rates. Furthermore, a modified two-phase local/global iterative decoding scheme for GC-LDPC codes is proposed. Numerical results show that the proposed decoding scheme can reduce the unnecessary cost of local decoder at low and moderate SNRs, without any increase in the number of decoding iterations in the global decoder at high SNRs.

[1]  Guosen Yue,et al.  Design of Rate-Compatible Irregular Repeat Accumulate Codes , 2007, IEEE Transactions on Communications.

[2]  David G. M. Mitchell,et al.  Robust Rate-Compatible Punctured LDPC Convolutional Codes , 2013, IEEE Transactions on Communications.

[3]  D.J.C. MacKay,et al.  Good error-correcting codes based on very sparse matrices , 1997, Proceedings of IEEE International Symposium on Information Theory.

[4]  William Ryan,et al.  Channel Codes: Classical and Modern , 2009 .

[5]  Wei Hou,et al.  Rate-compatible spatially coupled LDPC codes via repeat-accumulation extension , 2014, 2014 8th International Symposium on Turbo Codes and Iterative Information Processing (ISTC).

[6]  Daniel J. Costello,et al.  Low Latency Coding: Convolutional Codes vs. LDPC Codes , 2012, IEEE Transactions on Communications.

[7]  Hideki Imai,et al.  Reduced complexity iterative decoding of low-density parity check codes based on belief propagation , 1999, IEEE Trans. Commun..

[8]  Joachim Hagenauer,et al.  Rate-compatible punctured convolutional codes (RCPC codes) and their applications , 1988, IEEE Trans. Commun..

[9]  P. Viswanath,et al.  Fundamentals of Wireless Communication: The wireless channel , 2005 .

[10]  Lara Dolecek,et al.  Spatially coupled sparse codes on graphs: theory and practice , 2013, IEEE Communications Magazine.

[11]  Baoming Bai,et al.  A Combined Algebraic- and Graph-Based Method for Constructing Structured RC-LDPC Codes , 2016, IEEE Communications Letters.

[12]  Rudiger Urbanke,et al.  Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC , 2010, ISIT.

[13]  Jungwon Lee,et al.  Finite-Length Algebraic Spatially-Coupled Quasi-Cyclic LDPC Codes , 2016, IEEE Journal on Selected Areas in Communications.

[14]  William E. Ryan,et al.  LDPC Code Designs, Constructions, and Unification , 2017 .

[15]  William E. Ryan,et al.  Globally coupled LDPC codes , 2016, 2016 Information Theory and Applications Workshop (ITA).

[16]  William Ryan,et al.  Channel Codes by William Ryan , 2009 .

[17]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

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

[19]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[20]  Mikael Skoglund,et al.  Rate-Compatible LDPC Convolutional Codes Achieving the Capacity of the BEC , 2012, IEEE Transactions on Information Theory.

[21]  Achilleas Anastasopoulos,et al.  Capacity achieving LDPC codes through puncturing , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

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

[23]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .

[24]  Shu Lin,et al.  Reed-solomon based nonbinary globally coupled LDPC codes: Correction of random errors and bursts of erasures , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[25]  Robert Soni,et al.  Design of Rate-Compatible Irregular LDPC Codes Based on Edge Growth and Parity Splitting , 2007, 2007 IEEE 66th Vehicular Technology Conference.

[26]  Zulin Wang,et al.  Time-Invariant Quasi-Cyclic Spatially Coupled LDPC Codes Based on Packings , 2016, IEEE Transactions on Communications.

[27]  Aria Nosratinia,et al.  The design of rate-compatible protograph LDPC codes , 2010 .

[28]  Walter Nitzold,et al.  Rate-compatible spatially-coupled LDPC code ensembles with nearly-regular degree distributions , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[29]  Steven W. McLaughlin,et al.  Rate-compatible puncturing of low-density parity-check codes , 2004, IEEE Transactions on Information Theory.

[30]  Baoming Bai,et al.  Construction of Quasi-Cyclic LDPC Codes via Masking With Successive Cycle Elimination , 2016, IEEE Communications Letters.

[31]  Shu Lin,et al.  Reed-Solomon based globally coupled quasi-cyclic LDPC codes , 2017, 2017 Information Theory and Applications Workshop (ITA).