Improving Windowed Decoding of SC LDPC Codes by Effective Decoding Termination, Message Reuse, and Amplification

In this paper, we address a number of weaknesses of the windowed decoding of spatially coupled low-density parity-check (SC LDPC) codes and propose three modifications that simultaneously improve its performance, complexity, and latency. An effective termination method of the windowed decoding and the reuse of edge messages of previous target symbols provide a good performance-latency tradeoff when compared with the conventional windowed decoder. Also, we propose a scheme that lowers the error floor, in which the amplified edge messages of the previous window are used in the present window. The proposed windowed decoding, consisting of the three schemes, provides a significant performance gain with smaller latency. The validity of the new windowed decoding is verified by the evaluation with codes from different SC LDPC ensembles.

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

[2]  J. Thorpe.  Low-Density Parity-Check (LDPC) Codes Constructed from Protographs , 2003 .

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

[4]  Zongwang Li,et al.  A class of good quasi-cyclic low-density parity check codes based on progressive edge growth graph , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

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

[6]  Moon Ho Lee,et al.  Constructing Large Girth QC Protograph LDPC Codes Based on PSD-PEG Algorithm , 2017, IEEE Access.

[7]  Ali Emre Pusane,et al.  Deriving Good LDPC Convolutional Codes from LDPC Block Codes , 2010, IEEE Transactions on Information Theory.

[8]  Evangelos Eleftheriou,et al.  Progressive edge-growth Tanner graphs , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

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

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

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

[12]  Gerhard Fettweis,et al.  Non-uniform windowed decoding schedules for spatially coupled codes , 2013, 2013 IEEE Global Communications Conference (GLOBECOM).

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

[14]  Hua Xiao,et al.  Improved progressive-edge-growth (PEG) construction of irregular LDPC codes , 2004, IEEE Communications Letters.

[15]  T. Lestable,et al.  LDPC Options for Next Generation Wireless Systems , 2005 .

[16]  Paul H. Siegel,et al.  Latency constrained protograph-based LDPC convolutional codes , 2010, 2010 6th International Symposium on Turbo Codes & Iterative Information Processing.

[17]  D. Spielman,et al.  Computationally efficient error-correcting codes and holographic proofs , 1995 .

[18]  Rüdiger L. Urbanke,et al.  Design of capacity-approaching irregular low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[19]  Andrea Montanari,et al.  Maxwell Construction: The Hidden Bridge Between Iterative and Maximum a Posteriori Decoding , 2005, IEEE Transactions on Information Theory.

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

[21]  Daniel A. Spielman,et al.  Improved low-density parity-check codes using irregular graphs and belief propagation , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[22]  Gerhard Fettweis,et al.  Efficient message passing scheduling for terminated LDPC convolutional codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[23]  Gerhard Fettweis,et al.  Fully parallel window decoder architecture for spatially-coupled LDPC codes , 2016, 2016 IEEE International Conference on Communications (ICC).

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

[25]  Michael Lentmaier,et al.  Convergence analysis for a class of LDPC convolutional codes on the erasure channel , 2004 .