A Revisit to Ordered Statistics Decoding: Distance Distribution and Decoding Rules

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

[1]  Marc P. C. Fossorier,et al.  Probabilistic Sufficient Conditions on Optimality for Reliability Based Decoding of Linear Block Codes , 2006, 2006 IEEE International Symposium on Information Theory.

[2]  Johannes Van Wonterghem,et al.  On performance and complexity of OSD for short error correcting codes in 5G-NR , 2017 .

[3]  L. Litwin,et al.  Error control coding , 2001 .

[4]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[5]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[6]  Christoforos N. Hadjicostis,et al.  Soft-Decision Decoding of Linear Block Codes Using Preprocessing and Diversification , 2007, IEEE Transactions on Information Theory.

[7]  Saif E. A. Alnawayseh,et al.  Ordered statistics-based list decoding techniques for linear binary block codes , 2012, EURASIP Journal on Wireless Communications and Networking.

[8]  Christoforos N. Hadjicostis,et al.  Soft-Decision Decoding Using Ordered Recodings on the Most Reliable Basis , 2007, IEEE Transactions on Information Theory.

[9]  Shu Lin,et al.  Soft-decision decoding of linear block codes based on ordered statistics , 1994, IEEE Trans. Inf. Theory.

[10]  Johannes Van Wonterghem,et al.  Performance comparison of short-length error-correcting codes , 2016, 2016 Symposium on Communications and Vehicular Technologies (SCVT).

[11]  Branka Vucetic,et al.  Short Block-Length Codes for Ultra-Reliable Low Latency Communications , 2019, IEEE Communications Magazine.

[12]  Gianluigi Liva,et al.  Code Design for Short Blocks: A Survey , 2016, ArXiv.

[13]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[14]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[15]  Branka Vucetic,et al.  Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes , 2019, 2019 IEEE Global Communications Conference (GLOBECOM).

[16]  T. Sargent,et al.  The multivariate normal distribution , 1989 .

[17]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[18]  Singdhansu B Chatterjee.  Review of Order Statistics, third edition; by H. A. David and H. N. Nagaraja , 2004 .

[19]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[20]  P. Bickel.  Some contributions to the theory of order statistics , 1967 .

[21]  A. Valembois.  A Comparison between "Most-Reliable-Basis Reprocessing" Strategies , 2002 .

[22]  Marc P. C. Fossorier,et al.  Reliability-Based Soft-Decision Decoding With Multiple Biases , 2007, IEEE Transactions on Information Theory.

[23]  Branka Vucetic,et al.  Hamming Distance Distribution of the 0-reprocessing Estimate of the Ordered Statistic Decoder , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[24]  Marc P. C. Fossorier.  Reliability-based soft-decision decoding with iterative information set reduction , 2002, IEEE Trans. Inf. Theory.

[25]  Symeon Chatzinotas,et al.  On the error performance bound of ordered statistics decoding of linear block codes , 2016, 2016 IEEE International Conference on Communications (ICC).

[26]  Marc P. C. Fossorier,et al.  Box and match techniques applied to soft-decision decoding , 2002, IEEE Transactions on Information Theory.

[27]  Shu Lin,et al.  First-order approximation of the ordered binary-symmetric channel , 1996, IEEE Trans. Inf. Theory.