Successive Cancellation List Decoding of Product Codes With Reed-Muller Component Codes

This letter proposes successive cancellation list (SCL) decoding of product codes with Reed–Muller (RM) component codes. SCL decoding relies on a product code description based on the $2\times 2$ Hadamard kernel, which enables interpreting the code as an RM subcode. The focus is on a class of product codes considered in wireless communication systems, based on single parity-check and extended Hamming component codes. For short product codes, it is shown that SCL decoding with a moderate list size performs as well as (and, sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by concatenating a short product code with a high-rate outer code, SCL decoding outperforms BP decoding by up to 1.4 dB.

[1]  Santhosh Kumar,et al.  Reed–Muller Codes Achieve Capacity on Erasure Channels , 2015, IEEE Transactions on Information Theory.

[2]  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.

[3]  Norbert Stolte,et al.  Rekursive Codes mit der Plotkin-Konstruktion und ihre Decodierung , 2002 .

[4]  Ilya Dumer,et al.  Recursive decoding and its performance for low-rate Reed-Muller codes , 2004, IEEE Transactions on Information Theory.

[5]  F. Chiaraluce,et al.  Extended Hamming product codes analytical performance evaluation for low error rate applications , 2004, IEEE Transactions on Wireless Communications.

[6]  Ilya Dumer,et al.  Soft-decision decoding of Reed-Muller codes: recursive lists , 2006, IEEE Transactions on Information Theory.

[7]  Erdal Arikan,et al.  A two phase successive cancellation decoder architecture for polar codes , 2013, 2013 IEEE International Symposium on Information Theory.

[8]  Peter Elias,et al.  Error-free Coding , 1954, Trans. IRE Prof. Group Inf. Theory.

[9]  R. Pyndiah,et al.  An overview of turbo codes and their applications , 2005, The European Conference on Wireless Technology, 2005..

[10]  Valerio Bioglio,et al.  Construction and Decoding of Product Codes with Non-Systematic Polar Codes , 2019, 2019 IEEE Wireless Communications and Networking Conference (WCNC).

[11]  Henry D. Pfister,et al.  Approaching Miscorrection-Free Performance of Product Codes With Anchor Decoding , 2018, IEEE Transactions on Communications.

[12]  G. Taricco,et al.  Weight distribution and performance of the iterated product of single-parity-check codes , 1994, 1994 IEEE GLOBECOM. Communications: Communications Theory Mini-Conference Record,.

[13]  Ramesh Pyndiah,et al.  Near-optimum decoding of product codes: block turbo codes , 1998, IEEE Trans. Commun..

[14]  Giuseppe Durisi,et al.  Low-Complexity Joint Channel Estimation and List Decoding of Short Codes , 2019, ArXiv.

[15]  M. El-Khamy,et al.  The average weight enumerator and the maximum likelihood performance of product codes , 2005, 2005 International Conference on Wireless Networks, Communications and Mobile Computing.

[16]  Irving S. Reed,et al.  A class of multiple-error-correcting codes and the decoding scheme , 1954, Trans. IRE Prof. Group Inf. Theory.

[17]  Norman Abramson,et al.  Cascade Decoding of Cyclic Product Codes , 1968 .

[18]  William E. Ryan,et al.  Efficient Error-Correcting Codes in the Short Blocklength Regime , 2018, Phys. Commun..

[19]  R. Koetter,et al.  Performance of Iterative Algebraic Decoding of Codes Defined on Graphs: An Initial Investigation , 2007, 2007 IEEE Information Theory Workshop.

[20]  Ofer Amrani,et al.  Augmented product codes and lattices: Reed-Muller codes and Barnes-Wall lattices , 2005, IEEE Transactions on Information Theory.

[21]  David E. Muller,et al.  Application of Boolean algebra to switching circuit design and to error detection , 1954, Trans. I R E Prof. Group Electron. Comput..

[22]  Robert G. Gallager,et al.  A simple derivation of the coding theorem and some applications , 1965, IEEE Trans. Inf. Theory.

[23]  Michael Lentmaier,et al.  Successive cancellation decoding of single parity-check product codes , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[24]  Alexander Vardy,et al.  List decoding of polar codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[25]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

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