Generalized IRA Erasure Correcting Codes for Hybrid Iterative/Maximum Likelihood Decoding

The design of low-density parity-check (LDPC) codes under hybrid iterative / maximum likelihood decoding is addressed for the binary erasure channel (BEC). Specifically, we focus on generalized irregular repeat-accumulate (GeIRA) codes, which offer both efficient encoding and design flexibility. We show that properly designed GeIRA codes tightly approach the performance of an ideal maximum distance separable (MDS) code, even for short block sizes. For example, our (2048,1024) code reaches a codeword error rate of 10-5 at channel erasure probability isin= 0.450, where an ideal (2048,1024) MDS code would reach the same error rate at isin = 0.453.

[1]  William E. Ryan,et al.  Dual-mode decoding of product codes with application to tape storage , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[2]  Evangelos Eleftheriou,et al.  On the computation of the minimum distance of low-density parity-check codes , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[3]  H. Jin,et al.  Irregular repeat accumulate codes , 2000 .

[4]  Rüdiger L. Urbanke,et al.  Capacity-achieving ensembles for the binary erasure channel with bounded complexity , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[5]  Faramarz Fekri,et al.  On decoding of low-density parity-check codes over the binary erasure channel , 2004, IEEE Transactions on Information Theory.

[6]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[7]  Sarah J. Johnson,et al.  Combinatorial Interleavers for Systematic Regular Repeat-Accumulate Codes [Transactions Letters] , 2008, IEEE Transactions on Communications.

[8]  Marco Chiani,et al.  Simple reconfigurable low-density parity-check codes , 2005, IEEE Communications Letters.

[9]  Rüdiger L. Urbanke,et al.  Efficient encoding of low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[10]  William E. Ryan,et al.  Design of efficiently encodable moderate-length high-rate irregular LDPC codes , 2004, IEEE Transactions on Communications.

[11]  Rüdiger L. Urbanke,et al.  Weight Distribution of Low-Density Parity-Check Codes , 2006, IEEE Transactions on Information Theory.

[12]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[13]  Emre Telatar,et al.  Finite-length analysis of low-density parity-check codes on the binary erasure channel , 2002, IEEE Trans. Inf. Theory.

[14]  David Burshtein,et al.  Efficient maximum-likelihood decoding of LDPC codes over the binary erasure channel , 2004, IEEE Transactions on Information Theory.