Stochastic Decoding of LDPC Codes over GF(q)

Nonbinary LDPC codes have been shown to outperform currently used codes for magnetic recording and several other channels. Currently proposed nonbinary decoder architectures have very high complexity for high-throughput implementations and sacrifice error-correction performance to maintain realizable complexity. In this paper, we present an alternative decoding algorithm based on stochastic computation that has a very simple implementation and minimal performance loss when compared to the sum-product algorithm. We demonstrate the performance of the algorithm when applied to a GF(16) code and provide details of the hardware resources required for an implementation.

[1]  D. Mackay,et al.  Low density parity check codes over GF(q) , 1998, 1998 Information Theory Workshop (Cat. No.98EX131).

[2]  D. Mackay,et al.  Evaluation of Gallager Codes for Short Block Length and High Rate Applications , 2001 .

[3]  M. Fossorier,et al.  Architecture of a low-complexity non-binary LDPC decoder for high order fields , 2007, 2007 International Symposium on Communications and Information Technologies.

[4]  J. Tou.  Advances in Information Systems Science , 1970, Springer US.

[5]  William P. Marnane,et al.  FPGA Implementations of LDPC over GF(2m) Decoders , 2007, 2007 IEEE Workshop on Signal Processing Systems.

[6]  Hongxin Song,et al.  Reduced-complexity decoding of Q-ary LDPC codes for magnetic recording , 2003 .

[7]  Yong Li,et al.  Performance comparison between non-binary LDPC codes and Reed-Solomon codes over noise bursts channels , 2005, Proceedings. 2005 International Conference on Communications, Circuits and Systems, 2005..

[8]  Brian R. Gaines.  Advances in information systems science , 1969 .

[9]  Vincent C. Gaudet,et al.  Iterative decoding using stochastic computation , 2003 .

[10]  David Declercq,et al.  Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images , 2008, IEEE Transactions on Communications.

[11]  Brian R. Gaines,et al.  Stochastic Computing Systems , 1969 .

[12]  I.B. Djordjevic,et al.  Nonbinary LDPC codes for optical communication systems , 2005, IEEE Photonics Technology Letters.

[13]  David Declercq,et al.  Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$ , 2007, IEEE Transactions on Communications.

[14]  Vincent C. Gaudet,et al.  Stochastic iterative decoders , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[15]  Shie Mannor,et al.  Stochastic decoding of LDPC codes , 2006, IEEE Communications Letters.

[16]  Shie Mannor,et al.  Fully Parallel Stochastic LDPC Decoders , 2008, IEEE Transactions on Signal Processing.

[17]  Shie Mannor,et al.  An Area-Efficient FPGA-Based Architecture for Fully-Parallel Stochastic LDPC Decoding , 2007, 2007 IEEE Workshop on Signal Processing Systems.