Modified Low-Complexity Chase Soft-Decision Decoder of Reed–Solomon Codes

Reed–Solomon (RS) codes are widely used as error-correcting codes in digital communication and storage systems. Algebraic soft-decision decoding (ASD) of RS codes can achieve substantial coding gain with polynomial complexity. Among practical ASD algorithms, the low-complexity chase (LCC) algorithm that tests 2η vectors can achieve similar or higher coding gain with lower complexity. For applications such as magnetic recording, the performance of the LCC decoding is degraded by the inter-symbol interference from the channel. Improving the performance of the LCC decoding requires larger η, which leads to higher complexity. In this paper, a modified LCC (MLCC) decoding is proposed by adding erasures to the test vectors. With the same η, the proposed algorithm can achieve much better performance than the original LCC decoding. One major step of the LCC and MLCC decoding is the interpolation. To reduce the complexity of the interpolation, this paper also proposed a prioritized interpolation scheme to test a small proportion of the vectors at a time, starting with the ones with higher reliabilities. For a (458, 410) RS code, by testing 1/8 of the vectors at a time, the area requirement of the MLCC decoder with η = 8 can be reduced to 57%, and the average decoding latency is reduced to 73%.

[1]  Myung Hoon Sunwoo,et al.  Simplified Degree Computationless Modified Euclid's Algorithm and its Architecture , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[2]  Xinmiao Zhang,et al.  High-speed re-encoder design for algebraic soft-decision Reed-Solomon decoding , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[3]  Zhongfeng Wang,et al.  Low-Latency Factorization Architecture for Algebraic Soft-Decision Decoding of Reed–Solomon Codes , 2007, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[4]  Han Wang,et al.  A Chase-GMD Algorithm for Soft-Decision Decoding of Reed-Solomon Codes on Perpendicular Recording Channels , 2008, 2008 IEEE International Conference on Communications.

[5]  Alexander Vardy,et al.  Algebraic soft-decision decoding of Reed-Solomon codes , 2003, IEEE Trans. Inf. Theory.

[6]  Alexander Vardy,et al.  A complexity reducing transformation in algebraic list decoding of Reed-Solomon codes , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[7]  Xinmiao Zhang,et al.  Algebraic Soft-Decision Decoder Architectures for Long Reed–Solomon Codes , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Xinmiao Zhang,et al.  Hardware complexities of algebraic soft-decision Reed-Solomon decoders and comparisons , 2010, 2010 Information Theory and Applications Workshop (ITA).

[9]  Dhiraj K. Pradhan,et al.  A Routing-Aware ILS Design Technique , 2011, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[10]  Xinmiao Zhang.  Reduced Complexity Interpolation Architecture for Soft-Decision Reed–Solomon Decoding , 2006, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[11]  Xinmiao Zhang.  Further Exploring the Strength of Prediction in the Factorization of Soft-Decision Reed–Solomon Decoding , 2007, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[12]  R. McEliece.  The Guruswami-Sudan Decoding Algorithm for Reed-Solomon Codes , 2003 .

[13]  Frank R. Kschischang,et al.  A VLSI architecture for interpolation in soft-decision list decoding of Reed-Solomon codes , 2002, IEEE Workshop on Signal Processing Systems.

[14]  Keshab K. Parhi,et al.  Fast factorization architecture in soft-decision Reed-Solomon decoding , 2004, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[15]  Zhongfeng Wang,et al.  High-Speed Interpolation Architecture for Soft-Decision Decoding of Reed–Solomon Codes , 2006, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[16]  Krishna R. Narayanan,et al.  Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Bit-Level Soft Information , 2006, IEEE Transactions on Information Theory.

[17]  Venkatesan Guruswami,et al.  Improved decoding of Reed-Solomon and algebraic-geometry codes , 1999, IEEE Trans. Inf. Theory.

[18]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[19]  B. V. K. Vijaya Kumar,et al.  Soft-Decision Decoding of Reed-Solomon Codes Using Successive Error-and-Erasure Decoding , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[20]  Naresh R. Shanbhag,et al.  VLSI Architectures for Soft-Decision Decoding of Reed–Solomon Codes , 2004, IEEE Transactions on Information Theory.

[21]  Keshab K. Parhi,et al.  Area efficient parallel decoder architecture for long BCH codes , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  Xinmiao Zhang,et al.  Factorization-free Low-complexity Chase soft-decision decoding of Reed-Solomon codes , 2009, 2009 IEEE International Symposium on Circuits and Systems.

[23]  Zhongfeng Wang,et al.  Backward Interpolation Architecture for Algebraic Soft-Decision Reed–Solomon Decoding , 2009, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[24]  Xinmiao Zhang,et al.  Efficient Interpolation Architecture for Soft-Decision Reed-Solomon Decoding , 2007, 2007 IEEE Workshop on Signal Processing Systems.

[25]  Aleksandar Kavcic,et al.  A Low-Complexity Method for Chase-Type Decoding of Reed-Solomon Codes , 2006, 2006 IEEE International Symposium on Information Theory.

[26]  Zhongfeng Wang,et al.  Combined interpolation architecture for soft-decision decoding of Reed-Solomon codes , 2008, 2008 IEEE International Conference on Computer Design.