Algebraic Chase Decoding of Reed-Solomon Codes Using Module Minimisation

This paper proposes a low-complexity high performance soft-in hard-out decoding algorithm for Reed-Solomon (RS) codes. The Guruswami-Sudan (GS) algebraic list decoding algorithm can correct errors beyond half the distance bound by performing a curve-fitting decoding process. However, its extra error-correction capability is exchanged with a high computational cost which is dominated by the interpolation. In this paper, an algebraic Chase decoding (ACD) approach that utilises the module minimisation (MM) technique is introduced, namely the ACD-MM algorithm. The MM technique solves the interpolation problem with less computational cost than the conventional Koetter's interpolation. The proposal exploits the soft received information to formulate the interpolation test-vectors. The re encoding transform is further employed to reduce the size of the entries of the module, benefiting a simpler MM process. Our analyses show that the ACD-MM algorithm can outperform the legacy Koetter-Vardy (KV) soft-decision list decoding algorithm with a much lower complexity. Moreover, the proposal allows parallel execution of each Chase decoding trial, resulting in a low decoding latency for practical interest.