A New Chase-type Soft-decision Decoding Algorithm for Reed-Solomon Codes

This paper addresses three relevant issues arising in designing Chase-type algorithms for ReedSolomon codes: 1) how to choose the set of testing patterns; 2) given the set of testing patterns, what is the optimal testing order in the sense that the most-likely codeword is expected to appear earlier; and 3) how to identify the most-likely codeword. A new Chase-type soft-decision decoding algorithm is proposed, referred to as tree-based Chase-type algorithm. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns, and hence definitely delivers the most-likely codeword provided that the computational resources are allowed. All the testing patterns are arranged in an ordered rooted tree according to the likelihood bounds of the possibly generated codewords. While performing the algorithm, the ordered rooted tree is constructed progressively by adding at most two leafs at each trial. The ordered tree naturally induces a sufficient condition for the most-likely codeword. That is, whenever the tree-based Chase-type algorithm exits before a preset maximum number of trials is reached, the output codeword must be the most-likely one. When the tree-based Chase-type algorithm is combined with Guruswami-Sudan (GS) algorithm, each trial can be implement in an extremely simple way by removing from the gradually updated Gröbner basis one old point and interpolating one new point. Simulation results show that the tree-based Chase-type algorithm performs better than the recently proposed Chase-type algorithm by Bellorado et al with less trials (on average) given that the maximum number of trials is the same. Also proposed are simulation-based performance bounds on the maximum-likelihood decoding (MLD) algorithm, which are utilized to illustrate the near-optimality of the tree-based Chase-type algorithm in the high signal-to-noise ratio (SNR) region. In addition, the treebased Chase-type algorithm admits decoding with a likelihood threshold, that searches the most-likely codeword within an Euclidean sphere rather than a Hamming sphere. This work is supported by the 973 Program (No.2012CB316100) and the NSF (No.61172082) of China. The authors are with the Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou 510006, China (Emails: [email protected], [email protected]).