Sliding Encoding-Window for Reed-Solomon code decoding

Abstract:
Two major types of decoding schemes are used for the soft decoding of block codes: encoding-based and algebraic decoding-based algorithms. Both techniques generate a list of codewords used by the decoder to choose inside the most probable. If these techniques are optimal for binary block codes, their strict adaptation to q-ary block codes leads to a prohibitive complexity. Therefore, we often use sub-optimal versions of these schemes for the decoding of Reed-Solomon q-ary codes. In this paper, we present a simple but efficient soft-input soft-output encoding-based algorithm, which uses a sliding window. The proposed sliding encoding-window (SEW) algorithm exploits the cyclic and systematic properties of systematic RS codes in order to generate a list of candidates in the neighborhood of the received sequence. As the SEW algorithm naturally creates codeword diversity, it is also efficient in the generation of reliable soft outputs necessary in iterative processes. Moreover, this algorithm can be combined with decoding-based algorithms, such as Berlekamp-Massey or Chase algorithms, to increase the codeword diversity. In this case, the performance improvement is significant, while the added cost due to encoding is minor as it is a low-cost process compared to that of algebraic decoding.