Enhanced stochastic soft decoding algorithm for Reed-Solomon codes

Abstract

The Chase algorithm based on stochastic computing can significantly reduce the complexity of soft decoding while ensuring the decoding performance, so that the softdecoding algorithm of Reed-Solomon codes is practically applied. However, the time complexity of the stochastic Chase algorithm will increase as the number of test test-vectors increases. In addition, under high-order modulation, the search range of generating test-vectors in the symbol-level stochastic Chase algorithm (SSCA) will increase exponentially by the order of modulation, thus increasing the hardware storage consumption. In order to reduce the time complexity, this paper proposes an early output algorithm, which does not require all test-vectors to achieve successful decoding.Simulation results show that the proposed algorithm can approach the original stochastic decoding performance while reducing the time complexity to nearly $1/\\tau$ ($\\tau$ is the number of test-vectors).In view of the storage issue in the SSCA, this paper reduces the search range by search-radius-determination assisted selection method. Simulation results indicate that the proposed $3\\sigma$-SSCA can reduce the search range of a single symbol of a test-vector from $q$ ($q$ is the order of modulation) to less than ten at the cost of a small performance loss.