Successive cancellation permutation decoding of Reed-Solomon codes

Abstract

A novel soft-decision decoding algorithm for Reed- Solomon codes over F2m is considered. The proposed approach is based on their representation as Arikan polar codes with dynamic frozen symbols and application of the sequential successive cancellation decoding algorithm. Furthermore, permutation tech- niques are utilized in order to reduce the decoding complexity. I. INTRODUCTION Efficient soft-decision decoding of Reed-Solomon codes is a long-standing open problem. Numerous techniques were suggested for solving it. Major recent milestones include Koetter-Vardy algebraic soft decision method (1), adaptive belief propagation method (2), and a hybrid approach (3). However, neither of these techniques can provide near-ML decoding. In this paper a novel approach towards solving this problem is suggested. The proposed method exploits representation of Reed-Solomon codes as polar codes (4) with dynamic frozen symbols (5). This enables application of efficient sequential soft-decision decoding techniques developed in the area of po- lar coding (6). Furthermore, permutation decoding techniques are utilized in order to reduce the average number of iterations performed by the sequential decoder. This result is similar to the one presented in (7), where permutation techniques were used to significantly reduce the complexity of a list decoding algorithm for Reed-Muller codes. The paper is organized as follows. Section II introduces the necessary background on Reed-Solomon and polar codes. The proposed decoding algorithm is described in Section III. Numeric results illustrating the performance and complexity of this approach are provided in Section IV.