Successive Cancellation List Decoding of Extended Reed-Solomon Codes

TL;DR

This paper introduces a novel list decoding method for extended Reed-Solomon codes over binary fields, transforming them into polar codes and analyzing their decoding performance theoretically and numerically.

Contribution

It develops a new list decoding approach for extended RS codes over F_{2^n} by transforming them into polar codes and provides a theoretical analysis of decoding performance.

Findings

Decoding performance depends on the pre-transformed matrix properties.

The proposed method enables SC and SCL decoding of extended RS codes.

Numerical validation confirms the effectiveness of the decoding approach.

Abstract

Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to their distance property of reaching the Singleton bound, being the maximum distance separable (MDS) codes. This paper proposes a new list decoding for extended RS (eRS) codes defined over a finite field of characteristic two, i.e., F_{2^n}. It is developed based on transforming an eRS code into n binary polar codes. Consequently, it can be decoded by the successive cancellation (SC) decoding and further their list decoding, i.e., the SCL decoding. A pre-transformed matrix is required for reinterpretating the eRS codes, which also determines their SC and SCL decoding performances. Its column linear independence property is studied, leading to theoretical characterization of their SC decoding performance. Our proposed decoding and analysis are validated numerically.