Iterative algebraic soft-decision list decoding of Reed-Solomon codes

Abstract

Abstract-In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes.

Reed–Solomon Codes and Binary Transmission

“…Interestingly, all three codes have very good performance and are very close to the erasure-based binomial bound. Although not close to the sphere packing bound, this bound is for non-binary codes and there is an asymptotic loss of 0.187 dB for rate 1 2 binary codes in comparison to the sphere packing bound as the code length extends towards ∞.…”

“…We have constructed two binary (150, 75) codes from RS codes. It is interesting to compare these codes to the known best code of length 150 and rate 1 2 . The known, best codes are to be found in a database [2] These three binary codes, the RS-based (150, 75, 19) and (150, 75, 22) codes together with the (150, 75, 23) shortened cyclic code have been simulated using binary transmission for the AWGN channel.…”

Improved adaptive belief propagation decoding using edge-local complementation

“…Even comparing against this improved GE implementation in [6], the figures show thatp(p) grows linearily before flattening out at high p. By using p ⋆ , we may then get a further reduction in average number of ELC operations.…”

“…3(c) and 4(c) comparep(p) against the linear ELC-complexity of JN-ADP. As stated also in [6], a reduction can be achieved by simply improving the implementation of GE to do no work whenever an unreliable position is already in P. The plots , 12] extended QR code, the best performance is using local damping. The performance using ND damping is indicated by the lines in Fig.…”

“…Recently, these results have been extended to high-density parity-check (HDPC) codes, in order to facilitate the use of well-known strong families of codes, such as Bose-Chaudhuri-Hocquenghem [1,2], quadratic residue (QR) [3], and Reed-Solomon (RS) codes [4][5][6]. Constructions of these types have strong structural properties (most importantly, large automorphism group and minimum distance), as well as convenient algebraic descriptions to simplify hardware implementation.…”