Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code

Abstract

In this work, we present a new architecture for soft-decision Reed–Solomon (RS) Low-Complexity Chase (LCC) decoding. The proposed architecture is scalable and can be used for a high number of test vectors. We propose a novel Multiplicity Assignment stage that sorts and stores only the location of the errors inside the symbols and the powers of α that identify the positions of the symbols in the frame. Novel schematics for the Syndrome Update and Symbol Modification blocks that are adapted to the proposed sorting stage are also presented. We also propose novel solutions for the problems that arise when a high number of test vectors is processed. We implemented three decoders: a η = 4 LCC decoder and two decoders that only decode 31 and 60 test vectors of true η = 5 and η = 6 LCC decoders, respectively. For example, our η = 4 decoder requires 29% less look-up tables in Virtex-V Field Programmable Gate Array (FPGA) devices than the best soft-decision RS decoder published to date, while has a 0.07 dB coding gain over that decoder.

Performance Comparison of New Designs of Chien Search and Syndrome Blocks for BCH and Reed Solomon Codes

“…For calculing S1 we replace x by α1 in the following equation: S0 = (α 0 ) 14 +2(α 0 ) 13 (((((((((((1 α 3 + 2).α 3 + 3) α 3 + 4).α 3 + 5) α 3 + 11).α 3 + 7).α 3 + 8) α 3 + 9) α 3 + 10).α 3 + 11) S3 = 12…”

“…The proposed circuits are compared in terms of BER performance and Number of iterations, and number of minimized logic gates. Tables 1, 2 and 3, also Figure 10,11,12,13,14 and 15 show the evaluation of the performance based on the number of the used logic gates and the obtained values of bit error rate BER for all designs by using the modified circuit for different error locator polynomials, especially in the case of second factorization method both odd error locator and even error locator.…”

“…Their uses are in particular in communications by satellite DVB-S2, compact discs CD and DVD. A number of methods have been proposed to enhance the performance of the chien search block and syndrome architecture [9] [10] [11] [12] [13]. The goal of this work is to present a comparison analysis of the new chien search and new syndrome block with others designs in order to enhance these performances [14] [15] [16] [17].…”

Comparison of FPGA and Microcontroller Implementations of an Innovative Method for Error Magnitude Evaluation in Reed–Solomon Codes

“…RS codes are among the most implemented solutions in a wide set of areas, such as data storage, bar and QR (quick response) codes, space and TV transmission, and so on [14][15][16][17].As all communication systems, RS ECCs are composed of an encoder at the sender side and a decoder at the receiver side. Most of the works in the literature [18][19][20] focus on the decoder part, as it holds the most complex operations. Several approaches have been proposed to improve the performance of the decoder [21,22].…”

“…As all communication systems, RS ECCs are composed of an encoder at the sender side and a decoder at the receiver side. Most of the works in the literature [18][19][20] focus on the decoder part, as it holds the most complex operations. Several approaches have been proposed to improve the performance of the decoder [21,22].…”