A cellular structure for a versatile Reed-Solomon decoder

Abstract

A new cellular structure for a versatile Reed-Solomon (RS) decoder is introduced based on time domain decoding algorithm. The time domain decoding algorithm is restructured to be suitable for introducing the cellular structure. The main advantages of this structure are its versatility and very simple cellular structure. By versatile decoder we mean a decoder that can be programmed to decode any (n, k) RS code defined in Galois field 2 m with a fixed block length n and a fixed symbol size m. This decoder can correct both errors and erasures for any message length k. The introduced decoder is cellular and has a very simple structure and hence it is suitable for VLSI designs. Index Terms-Cellular structure, comparison of RS decoding structures, time domain RS decoder, versatile RS decoder, VLSI.

High-speed area-efficient versatile Reed-Solomon decoder design for multi-mode applications

“…At least 40.2 % increase in TSNT metric also demonstrates this point. For error-correction capability, [6] can correct more errors than other designs, however, in practical systems, 8-error-correction is fundamentally large enough for current applications. In short, Proposed-I achieves a good tradeoff between hardware performance and capability of errors correcting.…”

“…(6) After n iterations, Si=g(n-I) would be calculated. In (6) two Montgomery multiplications are required to for multiplying g(j) by «: Now applying (4) to (6), we have: (7), only one Montgomery multiplication is required for updating «». hence the previous universal multiplier can be totally replaced by a Montgomery multiplier, with half reduction of area and critical path delay.…”

“…Some prior efforts have been reported for designing versatile/universal RS decoders. In [6], cellular universal decoder was proposed based on Blahut's algorithm. [7] developed the reformulated inversionless BM (RiBM) [3] architecture into a folded reconfigurable codec.…”

Low-power channel coding via dynamic reconfiguration

“…In addition, the programmable codecs based on ASIC [7,8] and P G A [9] implementation style have been presented in the literature. In this paper, we employ the DAT approach for reconfiguring RS codecs.…”

Universal Reed-Solomon decoders based on the Berlekamp-Massey algorithm

“…Blahut [2] proposed two time-domain algorithms that do not require syndrome computations for universal decoders. Building on these time-domain algorithms, Shayan et al proposed noncellular [11] and cellular [12] universal decoders. These decoders use a fixed primitive polynomial of a fixed degree m, but can decode RS codes of different rates [13].…”