Using a particular construction of generator matrices of the -ary image of -ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding o...

Our study aims at bringing a software-based alternative for decoding Reed Solomon over the MPE-IFEC in the DVB-SH system, at the cost of a lower complexity and a good performance. The MPE-IFEC is operating in the Link layer, where the lost packets are considered as erasures. In this context, we propose to recover losses by decoding on a graph the binary image of the Reed Solomon code over a Bin...

Peak Signal-to-Noise Ratio (PSNR) is a serious issue in OFDM systems. Several techniques have been proposed by researchers to maintain PSNR. In this paper, the Peak Signal-to-Noise Ratio (PSNR) performance of conventional Fast Fourier Transform (FFT)-OFDM system and discrete cosine transform (DCT)-OFDM system is compared with discrete wavelet transform (DWT)-OFDM system in a Gaussian Noise envi...

We describe a new algorithm for the decoding of Reed Solomon codes. This algorithm was originally described in [12]. While the algorithm presented in this article is the same, the presentation is somewhat di erent. In particular we derive more precise bounds on the performance of the algorithm and show the following: For an [n; n; (1 )n]q Reed Solomon code, the algorithm in [12] corrects ( ( ) ...

Wireless communication is one of the speedily evolving and dynamic technology areas in realm communication. OFDM an acronym for Orthogonal Frequency Division Multiplexing. It a version FDM which orthogonal subcarriers are closely spaced to maximize bandwidth consumption. By decreasing Inter Symbol Interference (ISI) increasing Signal-to-Noise ratio (SNR), it has enhanced quality long-distance I...

Reed–Solomon codes are a well–studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size q of the underlying field Fq. In this paper we present a code construction which yields codes with lengths of factors of the field size. Furthermore a decoding algorithm beyond half the minimum distance is given and analyzed.

Power consumption is a critical issue for many applications running on autonomous battery operated devices. In the context of low power communications, the use of Forward Error Correction (FEC) schemes shall therefore not only be considered as a way to improve communication robustness but also as a way to reduce transmit power. The benefits of this approach can be assessed by analyzing the trad...

We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q log 2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast polynomial arithmetic were already known, but even if their complexity is similar, they are mostly impractical. By comparison our algorithm uses only a few Walsh tr...

We present an efficient erasure decoding algorithm for generalized Reed Solomon codes constructed by utilizing the structure of the inverse of the VanderMonde matrices. Given an [n, k] generalized Reed Solomon code, decoding for r erasures, where r = n − k, requires rk + n Galois field multiplications and r(k − 1) Galois field additions after setting up the decoding structures for an erasure pa...

In this letter, we propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speedup of the decoding process of Bose–Chaudhuri–Hocquenghem, Reed–Solomon, and some other error-correcting codes.