Construction and Decoding of BCH-Codes Over the Gaussian Field
Muhammad Sajjad, Tariq Shah, Maha Alammari, Huda Alsaud
Abstract
In this article, first we deliberate the theory of the Gaussian field and extension field of the Gaussian field. However, in the second phase, we provide a comprehensive construction scheme for BCH codes over the Gaussian field. The decoding of newly designed BCH codes is handled through a slightly amended modified Berlekamp-Massey algorithm. The coding gain is obtained by BCH codes over the Gaussian field. Accordingly, a better code rate and the number of code words are obtained as compared to the BCH codes over finite fields. Thus, this makes them a promising candidate for use in communication systems.
Topics & Concepts
BCH codeDecoding methodsBerlekamp–Welch algorithmComputer scienceList decodingSequential decodingField (mathematics)Concatenated error correction codeBlock codeAlgorithmMathematicsPure mathematicsDNA and Biological ComputingError Correcting Code TechniquesCoding theory and cryptography