Efficiency of two decoders based on hash techniques and syndrome calculation over a Rayleigh channel

The explosive growth of connected devices demands high quality and reliability in data transmission and storage. Error correction codes (ECCs) contribute to this in ways that are not very apparent to the end user, yet indispensable and effective at the most basic level of transmission. This paper presents an investigation of the performance and analysis of two decoders that are based on hash techniques and syndrome calculation over a Rayleigh channel. These decoders under study consist of two main features: a reduced complexity compared to other competitors and good error correction performance over an additive white gaussian noise (AWGN) channel. When applied to decode some linear block codes such as Bose, Ray-Chaudhuri, and Hocquenghem (BCH) and quadratic residue (QR) codes over a Rayleigh channel, the experiment and comparison results of these decoders have shown their efficiency in terms of guaranteed performance measured in bit error rate (BER). For example, the coding gain obtained by syndrome decoding and hash techniques (SDHT) when it is applied to decode BCH (31, 11, 11) equals 34.5 dB, i.e., a reduction rate of 75% compared to the case where the exchange is carried out without coding and decoding process.