Performance Analysis of Two Serial Concatenations of Decoders Over a Rayleigh Channel

The Hartmann & Rudolph (HR) decoder is a symbol-by-symbol decoding algorithm that relies on a probabilistic approach to compute the value of a symbol in a sequence. The HSDec and SDHT decoders are recent decoding algorithms based on hashing and syndrome calculation. The serial concatenation of two decoders consists of sequentially utilizing two decoders in the decoding process of a received sequence. The used concatenation aims at partially correcting the received sequence using HR algorithm, and then completing the decoding operation using HSDec or SDHT, depending on the studied context. In this paper, a performance study is presented for the HR decoder combined with the HSDec and SDHT decoding algorithms and applied to linear codes, specifically BCH codes having the length 31 and 63 through a Rayleigh channel. The simulation results have shown a significant coding gain. For example, when PHR-SDHT is used to decode the BCH(31, 16, 7) code, the coding gain reaches 34 dB compared to a situation when no coding is done by the transmitting and no decoding is performed on the receiving.