Linear Block Codes

Toyokazu Hiramatsu, Günter Köhler

Driss Khebbou, Reda Benkhouya, Idriss Chana +1 more

This paper aims to take advantage of the performances of polar decoding techniques for the benefit of binary linear block codes (BLBCs) with the main objective is to study the performances of the SSCL decoding for short-length BLBCs. Polar codes are one of the most recent error-correcting codes to be invented, and they have been mathematically demonstrated to be able to correct all errors under a specific situation, using the successive-cancellation decoder. However, their performances for real-time wireless communications at short block lengths remain less attractive. To take advantage of the performance of these codes in favor of error correction codes of short block length, an adaptation of the simplified successive-cancellation list as a decoder for polar codes for the benefit of short block length binary linear block codes is presented in this paper. This adaptation makes it possible to take advantage of the performances of less complex decoding methods for polar codes for BLBCs with latency and complexity optimization of the standard successive-cancellation list decoder. The experiment shows that the method can achieve the performances of the most famous order statistic decoder for binary linear block codes, which can achieve the performances of maximum-likelihood decoding with computational complexity and memory constraints.

Anton Betten, Harald Fripertinger, Adalbert Kerber +2 more

Tadao Kasami, Torleiv Kløve, Shu Lin

The probability of undetected error of linear block codes for use on a binary symmetric channel is investigated. Upper hounds are derived. Several classes of linear block codes are proved to have good error-detecting capability.

Rossitza Dodunekova, S.M. Dodunekov

Driss Khebbou, Idriss Chana, Hussain Ben-Azza

In the context of decoding binary linear block codes by polar code decoding techniques, we propose in this paper a new optimization of the serial nature of decoding the polar codes equivalent to binary linear block codes. In addition to the special nodes proposed by the simplified successive-cancellation list technique, we propose a new special node allowing to estimate in parallel the bits of its sub-code. The simulation is done in an additive white gaussian noise channel (AWGN) channel for several linear block codes, namely bose–chaudhuri–hocquenghem codes (BCH) codes, quadratic-residue (QR) codes, and linear block codes recently designed in the literature. The performance of the proposed technique offers the same performance in terms of frame error rate (FER) as the ordered statistics decoding (OSD) algorithm, which achieves that of maximum likelihood decoder (MLD), but with high memory requirements and computational complexity.