Improved Decoding Algorithm for High Reliable Reed Muller Coding

Danyo Danev, Daniel Puaca

R. Lucas, Martin Bossert, Armin Dammann

We present a new list-decoding algorithm for Reed-Muller (RM) codes based on the GMC decoding algorithm proposed previously. As a result, a SDML decoding algorithm for the 1st order RM codes is obtained. Furthermore, simulations showed that for RM codes of higher order and up to a length 1024, the performance of L-GMC decoding is more than 1 dB superior to conventional GMC decoding.

Ilya I. Dumer, Kirill Shabunov

Yong-Ting Ni, Cheng-Yu Pai, Chao‐Yu Chen

This paper presents an iterative bit-flipping (BF) decoding algorithm for binary Reed-Muller (RM) codes. The BF decoding algorithm is a hard-decision decoding algorithm. According to the updated hard reliability measures, one bit of the received hard-decision sequence is flipped at a time in each iteration. The simulation results show that the proposed BF decoding algorithm outperforms the conventional hard-decision majority decoding.

Ilya I. Dumer, Kirill Shabunov

Kin‐ichiroh Tokiwa, Nasao Kasahara, Toshihiko Namekawa

Abstract Recently, for the improvement of reliability of digital communication systems, various kinds of error‐correcting codes are being used. to improve system reliability through the use of more capable error‐correcting codes it is extremely important to simplify the decoder construction and to reduce the decoding delay. This paper studies a decoding algorithm for a class of simple iterated codes (SI codes) constructed by simply repeating I times a codeword (called block) in a given code (called subcode). Moreover, this paper discusses the decoding delay when this decoding algorithm is applied to decoding the Reed‐Muller codes constructed by the superimposing method.