A cyclic weight algorithm of decoding the (47, 24, 11) quadratic residue code

Abstract

In this article, a novel table lookup decoding algorithm, called the cyclic weight (CW) decoding algorithm, is developed to facilitate faster decoding of the binary systematic (47,24,11) quadratic residue (QR) code. It is based on the property of cyclic codes together with the weight of syndromes. This new algorithm requires a lookup table which consists of 20.43Kbytes. The advantage of the CW decoding algorithm over the previous table lookup method is that the memory size of the proposed lookup table is only about 1.89% of the lookup table needed in the decoding algorithm of Chen’s et al. These facts lead to significantly reduce the decoding complexity in terms of CPU time while maintaining the capability to correct up to five errors. Simulation results show that the decoding speed of the proposed algorithm is much faster than that of the algorithm of Chen et al.