Efficient Decoding of Systematic (23, 12, 7) and (41, 21, 9) Quadratic Residue Codes
Yan‐Haw Chen, Chih-Hua Chien, Chien‐Hsiang Huang, Trieu‐Kien Truong, Ming-Haw Jing · Journal of information science and engineering · 2010
In this paper, a new algorithms decoding the (23, 12, 7) and the (41, 21, 9) Quadratic Residue (QR) codes are presented. The key ideas behind this decoding technique are based on one-to-one mapping between the syndromes S 1 and correctable error patterns. Such algorithms determine the error locations directly by lookup tables without the operations of m ultiplication over a finite fiel d. Moreover, the m ethod of utilizing shift-search algorithm, to dr amatically reduce the memory requirement is given for decoding QR codes. The algorithm has been verified through a software simulation that program in C-language. The new approach is modular, regular and natur al ly suitable for DSP software implementation.