Efficient Decoding of Systematic (23,12,7) and (41,21,9) Quadratic Residue Codes
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 multiplication over a finite field. Moreover, the method of utilizing shiftsearch algorithm, to dramatically 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 naturally suitable for DSP software implementation.
quadratic residue syndrome error pattern finite field dsp