A Lookup Table Decoding of systematic (47,24,11) quadratic residue code
A new decoding algorithm for the binary systematic (47,24,11) quadratic residue (QR) code, a code that allows error-correction of up to five errors, is presented in this paper. The key idea behind this decoding technique is based on the existence of a one-to-one mapping between the syndromes S1 and correctable error patterns. By looking up a pre-calculated table, this algorithm determines the locations of errors directly, thus requires no multiplication operations over a finite field. Moreover, the algorithm dramatically reduces the memory required by approximately 89%. A full search confirms that when five or less errors occur, this algorithm decodes these errors perfectly. Since the implementation is written in the C-language, it is readily adaptable for use in Digital Signal Processing (DSP) applications.
quadratic residue syndrome error pattern finite field digital signal processing