A Novel Approach to the Quadratic Residue Code

Abstract

In this paper presents a novel hash table algorithm for high-throughput decoding of the (n, k, d) Quadratic Residue (QR) code. The main ideas behind this decoding technique are based on one-to-one map-ping between the syndromes “S1” and correctable error patterns. As compared with the binary lookup table method, the presented technique is faster than binary searching method for finding error pattern. In addition, it has the advantage that can be performed quickly with a masking operation as a choice hash table of size \( M = 2\left\lfloor {\log_{2} \overline{M} } \right\rfloor \) for decoding QR codes. Moreover, the presented high speed of the decoding procedure has potential applications in modern communication systems and digital signal processing (DSP) systems.