Developing Efficient Algorithms of Decoding the Systematic Quadratic Residue Code with Lookup Tables

Abstract

The lookup table methods for decoding binary systematic Quadratic Residue (QR) code are presented in this paper. The key ideas behind this decoding technique are based on one to one corresponding mapping between the syndromes and the correctable error patterns. Such algorithms determine the error locations directly by lookup tables without the operations of addition and multiplication over a finite field. Moreover, the methods to dramatically reduce the memory requirement by shift-search decoding are utilized. Two new algorithm have been verified through a software simulation in C language. The new approach is modular, regular and naturally suitable for System on Chip (SOC) software implementation.

Keywords

• QR code
• Lookup Table method