The Improved Decoding Algorithm of the (71, 36, 11) Quadratic Residue Code

In the context of informatization and big data, the demands for the reliability and real-time of information transmission in wireless communication channels are increasing. Quadratic residue (QR) codes have a high prospect on error correction for reliable data conveyance over channel with noise. This paper proposes an optimized algebraic scheme for decoding (71, 36, 11) QR code for correcting up to 5 errors on one-case-by-one-case basis. This scheme is mainly to improve its algebraic decoding algorithm based on the Lin’s algorithm, only in this paper, the Lin’s algorithm is called LTC71 algorithm. The key technology is to use the algebraic structure of QR code and give a new discriminant condition by mathematical derivation, which can quickly detect whether there are four errors in the code. Simulation results show that the proposed decoding scheme achieves the same bit error-rate performance as LTC71 algorithm, and the decoding time is reduced by about 28.72% owing to the reduced complexity of the decoder when there are four errors in the code.