High-speed decoding of the (71, 36, 11) quadratic residue code

A high-speed and memory-efficient table lookup decoding algorithm (TLDA), called the syndrome and syndrome difference decoding algorithm (SSDDA), is developed to decode the long binary systematic (71, 36, 11) quadratic residue (QR) code. The essential point of the SSDDA is based on the property of the weight of syndrome and the weight of syndrome difference to reduce the memory size of the lookup table. The proposed algorithm generates a novel compact lookup table (CLT), which only consists of 7,806 syndromes and their corresponding error patterns. Consequently, the memory size of the proposed CLT is only about 38.39% of the lookup table proposed by Lin et al.