Fast Decoding of the (47, 24, 11) Quadratic Residue Code Without Determining the Unknown Syndromes

In this paper, a hard-decision (HD) scheme is presented to facilitate faster decoding of the (47, 24, 11) quadratic residue (QR) code. The new HD algorithm uses the previous scheme of decoding the (47, 24, 11) QR code up to three errors, but corrects four and five errors with new different methods. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities and simplifies the condition that exactly indicates the occurrence of four errors. Subsequently, the reliability-based shift-search algorithm can be utilized to decode weight-5 error patterns. In other words, a five-error case can be decoded in terms of a four-error case after inverting an incorrect bit of the received word. Simulation results show that the new HD algorithm not only significantly reduces the decoding complexity in terms of CPU time but also saves a lot of memory while maintaining the same error-rate performance.