An Efficient Hard-Detection GRAND Decoder for Systematic Linear Block Codes

Guessing random additive noise decoding (GRAND) has been recently proposed as a code-agnostic decoding technique for linear block codes, which attempts to guess the possible error pattern applied on the received word to check if the result is a valid codeword. The GRAND with abandonment (GRANDAB) is a hard-detection decoder by limiting the number of generated test error patterns. This article presents efficient algorithms to reduce the number of queries for the GRANDAB when the codes are systematic and cyclic. These methods exploit the properties of the syndrome weight and cyclic codes to significantly improve the decoding latency as the GRANAB corrects up to the error-correcting capability of the code. The VLSI architecture of novel hard-detection GRANDAB is presented, which provides efficient decoding up to 128 bits and can correct up to 3 bit errors at or above the error-correcting capability of the code. The property of syndrome weight is integrated with the dial structure for parallelism, supporting the default mode and the mode of systematic encoding with the known error-correcting capability. When compared to the architecture developed by Abbas et al., the average decoding cycles of two and three errors for the (127, 106) Bose–Chaudhuri–Hocquenghem (BCH) code are improved by 30.90% and 48.63%, respectively. For the (128, 96) cyclic redundancy check (CRC) code, the average decoding cycles of two and three errors are reduced by 45.19% and 65.71%, respectively. At the signal-to-noise ratio (SNR) of 5 dB, the average latencies for decoding (128, 96) CRC and (127, 106) BCH codes are improved by 21.34% and 12.29%. The worst-case latency for decoding the (127, 113) BCH code in the presented design is shorter than that of the work implemented by Riaz et al. with the reduction of 98.02%. The developed hardware architecture is also superior to the original dial-based design by Abbas et al. in terms of area–time (AT) complexity.