Block Code Design Based on Golay Code for Future Communication Systems

In Long Term Evolution (LTE) and New Radio (NR) systems, Reed-Muller (RM) code-based block codes have been employed to encode Uplink Control Information (UCI) with very small payload sizes. However, there is room for further improvement in the performance of these block codes. In this paper, we propose a unified block code design based on Golay code for UCI, considering codeword lengths of 20, 24, and 32 bits, which are potentially relevant for 6G systems. The block codes with a codeword length of 20 bits are initially constructed by shortening the extended Golay code (24,12) and subsequently adding parity check bits. These parity check bits are obtained through a nested exhaustive search, aiming to maximize the minimum Hamming distance and achieve the best weight distribution. We carefully select candidate generator matrices with the fewest low weights. Subsequently, we construct block codes with codeword lengths of 24 bits and 32 bits by extending the 20-bit block codes. Our proposed Golay-based block codes outperform RM-based block codes in LTE and NR systems in terms of both performance and complexity. Notably, for the case of a 24-bit codeword length, the proposed Golay-based block codes exhibit approximately 0.5 dB better performance than RM-based block codes for the majority of payload sizes.