A Low-Complexity Approach for Constructing the Optimal Binary Finite-Length Block Code

Improving the bit error rate (BER) performance of finite-length block code is required in the scenarios of ultra-reliable and low latency communications. Nonetheless, the complexity of algorithms to find such a high performance block code increases dramatically as blocklength increases. Towards this end, the paper proposes a low-complexity recursive algorithm to search the optimal binary block codes subject to the requirement of the minimum Hamming distance. As a result, two optimal code sets of code-length 16 and 32 are found with code rate of 1/2. The simulation results show that the constructed codes under binary phase shift keying (BPSK) modulation outperform the systematic polar codes in the same blocklength in terms of the BER performance.