A Parallel Algorithm for Enumerating Joint Weight of a Binary Linear Code in Network Coding

Abstract-In this paper, we present a parallel algorithm for enumerating joint weight of a binary linear (n, k) code, aiming at accelerating assessment of its decoding error probability for network coding. To reduce the number of pairs of codewords to be investigated, our parallel algorithm reduces dimension k by focusing on the all-one vector included in many practical codes. We also employ a population count instruction to compute joint weight of codewords with a less number of instructions. Our algorithm is implemented on a multi-core CPU system and an NVIDIA GPU system using OpenMP and compute unified device architecture (CUDA), respectively. We apply our implementation to a subcode of a (127,22) BCH code to evaluate the impact of acceleration