An Improved $A^{\ast}$ Decoding Algorithm With List Decoding

Abstract

Comparing with hard decision decoding algorithms, soft decoding has a lower probability of bit error but a higher computational complexity. As a maximum-likelihood soft decoding method, the $A^{\ast }$ algorithm is the most basic and widely used to minimize bit error probability. However, its average computational complexity strongly depends on a seed codeword and a heuristic function utilized during the decoding process. To efficiently reduce the computational complexity while maintaining the decoding accuracy theoretically and practically, this paper proposes an improved $A^{\ast }$ decoding algorithm consisting of two phases. The first phase applies the greedy list decoding to the linear block code to obtain a seed codeword. According to the seed, the second phase applies the improved $A^{\ast }$ algorithm to obtain the final decoding output. The heuristic function used in the $A^{\ast }$ algorithm is modified in two aspects: 1) use more information of partial decoded symbols to improve the accuracy of the function and 2) take advantage of Hamming distance to reduce the search space. Simulations on the $RM(5,2)$ Reed–Muller codes and [128, 64] binary extended BCH code show that this improved $A^{\ast }$ algorithm is more efficient in average decoding complexity than many other algorithms while maintaining the decoding accuracy.