Fast Soft Decision Decoding Algorithm for Linear Block Codes Using Permuted Generator Matrices

Abstract

The Gaussian elimination algorithm is an essential part of the ordered statistics-based decoding (OSD); the algorithm is required to be executed at least once for a typical OSD algorithm, with its computational complexity serving as the lower bound of the total computational complexity. When the signal-to-noise ratio (SNR) is relatively low, the computational complexity of the Gaussian elimination algorithm can be ignored as the decoding process is relatively complex. However, with an increase in the SNR, this cannot be ignored. In this letter, we propose a fast soft decision decoding algorithm using templates that are precalculated and permuted generator matrices, enabling us to decode a received vector without having to perform the OSD algorithm. In particular, if the Hamming distance between the received vector and the candidate codeword generated by one of the templates is less than a certain threshold, we can terminate the decoding process without executing the typical OSD algorithm. This aids in reducing the computational complexity in high SNR regimes without compromising the decoding performance.