On the reliability-order-based decoding algorithms for binary linear block codes

• Main Authors: Tang, Yuansheng, Ling, San, Fu, Fang-Wei
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory
• Online Access: https://hdl.handle.net/10356/96305; http://hdl.handle.net/10220/9849
• Institution: Nanyang Technological University

In this correspondence, we consider the decoding of binary block codes over the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) signaling. By a reliability-order-based decoding algorithm (ROBDA), we mean a soft-decision decoding algorithm which decodes to the best (most likely) codeword of the form that is the sum of the hard-decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions. Examples of ROBDAs include many well-known decoding algorithms, such as the generalized-minimum-distance (GMD) decoding algorithm, Chase decoding algorithms, and the reliability-based decoding algorithms proposed by Fossorier and Lin. It is known that the squared error-correction-radii of ROBDAs can be computed from the minimal squared Euclidean distances (MSEDs) between the all-one sequence and the polyhedra corresponding to the error patterns. For the computation of such MSEDs, we give a new method which is more compact than the one proposed by Fossorier and Lin. These results are further used to show that any bounded-distance ROBDA is asymptotically optimal: The ratio between the probability of decoding error of a bounded-distance ROBDA and that of the maximum-likelihood (ML) decoding approaches 1 when the signal-to-noise ratio (SNR) approaches infinity, provided that the minimum Hamming distance of the code is greater than 2.