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New Approach to Order Statistics Decoding of Long Linear Block Codes

In this paper we propose the Arranged List of the Most a priori Likely Tests (ALMLT) algorithm, which is an efficient algorithm for reliability-based soft-decision decoding of long linear block codes. Based on order statistics, we define the mean bit reliabilities and use them to estimate the a priori weight of an error pattern. Each error pattern is represented by a test vector. All the test vectors are sorted according to the increasing order of their weights and saved in a list. Since these weights only depend on the channel SNR, the generation of the list is performed off the transmission. The list of test vectors is then used to decode the received binary sequence similarly as in the Ordered Statistic Decoding (OSD) algorithm. The ALMLT algorithm outperforms the OSD(2) algorithm as illustrated by decoding the binary image of the (255, 239,17) RS code and has a lower mean number of tests, while using the same stopping criterion.