On the Sensibility of the "Arranged List of the Most a Priori Likely Tests" Algorithm

In this paper we study the sensibility of the recently proposed Arranged List of the Most a priori Likely Tests (ALMLT) algorithm to the real signal to noise ratio (SNR) of the received bits for a list of tests generated off-line at a given SNR. The ALMLT algorithm is an efficient method for reliability-based soft-decision decoding of long linear block codes. Based on order statistics and SNR, 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 estimated SNR, the generation of the list is performed once for all, off the transmission. The list of test vectors is then used to decode the received binary sequence as in the Ordered Statistic Decoding (OSD) algorithm. The ALMLT algorithm with the same maximal number of tests as the OSD(2) and while using the same stopping criterion, outperforms it, as illustrated by decoding the binary image of the (255, 239, 17) RS code and has a lower mean number of tests. Moreover, the algorithm designed for a given SNR proves to be insensible to small SNR variations when decoding the (255, 239, 17) RS code.