Abstract
The ordered statistics-based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of a list of the test error patterns is considered. The original ordered-statistics decoding (OSD) is generalized by assuming segmentation of the most reliable independent positions (MRIPs) of the received bits. The segmentation is shown to overcome several drawbacks of the original OSD. The complexity of the ordered statistics-based decoding is further reduced by assuming a partial ordering of the received bits in order to avoid the complex Gauss elimination. The probability of the test error patterns in the decoding list is derived. The bit error rate performance and the decoding complexity trade-off of the proposed decoding algorithms is studied by computer simulations. Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original OSD in terms of both the bit error rate performance as well as the decoding complexity.
Highlights
A major difficulty in employing forward error correction (FEC) coding is the implementation complexity especially of the decoding at the receiver, and the associated decoding latency for long codewords
The low-complexity soft-decision decoding techniques employing the list of the test error patterns for linear binary block codes of small to medium block length were investigated
The original ordered-statistics decoding (OSD) algorithm was generalized by assuming segmentation of the most reliable independent positions (MRIPs)
Summary
A major difficulty in employing forward error correction (FEC) coding is the implementation complexity especially of the decoding at the receiver, and the associated decoding latency for long codewords. List decoding algorithms Using Theorems 1 and 2 in [4], the original OSD assumes the following list of the test error patterns, EL = {eG : 0 ≤ wH[e] ≤ I, e ∈ ZK2 }. For given K, the maximum value of I is limited by the acceptable OSD complexity to achieve a certain target BER We can address these inefficiencies of the original OSD by more carefully exploiting the properties of the joint probability of bit errors given by Lemma 1 and Theorem 1. One can consider the Hamming distances for one or more segments of the MRIPs between the received hard decisions (before the decoding) and the temporary decisions obtained using the test error patterns from the list. The overall complexity of the OSD-based schemes can be substantially reduced by avoiding the Gauss (Gauss-Jordan) elimination
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