Order Statistics Based List Decoding Techniques for Linear Binary Block Codes

TL;DR

This paper investigates and improves order statistics list decoding techniques for linear binary block codes, introducing segmentation and partial ordering to enhance performance and reduce complexity, with validation through simulations.

Contribution

It generalizes original order statistics decoding by segmentation and partial ordering, overcoming drawbacks and improving performance and complexity.

Findings

Proposed decoding schemes outperform original in some cases

Segmentation reduces decoding complexity

Numerical results confirm improved bit error rate

Abstract

The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics decoding is generalized by assuming segmentation of the most reliable independent positions of the received bits. The segmentation is shown to overcome several drawbacks of the original order statistics decoding. The complexity of the order 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 order statistics decoding in terms of both the bit error rate performance as well as the decoding complexity.