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arXiv:1101.5025

Order Statistics Based List Decoding Techniques for Linear Binary Block Codes

Saif E. A. Alnawayseh, Pavel Loskot

Published Jan 26, 2011• 0 citations
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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.

DOI
10.48550/arxiv.1101.5025

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IEEE Transactions on Information Theory•May 1, 1996•63 citations
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.
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.
This dissertation presents a novel approach to soft decision decoding for binary linear block codes. The basic idea of this approach is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is highly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the trade-off between performance and decoding complexity is provided. The proposed decoding is based on the reordering of the received symbols according to their reliability measure. In the dissertation, we evaluate the statistics of the noise after ordering. Based on these statistics, we derive two monotonic properties which dictate the reprocessing strategy. Each codeword is decoded in two steps: (1) hard-decision decoding based on reliability information and (2) reprocessing of the hard-decision decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test highly related to the reprocessing strategy is introduced to reduce the number of computations for each reprocessing stage. For short codes of lengths N ≤ 32 or medium codes with 32 < N ≤ 64 with rate R ≥ 0.6, near-optimum bit error performance is achieved in two stages of reprocessing with at most a computation complexity of o(K2) constructed code-words, where K is the dimension of the code. For longer codes, three or more reprocessing stages are required to achieve near-optimum decoding. However, most of the coding gain is obtained within the first two reprocessing stages for error performances of practical interest. The proposed decoding algorithm applies to any binary linear code, does not require any data storage and is well suitable for parallel processing. Furthermore, the maximum number of computations required at each reprocessing stage is fixed, which prevents buffer overflow at low SNR. Further reductions of the number of computations based on probabilistic or decomposable properties of the code considered are also investigated. The generalization of the algorithm to other channels is discussed. Finally, the discrete time channel associated with the AWGN model after ordering is greatly simplified. This simplification allows an important reduction of the number of computations required to evaluate the theoretical error performance of any algorithm based on a partial or total ordering.
In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation- discarding technique is proposed along with the stopping rule to significantly reduce the decoding complexity without a significant performance degradation compared to ordered statistics decoding (OSD). In the proposed decoder, the list of test error patterns (TEPs) is divided into several segments according to carefully selected boundaries and every segment is checked separately during the reprocessing stage. Decoding is performed under the constraint of the discarding rule and stopping rule. Simulations results for different codes show that our proposed algorithm can significantly reduce the decoding complexity compared to the existing OSD algorithms in literature.
The order statistic decoding (OSD) algorithm is a probabilistic list decoding algorithm which allows to achieve practically optimum soft decision decoding of binary linear block codes of length up to 128. Recently, matching techniques were applied to the OSD algorithm to reduce both the worst case and average complexities of decoding at the expense of memory. The corresponding box-and-match algorithm (BMA) allows to achieve near optimum decoding of codes of length up to 192. In this work, we investigate the application of iterative information set reduction to the BMA, which provides further refinements in the trade-offs between error performance and decoding complexity.
This letter proposes an efficient probability-based ordered-statistics decoding (PB-OSD) algorithm for short block-length codes. In PB-OSD, we derive two probabilistic measures on the codeword estimates and test error patterns, respectively referred to as the success probability and promising probability. Based on these probabilities, a stopping criterion and a discarding criterion are developed to reduce the number of test error patterns and limit the decoding complexity. To further reduce the complexity, we propose a tree-based search strategy to find the most likely test error patterns in reprocessing stage of the OSD algorithm. Simulation results show that PB-OSD significantly reduces the decoding complexity under the same error performance, compared to the original OSD algorithm.
Soft-decision decoding of a linear block code using the most reliable basis corresponding to each received word is investigated. Based either on probabilistic properties or on the structure of the code considered, three improvements to the algorithm devised by Fossorier and Lin (see ibid., vol.41, no.9, p.1379-1396, 1995) are presented. These modifications allow large computation savings or significant decoding speedup with little error performance degradation. First, a reduced probabilistic list of codeword candidates is associated with order-i reprocessing of a given code. It results in a large reduction of the maximum number of computations with a very small degradation in performance. Then, a probabilistic stopping criterion is introduced for order-0 reprocessing. This new test significantly decreases the average number of computations when appropriately implemented. Finally, the application of the algorithm to coset decoding is considered for |u|u+v| constructed codes. In addition to the conventional coset decoding, a new adaptive practically optimum coset decoding method is presented where at each reprocessing stage, the number of surviving cosets decreases. Suboptimum closest coset decoding is also investigated. It is shown that two-stage decoding with the algorithm of Fossorier and Lin offers a large variety of choices, since the reprocessing order of each stage can be determined independently.