Ordered statistics-based list decoding techniques for linear binary block codes

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.

Constrained Turbo Block Convolutional Codes for 100 G and Beyond Optical Transmissions

“…The proposed codes CTBC-1 through CTBC-4 can each be decoded as a single concatenation by running SISO iterations. The accumulator can be soft decoded using the standard BCJR algorithm [14] or the min-sum algorithm [15], while the BCH code B can be soft decoded using the reduced complexity versions of either the Pyndiah algorithm [16], [17], ordered statistics decoding (OSD) [18], [19], or using other known methods of soft decoding block codes [14]. The combined inner decoder in CTBC-2 and CTBC-3 can be soft decoded using the BCJR algorithm according to the state diagram in Fig.…”

“…Parallel decoding of codewords reduces latency. OSD decoding [14] with a complexity on the order of O(k 2 ), reduced complexity OSD decoding [19] or other algorithms for soft decoding of block codes [14] can be used to achieve the NCGs reported herein with OSD with an increase in the complexity beyond that of Pyndiah decoding.…”

Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes

“…Much previous work has focused on improving OSD in terms of efficiency and some remarkable progresses have been achieved [8]- [15]. The Box-and-Match algorithm [10] can greatly reduce the size of the candidates list, while it brings other computations due to the matching process.…”

“…All of the above methods can be combined with the iterative information set reduction (IISR) technique in [9] to further reduce the complexity. Recently an approach proposed in [15] cuts the most reliable basis (MRB) to several partitions and performs independent OSD over each of them, but it overlooks candidates generated across partitions so that a dramatic performance degradation is resulted. Also a fast OSD algorithm combining stopping rules from [13] and sufficient conditions from [14] was proposed in [16], which can reduce the complexity from O(K m ) to O(K m−2 ) in high signal-tonoise ratios (SNRs).…”