On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes

In this work, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m <= q. In the literature, the minimum/stopping distance of these codes (denoted by d(q,m) and h(q,m), respectively) has been thoroughly studied for m <= 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m=6, the best known minimum distance upper bound, derived by Mittelholzer (IEEE Int. Symp. Inf. Theory, Jun./Jul. 2002), is d(q,6) <= 32. In this work, we derive an improved upper bound of d(q,6) <= 20 and a new upper bound d(q,7) <= 24 by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m <= 7 and low-to-moderate values of q <= 79.Comment: To appear in IEEE Trans. Inf. Theory. The material in this paper was presented in part at the 2014 IEEE International Symposium on Information Theory, Honolulu, HI, June/July 201

ON TURBO CODES AND OTHER CONCATENATED SCHEMES IN COMMUNICATION SYSTEMS

The advent of turbo codes in 1993 represented a significant step towards realising the ultimate capacity limit of a communication channel, breaking the link that was binding very good performance with exponential decoder complexity. Turbo codes are parallel concatenated convolutional codes, decoded with a suboptimal iterative algorithm. The complexity of the iterative algorithm increases only linearly with block length, bringing previously unprecedented performance within practical limits.. This work is a further investigation of turbo codes and other concatenated schemes such as the multiple parallel concatenation and the serial concatenation. The analysis of these schemes has two important aspects, their performance under optimal decoding and the convergence of their iterative, suboptimal decoding algorithm. The connection between iterative decoding performance and the optimal decoding performance is analysed with the help of computer simulation by studying the iterative decoding error events. Methods for good performance interleaver design and code design are presented and analysed in the same way. The optimal decoding performance is further investigated by using a novel method to determine the weight spectra of turbo codes by using the turbo code tree representation, and the results are compared with the results of the iterative decoder. The method can also be used for the analysis of multiple parallel concatenated codes, but is impractical for the serial concatenated codes. Non-optimal, non-iterative decoding algorithms are presented and compared with the iterative algorithm. The convergence of the iterative algorithm is investigated by using the Cauchy criterion. Some insight into the performance of the concatenated schemes under iterative decoding is found by separating error events into convergent and non-convergent components. The sensitivity of convergence to the Eb/Ng operating point has been explored.SateUite Research Centre Department of Communication and Electronic Engineerin

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

New effective power terms and right-angled triangle (RAT) power theory

publisher: Elsevier articletitle: New effective power terms and right-angled triangle (RAT) power theory journaltitle: International Journal of Electrical Power & Energy Systems articlelink: http://dx.doi.org/10.1016/j.ijepes.2016.12.009 content_type: article copyright: Crown Copyright © 2016 Published by Elsevier Ltd. All rights reserved