Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain

The Extended Min-Sum (EMS) algorithm for nonbinary low-density parity-check (LDPC) defined over an alphabet of size q operates on truncated messages of length q0 to achieve a complexity of the order q02. In contrast, Walsh-Hadamard (WH) transform based iterative decoders achieve a complexity of the order q log q, which is much larger for q0 << q. In this paper, we demonstrate that considerable savings can be achieved by letting WH based decoders operate on truncated messages as well. We concentrate on the direct WH transform and compute the number of operations required if only q0 of the q inputs are non-zero. Our paper does not cover the inverse WH transform and hence further research is needed to construct WH based decoders that can compete with the EMS algorithm on complexity terms.Funded in part by the European Research Council under ERC grant agreement 259663 and by the FP7 Network of Excellence NEWCOM# under grant agreement 318306.This is the accepted manuscript. The final version is available from IEEE at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6979794&refinements%3D4272515215%26sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A6979787%29

The Role Model Estimator Revisited

We re-visit the role model strategy introduced in an earlier paper, which allows one to train an estimator for degraded observations by imitating a reference estimator that has access to superior observations. We show that, while it is true and surprising that this strategy yields the optimal Bayesian estimator for the degraded observations, it in fact reduces to a much simpler form in the non-parametric case, which corresponds to a type of Monte Carlo integration. We then show an example for which only parametric estimation can be implemented and discuss further applications for discrete parametric estimation where the role model strategy does have its uses, although it loses claim to optimality in this context.Funded in part by the European Research Council under ERC grant agreement 259663 and by the FP7 Network of Excellence NEWCOM# under grant agreement 318306.Published by the IEEE where the final published version can be viewed: http://dx.doi.org/10.1109/ISIT.2014.687511

An investigation of SUDOKU-inspired non-linear codes with local constraints

Codes with local permutation constraints are described. Belief propagation decoding is shown to require the computation of permanents, and trellis-based methods for computing the permanents are introduced. New insights into the asymptotic performance of such codes are presented. A universal encoder for codes with local constraints is introduced, and simulation results for two code structures, SUDOKU and semi-pandiagonal Latin squares, are presented.This is the author accepted manuscript. The final version is available from IEEE via 10.1109/ISIT.2015.728279

Density evolution for SUDOKU codes on the erasure channel

Codes based on SUDOKU puzzles are discussed, and belief propagation decoding introduced for the erasure channel. Despite the non-linearity of the code constraints, it is argued that density evolution can be used to analyse code performance due to the invariance of the code under alphabet permutation. The belief propagation decoder for erasure channels operates by exchanging messages containing sets of possible values. Accordingly, density evolution tracks the probability mass functions of the set cardinalities. The equations governing the mapping of those probability mass functions are derived and calculated for variable and constraint nodes, and decoding thresholds are computed for long SUDOKU codes with random interleavers.Funded in part by the European Research Council under ERC grant agreement 259663 and by the FP7 Network of Excellence NEWCOM# under grant agreement 318306.This is the accepted manuscript. The final version is available from IEEE at http://dx.doi.org/10.1109/ISTC.2014.6955120

Challenges and Some New Directions in Channel Coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: spatially coupled Low-Density Parity-Check (LDPC) codes, nonbinary LDPC codes, and polar coding.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/JCN.2015.00006

D11.2 Consolidated results on the performance limits of wireless communications

Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin