arXiv subjects

Jossy Sayir

Publications and source records attributed to Jossy Sayir.

7 recordsLinked to original sources

arXiv2015

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.

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arXiv2015

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, non-binary LDPC codes, and polar coding.

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arXiv2014

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

The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check (LDPC) defined over an alphabet of size $q$ operates on truncated messages of length $q'$ to achieve a complexity of the order $q'^2$. In contrast, Walsh-Hadamard (WH) transform based iterative decoders achieve a complexity of the order $q\log q$, which is much larger for $q'<<q$. 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 $q'$ 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.

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arXiv2014

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.

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arXiv2014

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.

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arXiv2010

EXIT Chart Approximations using the Role Model Approach

Extrinsic Information Transfer (EXIT) functions can be measured by statistical methods if the message alphabet size is moderate or if messages are true a-posteriori distributions. We propose an approximation we call mixed information that constitutes a lower bound for the true EXIT function and can be estimated by statistical methods even when the message alphabet is large and histogram-based approaches are impractical, or when messages are not true probability distributions and time-averaging approaches are not applicable. We illustrate this with the hypothetical example of a rank-only message passing decoder for which it is difficult to compute or measure EXIT functions in the conventional way. We show that the role model approach (arXiv:0809.1300) can be used to optimize post-processing for the decoder and that it coincides with Monte Carlo integration in the non-parametric case. It is guaranteed to tend towards the optimal Bayesian post-processing estimator and can be applied in a blind setup with unknown code-symbols to optimize the check-node operation for non-binary Low-Density Parity-Check (LDPC) decoders.

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arXiv2008

What makes a good role model

The role model strategy is introduced as a method for designing an estimator by approaching the output of a superior estimator that has better input observations. This strategy is shown to yield the optimal Bayesian estimator when a Markov condition is fulfilled. Two examples involving simple channels are given to illustrate its use. The strategy is combined with time averaging to construct a statistical model by numerically solving a convex program. The role model strategy was developed in the context of low complexity decoder design for iterative decoding. Potential applications outside the field of communications are discussed.

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