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Simon Litsyn

Publications and source records attributed to Simon Litsyn.

12 recordsLinked to original sources
arXiv2015

Recursive Descriptions of Polar Codes

Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such description allows an easy development of these algorithms for arbitrary polarizing kernels. Hardware architectures for these decoding algorithms are also described in a recursive way, both for Arikan's standard polar codes and for arbitrary polarizing kernels.

cs.IT↗
arXiv2015

Polar Codes with Mixed-Kernels

A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its polarization properties are strongly related to the ones of the constituent kernels. Simulation of finite length instances of the scheme indicate their advantages both in error correction performance and complexity compared to the known polar coding structures.

cs.IT↗
arXiv2015

Binary Polarization Kernels from Code Decompositions

In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general non-linear. They provide a better polarization exponent than the previously known kernels of the same dimensions. In particular, non-linear kernels of dimensions 14, 15, and 16 are constructed and are shown to have optimal asymptotic error-correction performance. The optimality is proved by showing that the exponents of these kernels achieve a new upper bound that is developed in this paper.

cs.IT↗
arXiv2013

Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization

An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low error-floor. The efficiency of the algorithm is demonstrated by generating good codes of short to moderate length over small fields, outperforming codes generated by the known methods.

cs.IT↗
arXiv2012

The PAPR Problem in OFDM Transmission: New Directions for a Long-Lasting Problem

Peak power control for multicarrier communications has been a long-lasting problem in signal processing and communications. However, industry and academia are confronted with new challenges regarding energy efficient system design. Particularly, the envisioned boost in network energy efficiency (e.g. at least by a factor of 1000 in the Green Touch consortium) will tighten the requirements on component level so that the efficiency gap with respect to single-carrier transmission must considerably diminish. This paper reflects these challenges together with a unified framework and new directions in this field. The combination of large deviation theory, de-randomization and selected elements of Banach space geometry will offer a novel approach and will provide ideas and concepts for researchers with a background in industry as well as those from academia.

cs.IT↗
arXiv2011

Binary Polar Code Kernels from Code Decompositions

Code decompositions (a.k.a code nestings) are used to design good binary polar code kernels. The proposed kernels are in general non-linear and show a better rate of polarization under successive cancelation decoding, than the ones suggested by Korada et al., for the same kernel dimensions. In particular, kernels of sizes 14, 15 and 16 are constructed and shown to provide polarization rates better than any binary kernel of such sizes.

cs.IT↗
arXiv2005

New Upper Bounds on A(n,d)

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds improve on the best known analytic bounds. Several new record bounds are obtained for codes with small lengths.

cs.IT↗
arXiv2004

A Lower Bound on the Density of Sphere Packings via Graph Theory

Using graph-theoretic methods we give a new proof that for all sufficiently large $n$, there exist sphere packings in $\R^n$ of density at least $cn2^{-n}$, exceeding the classical Minkowski bound by a factor linear in $n$. This matches up to a constant the best known lower bounds on the density of sphere packings due to Rogers, Davenport-Rogers, and Ball. The suggested method makes it possible to describe the points of such a packing with complexity $\exp(n\log n)$, which is significantly lower than in the other approaches.

math.CO↗
arXiv1999

Quantum Error Detection I: Statement of the Problem

I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of undetected error under natural physical assumptions concerning transmission with error detection over the depolarizing channel. We discuss possible transmission protocols with stabilizer and unrestricted quantum codes. The set of results proved in Part I shows that in all the cases considered the average probability of undetected error for a given code is essentially given by one and the same function of its weight enumerators. This enables us to give a consistent definition of the undetected error event.

quant-ph↗
arXiv1998

On binary constructions of quantum codes

Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.

quant-ph↗
arXiv1997

Upper Bounds on the Size of Quantum Codes

Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.

quant-ph↗