Simon Litsyn

Tel Aviv University, Electrical Engineering, Faculty Member

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Expert in coding theory, discrete mathematics, communications and storage
Phone: +972-544424175
Address: Department of Electrical Engineering - Systems, Tel Aviv University, Ramat Aviv 69978 Israel

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Randy Barnett

nada alaa

The American University In Cairo

Barbara Rogoff

Thomas Wien

Université de Montréal

Lehigh University

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Papers by Simon Litsyn

Codes and Association Schemes

DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2001

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An efficient message-passing schedule for LDPC decoding

2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel

An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the con... more An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the conventional approach both in terms of complexity and performance is presented. Conventionally, in each iteration all symbol nodes and subsequently all the check nodes send messages to their neighbors ("flooding schedule"). In contrast, in the proposed method, the updating of nodes is performed according to a serial schedule which propagates the information twice as fast. A Density Evolution (DE) algorithm for asymptotic analysis of the new schedule is derived, showing that when working near the code's capacity, the decoder converges in approximately half the number of iterations. In addition a Concentration Theorem is proved, showing that for a randomly chosen serial schedule, code graph, and decoder input, the decoder's performance approaches its expected one as predicted by the DE algorithm, when the code length increases.

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A lower bound on the probability of decoding error over a BSC channel

21st IEEE Convention of the Electrical and Electronic Engineers in Israel. Proceedings (Cat. No.00EX377)

Abstract For a code C of length n and size| C, we estimate the error probability of the maximum l... more Abstract For a code C of length n and size| C, we estimate the error probability of the maximum likelihood decoding. In this paper we address this problem for the binary symmetric channel (BSC) defined by its transition probability p. We discuss the case when we know the distance distribution of the code. We also assume that the code is regular in the sense that the distribution of the distances from a codeword to other codewords does not depend on the choice of the initial codeword

On the capacity of two-dimensional weight-constrained memories

Algebraic Coding Theory and Information Theory, 2005

DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 68, 2005 On the Cap... more DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 68, 2005 On the Capacity of Two-Dimensional Weight-Constrained Memories Simon Litsyn and Alexander Shpunt ABSTRACT. For a constant a, a£(0, 1), such that aM, aN are integers, let Ti (M, N, a) be the number of regular M x N, M= Q (N), binary matrices with row sums aN and column sums aM. Let H (a)=—olog2 a—(1—a) Iog2 (l—a), stand for the binary entropy. It is shown that Iog2 K (M, N, a)= NM = MN• H (a) Iog2 (2ira (la) M) Iog2 (27ra (la) N)+ O (NS), for arbitrary e&amp;gt; ...

Survey of binary Krawtchouk polynomials

Codes and Association Schemes, 2001

DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 56. 2001 Survey of ... more DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 56. 2001 Survey of binary Krawtchouk polynomials Ilia Krasikov and Simon Litsyn ABSTRACT. Krawtchouk polynomials play a crucial role in many combinatorial problems related to the Hamming association scheme. We survey some old and new results concerning binary Krawtchouk polynomials. Binary Krawtchouk polynomials play an important role in combinatorial problems related to the binary Hamming association schemes. In the paper we attempt to review what is known about ...

On a Sequence Arising in Algebraic Geometry

We derive recurrence relations for the sequence of Maclaurin coefficients of the function χ = χ(t... more

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Foundations of quantum error correction

Recent Trends in Coding Theory and Its Applications, 2007

ABSTRACT. This tutorial gives an introduction into the theory of quantum error correcting codes f... more ABSTRACT. This tutorial gives an introduction into the theory of quantum error correcting codes for researchers with background in mathematics and the combinatorial coding theory. We first give a short introduction into main notions of quantum computations such as qubits, measurement, and quantum gates. Next, we give a formal definition of unrestricted quantum error correcting codes and the quantum completely depolarizing channel. Further, we consider generalization of fundamental notions and results of the classical coding theory ...

Reduced complexity LDPC decoder

Abstract: To decode a manifestation of a codeword in which K information bits are encoded as N&am... more Abstract: To decode a manifestation of a codeword in which K information bits are encoded as N&amp;gt; K codeword bits, messages are exchanged between N bit nodes and NK check nodes. During computation, messages are expressed with a full message length greater than two bits. In each iteration, representations of at least some of the exchanged messages are stored. For at least one node, if representations of messages sent from that node are stored, then the representation of one or more of the messages is stored using at least two ...

Memory-Efficient LDPC Decoding

To decode a representation of a codeword that encodes K information bits as N&amp;gt; K codew... more To decode a representation of a codeword that encodes K information bits as N&amp;gt; K codeword bits, messages are exchanged between N bit nodes and N− K check nodes of a graph in which E edges connect the bit nodes and the check nodes. While messages are exchanged, fewer than E of the messages are stored, and/or fewer than N soft estimates of the codeword bits are stored. In some embodiments, the messages are exchanged only within sub-graphs and between the sub-graphs and one or more external check nodes. ...

Discrete and continuous maxima in OFDM signals

2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel

ABSTRACT We derive new relations between the continuous and discrete maxima of OFDM signals. The ... more ABSTRACT We derive new relations between the continuous and discrete maxima of OFDM signals. The discretization of the signals is done with oversampling factor I .S. ... The main disadvantage of multicarrier modulation is that it exhibits a high peak-to-average power ratio (PAPR). Namely. the peak values of some of the transmitted signals could be much larger than the typical values. Let us give a more detailed description of the signals in the multicamer communication system. Let n be the number of carriers (tones). The system receives at each time 0, T, 2T, ...

Perfect Tilings of Binary Spaces

Proceedings. IEEE International Symposium on Information Theory

We study partitions of the space F,” of all the binary n-tuples into disjoint sets, such that eac... more We study partitions of the space F,” of all the binary n-tuples into disjoint sets, such that each set is an additive coset of a given set V. Such a partition is called a perfect tiling of qn and denoted (V, A), where A is the set of coset representatives. A sufficient condition for a set V to be a tile is given in terms of the cardinality of V+ V. A perfect tiling (V, A) is said to be proper if V generates F,”. We show that the classification of perfect tilings can be reduced to the study of proper perfect tilings. We then prove that each proper perfect tiling is uniquely ...

Generalized hashing and applications to digital fingerprinting

Proceedings IEEE International Symposium on Information Theory,

Let C be a code of length n over an alphabet of q letters. An n-word y is called a descendant of ... more Let C be a code of length n over an alphabet of q letters. An n-word y is called a descendant of a set of t codewords x 1 ,. .. , x t if y i ∈ {x 1 i ,. .. , x t i } for all i = 1,. .. , n. A code is said to have the t-identifying parent property if for any n-word that is a descendant of at most t parents it is possible to identify at least one of them. We study a generalization of hashing, (t, u)-hashing, which ensures identification, and provide tight estimates of the rates.

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Improvement on the Johnson upper bound for error-correcting codes

Proceedings IEEE International Symposium on Information Theory,

Abstract Let A (n, d) denote the maximum possible number of codewords in a binary code of length ... more Abstract Let A (n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound.

On signals with very high peak-to-average power ratio

Abstract This paper address the problem of classification of BPSK-modulated multicarrier signals ... more Abstract This paper address the problem of classification of BPSK-modulated multicarrier signals with the peak-to-average power ratio (PAPR) exceeding 3/4 of the maximal possible value. By providing a simple characterization of such signals, an upper bound on their number are derived and propose a simple sufficient condition for the signals to have low PAPR. Based on this, a simple method for generation of signals with guaranteed PAPR gain of more than 2.5 dB using only two redundant tones are described.

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

International Mathematics Research Notices

Using graph-theoretic methods we give a new proof that for all sufficiently large n, there exist ... more 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 [9], Davenport-Rogers [4], and Ball [2]. 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.

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On the statistical distribution of the crest-factor of codes in OFDM transmission

Abstract The paper presents a new approach to the calculation of the crest-factor (CF) distributi... more Abstract The paper presents a new approach to the calculation of the crest-factor (CF) distribution in coded OFDM systems. The approach reveals an interesting connection between the weight distribution and the CF distribution of linear, binary codes that can be exploited to give an upper bound. The weight distribution of codes has attracted a great deal of attention in the past and many expressions and bounds are known. Thus we can expect to obtain a large number of bounds on the CF distribution. The upper bounds can serve as ...

On the Identification of Vertices and Edges Using Cycles

Lecture Notes in Computer Science, 2001

The subgraphs C 1, C 2,..., C k of a graph G are said to identify the vertices (resp. the edges) ... more The subgraphs C 1, C 2,..., C k of a graph G are said to identify the vertices (resp. the edges) of G if the sets j: v∈ C j (resp. j: e∈ C j) are nonempty for all the vertices v (edges e) and no two are the same. We consider the problem of minimizing k when the subgraphs Ci are required to be cycles or closed walks. The motivation comes from maintaining multiprocessor systems, and we study the cases when G is the binary hypercube, or the two-dimensional p-ary space with respect to the Lee metric.

Long Extended BCH Codes Are Spanned by Minimum Weight Words

Lecture Notes in Computer Science, 2006

The (binary, primitive, narrow-sense) BCH codes are among the most studied algebraic codes. It is... more The (binary, primitive, narrow-sense) BCH codes are among the most studied algebraic codes. It is not always simple to determine their combinatorial parameters such as minimum distance, covering radius, and distance distribution. However, when the length of the considered codes is large enough these parameters ”stabilize”, and exact results can be derived. For instance, it was shown by Farr (see [23]) that the actual minimum distance of long t-error correcting BCH codes, Ct, equals to its designed distance, 2t+1. Skorobogatov and Vladuts [27] (see ...

Fast algorithms for decoding orthogonal and related codes

Lecture Notes in Computer Science, 1991

If we require not a whole spectrum but only its maximal element, we may truncate well-known fast ... more

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A fast search for the maximum element of the fourier spectrum

Lecture Notes in Computer Science

An algorithm for determining the index of the maximum spectrum element of the Fourier transform i... more An algorithm for determining the index of the maximum spectrum element of the Fourier transform is proposed. Its complexity is linear in the length of the processed sequence. The algorithm leads to the correct decision if the Euclidean distance between the sequence and a basis vector does not exceed (q/2), where q is the length of the sequence.

Codes and Association Schemes

DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2001

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An efficient message-passing schedule for LDPC decoding

2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel

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A lower bound on the probability of decoding error over a BSC channel

21st IEEE Convention of the Electrical and Electronic Engineers in Israel. Proceedings (Cat. No.00EX377)