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A quasi-Gray code of dimension $n$ and length $\ell$ over an alphabet $\Sigma$ is a sequence of distinct words $w_1,w_2,\dots,w_\ell$ from $\Sigma^n$ such that any two consecutive words differ in at most $c$ coordinates, for some fixed…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
In this paper, we focus on the design of binary constant weight codes that admit low-complexity encoding and decoding algorithms, and that have a size $M=2^k$. For every integer $\ell \geq 3$, we construct a $(n=2^\ell, M=2^{k_{\ell}},…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
Resistive memories have limited lifetime caused by limited write endurance and highly non-uniform write access patterns. Two main techniques to mitigate endurance-related memory failures are 1) wear-leveling, to evenly distribute the writes…
The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
We show how to build several data structures of central importance to string processing, taking as input the Burrows-Wheeler transform (BWT) and using small extra working space. Let $n$ be the text length and $\sigma$ be the alphabet size.…
We present the first linear time algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working space. A simpler variant of this algorithm computes the plain ($n\lg n$-bit)…
Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of…
In this paper, we further investigate the constructions on three-dimensional $(u\times v\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\times v\times…
High density Solid State Drives, such as QLC drives, offer increased storage capacity, but a magnitude lower Program and Erase (P/E) cycles, limiting their endurance and hence usability. We present the design and implementation of…
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding…
Reducing the cost of sequencing genomes provided by next-generation sequencing technologies has greatly increased the number of genomic projects. As a result, there is a growing need for better assembly and assembly validation methods. One…
In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system in the presence of log-normal fading. In this scenario, a general criterion for the design of full-diversity space code (FDSC) with…