arXiv subjects

Ohad Elishco

Publications and source records attributed to Ohad Elishco.

23 records · Page 2Linked to original sources

arXiv2018

The Capacity of Some Pólya String Models

We study random string-duplication systems, which we call Pólya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the combinatorial capacity of string-duplication systems, or various string statistics, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we study the capacity of noisy string-duplication systems, including the tandem-duplication, end-duplication, and interspersed-duplication systems. Interesting connections are drawn between some systems and the signature of random permutations, as well as to the beta distribution common in population genetics.

cs.IT↗

arXiv2017

On Independence and Capacity of Multidimensional Semiconstrained Systems

We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting capacity in terms of the independence entropy. We show the new bound improves upon the best-known bound in a case study of $(0,k,p)$-RLL.

math.DS↗

arXiv2016

Encoding Semiconstrained Systems

Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply techniques from constrained systems, we study sequences of constrained systems that are contained in, or contain, a given semiconstrained system, while approaching its capacity. In the case of contained systems we describe to such sequences resulting in constant-to-constant bit-rate block encoders and sliding-block encoders. Surprisingly, in the case of containing systems we show that a "generic" semiconstrained system is never contained in a proper fully-constrained system.

cs.IT↗

arXiv2015

Semi-constrained Systems

When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper we analyze a middle road, which we call a semiconstrained system. In such a system, which is an extension of the channel with cost constraints model, we do not eliminate the error-causing sequences entirely, but rather restrict the frequency in which they appear. We address several key issues in this study. The first is proving closed-form bounds on the capacity which allow us to bound the asymptotics of the capacity. In particular, we bound the rate at which the capacity of the semiconstrained $(0,k)$-RLL tends to $1$ as $k$ grows. The second key issue is devising efficient encoding and decoding procedures that asymptotically achieve capacity with vanishing error. Finally, we consider delicate issues involving the continuity of the capacity and a relaxation of the definition of semiconstrained systems.

cs.IT↗

arXiv2012

Capacity and coding for the Ising Channel with Feedback

The Ising channel, which was introduced in 1990, is a channel with memory that models Inter-Symbol interference. In this paper we consider the Ising channel with feedback and find the capacity of the channel together with a capacity-achieving coding scheme. To calculate the channel capacity, an equivalent dynamic programming (DP) problem is formulated and solved. Using the DP solution, we establish that the feedback capacity is the expression $C=(\frac{2H_b(a)}{3+a})\approx 0.575522$ where $a$ is a particular root of a fourth-degree polynomial and $H_b(x)$ denotes the binary entropy function. Simultaneously, $a=\arg \max_{0\leq x \leq 1} (\frac{2H_b(x)}{3+x})$. Finally, a simple, error-free, capacity-achieving coding scheme is provided together with outlining a strong connection between the DP results and the coding scheme.

cs.IT↗