Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1804.05977

Non-existence of certain kind of finite-letter mutual information characterization for a class of time-invariant Markoff channels

Mukul Agarwal
View original source ↗Read source document ↗Export metadata ↓

Abstract

We provide a rigorous definition of a certain kind of characterization for capacity regions of a family of Markoff networks which is based on optimization problems resulting out of calculating conditional mutual information from a finite number of random variables and by constraining these random variables in a certain way. This definition is partly motivated by the definition of single-letter characterizations in information theory. For a point-to-point Markoff channel, we prove that approximating the solution to these characterizations within an additive constant is a computable problem. Based on previous undecidability results concerning capacities of certain class of finite state machine channels (FSMCs), it will follow that there exists an example of family of FSMCs for which given such a characterization, this characterization cannot represent the capacity of this family of FSMCs.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mukul Agarwal. 2020-02-21. Non-existence of certain kind of finite-letter mutual information characterization for a class of time-invariant Markoff channels. https://arxiv.org/abs/1804.05977

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

cs.IT↗
arXiv2026

Sequence Reconstruction over the Deletion Channel

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $ n \geq t+\ell-1$ and $t \geq 1$.

cs.IT↗
arXiv2026

A generalization of the map $χ$

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

cs.IT↗