On Characterization of Entropic Vectors at the Boundary of Almost Entropic Cones

The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This paper focuses on characterization of the entropic points at the boundary of the Shannon region for three random variables. The proper faces of the Shannon region form its boundary. We give new outer bounds for the entropy region in certain faces and show by explicit construction of distributions that the existing inner bounds for the entropy region in certain faces are not tight.Comment: ITW'19 (c) 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

A Minimal Set of Shannon-type Inequalities for Functional Dependence Structures

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given inequality is a constrained Shannon-type inequality. Another important application of elemental inequalities is to formulate and compute the Shannon outer bound for multi-source multi-sink network coding capacity. Under this formulation, it is the region of feasible source rates subject to the elemental inequalities and network coding constraints that is of interest. Hence it is of fundamental interest to identify the redundancies induced amongst elemental inequalities when given a set of functional dependence constraints. In this paper, we characterize a minimal set of Shannon-type inequalities when functional dependence constraints are present.Comment: 5 pagers, accepted ISIT201

Spatial variability of groundwater recharge - I. Is it really variable?

The spatial variability of recharge is an important consideration in estimating recharge especially as all methods of estimating it are 'point' estimates and in most places recharge varies in space. This paper along with the accompanying paper attempts to find a suitable answer to the question of taking this variability into account in estimating groundwater recharge. This paper attempts to determine if recharge is actually varying in space and that this is 'true' variability and that it is not an artefact of the method used for estimating recharge. It also pulls together information on spatial variability of recharge reported by various workers in the literature, in order to determine if recharge is truly variable in space