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

Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality

Symmetric Projections of the Entropy Region

Entropy inequalities play a central role in proving converse coding theorems for network information theoretic problems. This thesis studies two new aspects of entropy inequalities. First, inequalities relating average joint entropies rather than entropies over individual subsets are studied. It is shown that the closures of the average entropy regions where the averages are over all subsets of the same size and all sliding windows of the same size respectively are identical, implying that averaging over sliding windows always suffices as far as unconstrained entropy inequalities are concerned. Second, the existence of non-Shannon type inequalities under partial symmetry is studied using the concepts of Shannon and non-Shannon groups. A complete classification of all permutation groups over four elements is established. With five random variables, it is shown that there are no non-Shannon type inequalities under cyclic symmetry

Asymmetric Gaussian Multiple Descriptions and Asymmetric Multilevel Diversity Coding

We consider multiple description source coding problem with Gaussian source and mean squared error, for $K=3$ descriptions. We obtain an outer bound for the rate region of the problem. We also derive an inner bound for the problem based on successively refineability of the Gaussian source and multi-level diversity coding. Our gap analysis shows that the difference between two bounds is less than $1.3$ bits, in the worst case