A Generalized Cut-Set Bound

In this paper, we generalize the well known cut-set bound to the problem of lossy transmission of functions of arbitrarily correlated sources over a discrete memoryless multiterminal network.Comment: 22 pages, 1 figure, a short version of it appears in ISIT 200

A Generalized Cut-Set Bound for Deterministic Multi-Flow Networks and its Applications

We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for deterministic networks, a recent result relating the capacity of AWGN KxKxK networks and the capacity of a deterministic counterpart allows us to establish an outer bound to the DoF of KxKxK wireless networks with general connectivity. This bound is tight in the case of the "adjacent-cell interference" topology, and yields graph-theoretic necessary and sufficient conditions for K DoF to be achievable in general topologies.Comment: A shorter version of this paper will appear in the Proceedings of ISIT 201

Capacity Region of the Symmetric Injective K-User Deterministic Interference Channel

We characterize the capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.Comment: A shorter version of this paper to appear in International Symposium on Information Theory (ISIT) 201

Generalized Cut-Set Bounds for Broadcast Networks

A broadcast network is a classical network with all source messages collocated at a single source node. For broadcast networks, the standard cut-set bounds, which are known to be loose in general, are closely related to union as a specific set operation to combine the basic cuts of the network. This paper provides a new set of network coding bounds for general broadcast networks. These bounds combine the basic cuts of the network via a variety of set operations (not just the union) and are established via only the submodularity of Shannon entropy. The tightness of these bounds are demonstrated via applications to combination networks.Comment: 30 pages, 4 figures, submitted to the IEEE Transaction on Information Theor

On the Fundamental Limits and Symmetric Designs for Distributed Information Systems

Many multi-terminal communication networks, content delivery networks, cache networks, and distributed storage systems can be modeled as a broadcast network. An explicit characterization of the capacity region of the general network coding problem is one of the best known open problems in network information theory. A simple set of bounds that are often used in the literature to show that certain rate tuples are infeasible are based on the graph-theoretic notion of cut. The standard cut-set bounds, however, are known to be loose in general when there are multiple messages to be communicated in the network. This dissertation focuses on broadcast networks, for which the standard cut-set bounds are closely related to union as a specific set operation to combine different simple cuts of the network. A new set of explicit network coding bounds, which combine different simple cuts of the network via a variety of set operations (not just the union), are established via their connections to extremal inequalities for submodular functions. The tightness of these bounds are demonstrated via applications to combination networks. The tightness of generalized cut-set bounds has been further explored by studying the problem of “latency capacity region” for a broadcast channel. An implicit characterization of this region has been proved by Tian, where a rate splitting based scheme was shown to be optimal. However, the explicit characterization of this region was only available when the number of receivers are less than three. In this dissertation, a precise polyhedral description of this region for a symmetric broadcast channel with complete message set and arbitrary number of users has been established. It has been shown that a set of generalized cut-set bounds, characterizes the entire symmetrical multicast region. The achievability part is proved by showing that every maximum rate vector is feasible by using a successive encoding scheme. The framework for achievability strongly relies on polyhedral combinatorics and it can be useful in network information theory problems when a polyhedral description of a region is needed. Moreover, it is known that there is a direct relationship between network coding solution and characterization of entropy region. This dissertation, also studies the symmetric structures in network coding problems and their relation with symmetrical projections of entropy region and introduces new aspects of entropy inequalities. First, inequalities relating average joint entropies rather than entropies over individual subsets are studied. Second, the existence of non-Shannon type inequalities under partial symmetry is studied using the concepts of Shannon and non-Shannon groups. Finally, due to the relationship between linear entropic vectors and representability of integer polymatroids, construction of such vector has been discussed. Specifically, It is shown that representability of the particularly constructed matroid is a sufficient condition for integer polymatroids to be linearly representable over real numbers. Furthermore, it has been shown that any real-valued submodular function (such as Shannon entropy) can be approximated (arbitrarily close) by an integer polymatroid

Capacity Results for Interference Networks and Nested Cut-Set Bound

In this thesis, a full characterization of the sum-rate capacity for degraded interference networks with any number of transmitters, any number of receivers, and any possible distribution of messages among transmitters and receivers is established. It is proved that a successive decoding scheme is sum-rate optimal for these networks. Moreover, it is shown that the transmission of only a certain subset of messages is sufficient to achieve the sum-rate capacity for such networks. Algorithms are presented to determine this subset of messages explicitly. The sum-rate expression for the degraded networks is then used to derive a unified outer bound on the sum-rate capacity of arbitrary (non-degraded) interference networks. Several variations of degraded networks are identified for which the derived outer bound is sum-rate optimal. Specifically, noisy interference regimes are derived for certain classes of multi-user/multi-message large interference networks. Also, network scenarios are identified where the incorporation of both successive decoding and treating interference as noise achieves their sum-rate capacity. Next, by taking insight from the results for degraded networks, an extension to the standard cut-set bound for general communication networks is presented which is referred to as nested cut-set bound. This bound is derived by applying a series of cuts in a nested configuration to the network first and then bounding the information rate that flows through the cuts. The key idea for bounding step is indeed to impose a degraded arrangement among the receivers corresponding to the cuts. Therefore, the bound is in fact a generalization of the outer bound for interference networks: here cooperative relaying nodes are introduced into the problem as well but the proof style for the derivation of the outer bound remains the same. The nested cut-set bound, which uniformly holds for all general communication networks of arbitrary large sizes where any subset of nodes may cooperatively communicate to any other subset of them, is indeed tighter than the cut-set bound for networks with more than one receiver. Moreover, it includes the generalized cut-set bound for deterministic networks reported by Shomorony and Avestimehr which was originally a special case of the outer bound established for the interference networks by the author (2012). Finally, capacity bounds for the two-user interference channel with cooperative receivers via conferencing links of finite capacities are investigated. The capacity results known for this communication scenario are limited to a very few special cases of the one-sided channel. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer iv bounds for them. In this thesis, by applying new techniques, novel capacity outer bounds are presented for the interference channels with conferencing users. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A fact is that the conferencing link (between receivers) may be utilized to provide one receiver with information about its corresponding signal or its non-corresponding signal (interference signal). As an interesting consequence, it is demonstrated that both strategies can be helpful to achieve the capacity of the channel. Lastly, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse