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

Opportunistic Interference Management for Multicarrier systems

We study opportunistic interference management when there is bursty interference in parallel 2-user linear deterministic interference channels. A degraded message set communication problem is formulated to exploit the burstiness of interference in M subcarriers allocated to each user. We focus on symmetric rate requirements based on the number of interfered subcarriers rather than the exact set of interfered subcarriers. Inner bounds are obtained using erasure coding, signal-scale alignment and Han-Kobayashi coding strategy. Tight outer bounds for a variety of regimes are obtained using the El Gamal-Costa injective interference channel bounds and a sliding window subset entropy inequality. The result demonstrates an application of techniques from multilevel diversity coding to interference channels. We also conjecture outer bounds indicating the sub-optimality of erasure coding across subcarriers in certain regimes.Comment: 8 pages, 5 figures, a shorter version of this work will appear in the proceedings of ISIT 201

Capacity Bounds for a Class of Interference Relay Channels

The capacity of a class of Interference Relay Channels (IRC) -the Injective Semideterministic IRC where the relay can only observe one of the sources- is investigated. We first derive a novel outer bound and two inner bounds which are based on a careful use of each of the available cooperative strategies together with the adequate interference decoding technique. The outer bound extends Telatar and Tse's work while the inner bounds contain several known results in the literature as special cases. Our main result is the characterization of the capacity region of the Gaussian class of IRCs studied within a fixed number of bits per dimension -constant gap. The proof relies on the use of the different cooperative strategies in specific SNR regimes due to the complexity of the schemes. As a matter of fact, this issue reveals the complex nature of the Gaussian IRC where the combination of a single coding scheme for the Gaussian relay and interference channel may not lead to a good coding scheme for this problem, even when the focus is only on capacity to within a constant gap over all possible fading statistics.Comment: 23 pages, 6 figures. Submitted to IEEE Transactions on Information Theory (revised version

Interference alignment for the MIMO interference channel

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio

A static analysis for quantifying information flow in a simple imperative language

We propose an approach to quantify interference in a simple imperative language that includes a looping construct. In this paper we focus on a particular case of this definition of interference: leakage of information from private variables to public ones via a Trojan Horse attack. We quantify leakage in terms of Shannon's information theory and we motivate our definition by proving a result relating this definition of leakage and the classical notion of programming language interference. The major contribution of the paper is a quantitative static analysis based on this definition for such a language. The analysis uses some non-trivial information theory results like Fano's inequality and L1 inequalities to provide reasonable bounds for conditional statements. While-loops are handled by integrating a qualitative flow-sensitive dependency analysis into the quantitative analysis

The two-user Gaussian interference channel: a deterministic view

This paper explores the two-user Gaussian interference channel through the lens of a natural deterministic channel model. The main result is that the deterministic channel uniformly approximates the Gaussian channel, the capacity regions differing by a universal constant. The problem of finding the capacity of the Gaussian channel to within a constant error is therefore reduced to that of finding the capacity of the far simpler deterministic channel. Thus, the paper provides an alternative derivation of the recent constant gap capacity characterization of Etkin, Tse, and Wang. Additionally, the deterministic model gives significant insight towards the Gaussian channel.Comment: 34 pages, 20 figure