Impact of Interference in Coexisting Wireless Networks with Applications to Arbitrarily Varying Bidirectional Broadcast Channels

Abstract

The paradigm shift from an exclusive allocation of frequency bands, one for each system, to a shared use of frequencies comes along with the need of new concepts since interference will be an ubiquitous phenomenon. In this paper, we use the concept of arbitrarily varying channels to model the impact of unknown interference caused by coexisting wireless systems which operate on the same frequencies. Within this framework, capacity can be zero if pre-specified encoders and decoders are used. This necessitates the use of more sophisticated coordination schemes where the choice of encoders and decoders is additionally coordinated based on common randomness. As an application we study the arbitrarily varying bidirectional broadcast channel and derive the capacity regions for different coordination strategies. This problem is motivated by decode-and-forward bidirectional or two-way relaying, where a relay establishes a bidirectional communication between two other nodes while sharing the resources with other coexisting wireless networks.Keywords: unknown interference; arbitrarily varying channel; bidirectional relaying; bidirectional broadcast channel; input and state constraints; capacity region; coexisting networks Entropy 2012, 14 NotationIn this paper we denote discrete random variables by non-italic capital letters and their corresponding realizations and ranges by lower case italic letters and script letters, e.g., X, x, and X , respectively; the notation X n stands for the sequence X 1 , X 2 , ..., X n of length n; N and R + denote the set of positive integers and non-negative real numbers; all logarithms, exponentials, and information quantities are taken to the basis 2; I(·; ·), H(·), and D(·∥·) are the mutual information, entropy, and Kullback-Leibler (information) divergence; E[·] and P{·} denote the expectation and probability; ⟨·, ·⟩ is the inner product and | · | + = max{·, 0}; P(·) is the set of all probability distributions and (·) c is the complement of a set; W ⊗n is the n-th memoryless extension of the stochastic matrix W ; lhs := rhs means the value of the right hand side (rhs) is assigned to the left hand side (lhs); lhs =: rhs is defined accordingly.