Coding for the deterministic network model

The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate wireless networks. For multicast, they have shown that the capacity for the deterministic model is equal to the minimal rank of the incidence matrix of a certain cut between the source and any of the sinks. Their proposed code construction, however, is not guaranteed to be efficient and may potentially involve an infinite block length. We propose an efficient linear code construction for the deterministic wireless multicast relay network model. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.

I. Introduction

Establishing the capacity and finding codes for multiuser networks have been long-standing problems in information theory. Multiuser channels generally have two sources of disturbances: noise at the receivers and interference among different users in the network. Recently, a deterministic model which approximates Gaussian wireless networks has been introduced in [1], [2]. The deterministic model takes into account the multi-user interference but not the noise and is especially applicable for high SNR. It is shown in [2] that the capacity of the deterministic model for multicast is equal to the minimal rank of the incidence matrix of a certain cut between the source and any of the sinks. The gap between the capacity of the deterministic model and that of the corresponding Gaussian network has been shown for several networks to be bounded by a constant number of bits, which does not depend on the channel fading parameters [1], [3], [4]. For multicast relay networks, the achievability proof in [2] is not constructive and involves information-theoretical arguments. As a consequence, the code construction is not guaranteed to be efficient and may potentially involve an infinite alphabet size. An important problem is to find an efficient code construction for the deterministic model of wireless multicast relay networks.