Network Decoding

Abstract

We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proper subset</i> of the network edges. We model this problem via an adversarial noise, presenting a formal framework and a series of techniques to obtain upper and lower bounds on the network’s (1-shot) capacity, improving on the best currently known results. In particular, we show that traditional cut-set bounds are not tight in general in the presence of a restricted adversary, and that the non-tightness of these is caused precisely by the restrictions imposed on the noise (and not, as one may expect, by the alphabet size). We also show that, in sharp contrast with the typical situation within network coding, capacity cannot be achieved in general by combining linear network coding with end-to-end channel coding, not even when the underlying network has a single source and a single terminal. We finally illustrate how network <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decoding</i> techniques are necessary to achieve capacity in the scenarios we examine, exhibiting capacity-achieving schemes and lower bounds for various classes of networks.