Optimal Multichannel Communication under Failure (Extended Abstract)

Tanya Y. Berger-Wolf Edward M. Reingold y October 19, 1998 Abstract We consider the problem of communication over multiple channels in which channels can fail and the information sent over those channels is lost. The goal is to recover as much of the original information as possible while having as little redundancy as possible. We analyze the problem of designing an encoding that minimizes the decoding error in case of channel failure; we give tight lower bounds and an optimal algorithm. 1 Problem Statement Consider sending lg m bits of information over k independent channels. We want to partition the lg m bits into k subsets so that if all k subsets are received, the original information can be completely reconstructed. A trivial solution would be to send k blocks of (lg m)=k bits each; if any block fails to arrive, that part of the information is lost. Alternatively, we could send k complete copies, a total of k lg m bits, so that even if all but one of the channels f..