B.S.T.J. Briefs: On Source Networks with Minimal Breakdown Degradation

A source is encoded into two data streams for transmission to a receiver over two noiseless (or error-corrected) channels. This receiver is able to reproduce the source stream without error until there is a breakdown of one of the channels. If such a breakdown can be sensed both at the transmitter and the receiver, then they can prearrange that, in case of breakdown, they will switch to a different encoder and decoder designed to achieve the minimum distortion possible for the capacity of the remaining channel. However, it is assumed that the transmitter will be, at least for some time, unaware of the breakdown. If one channel is highly reliable and only breakdowns of the other need be considered, then one can use an encoding over the reliable channel as if it were the only one, achieving the rate distortion bound for the capacity of the reliable channel. The theory of side information shows that, if the total capacity is sufficient for reconstruction of the source output, which we assume, then there is an encoding for the unreliable channel that provides the "complementary" data such that, when both channels are up, reconstruction is still possible, at least in the Shannon sense. However, we assume that both channels are susceptible to breakdowns, and this produces a new type of problem, which is of interest also in connection with packet transmission schemes.