Time-asynchronous Gaussian multiple access channel with correlated sources

We study the transmission of a pair of correlated sources over a Gaussian multiple access channel with weak time asynchronism between the encoders. In particular, we assume that the maximum possible offset d_max(n) between the transmitters grows without bound as the block length n → ∞ while the ratio d_max(n)/n of the maximum possible offset to the block length asymptotically vanishes. For such a joint source-channel coding problem, we derive the capacity region and also show that separate source and channel coding achieves optimal performance. Specifically, we first derive an outer bound on the source entropy content as our main result. Then, using Slepian-Wolf source coding combined with the channel coding introduced in [1], we show that the thus achieved inner bound matches the outer bound.