We consider a state-dependent multiaccess channel (MAC) with state non-causally known to some encoders. For simplicity of exposition, we focus on a two-encoder model in which one of the encoders has non-causal access to the channel state. The results can in principle be extended to any number of encoders with a subset of them being informed. We derive an inner bound for the capacity region in the general discrete memoryless case and specialize to a binary noiseless case. In binary noiseless case, we compare the inner bounds with trivial outer bounds obtained by providing the noiseless channel state to the decoder. In the case of maximum entropy channel state, we obtain the capacity region for binary noiseless MAC with one informed encoder by deriving a non-trivial outer bound for this case. For a Gaussian state-dependent MAC with one encoder being informed of the channel state, we present an inner bound by applying a slightly generalized dirty paper coding (GDPC) at the informed encoder that allows for partial state cancellation, and a trivial outer bound by providing channel state to the decoder also. In particular, if the channel input is negatively correlated with the channel state in the random coding distribution, then GDPC can be interpreted as partial state cancellation followed by standard dirty paper coding. The uninformed encoders benefit from the state cancellation in terms of achievable rates, however, appears that GDPC cannot completely eliminate the effect of the channel state on the achievable rate region, in contrast to the case of all encoders being informed. In the case of infinite state variance, we analyze how the uninformed encoder benefits from the informed encoder's actions using the inner bound and also provide a non-trivial outer bound for this case which is better than the trivial outer bound. Multiple access channel (MAC), channel state, dirty paper coding (DPC).
Kotagiri et al. REF study the state-dependent two-user MAC with state non-causally known to a transmitter, and for the Gaussian case they characterize the capacity asymptotically at infinite interference (K = 2, Q 1 = ∞, Q 2 = 0) as the informed transmitter's power grows to infinity.
Multiaccess Channels with State Known to Some Encoders and Independent Messages
arXiv: Information Theory
Mathematics Computer Science