Multiple Access Channel with States Known Noncausally at One Encoder and Only Strictly Causally at the Other Encoder

TL;DR

This paper investigates the capacity region of a two-user multiaccess channel with asymmetric state knowledge, showing how strictly causal and non-causal state information at encoders influence achievable rates, with explicit results for discrete and Gaussian cases.

Contribution

It provides new inner and outer bounds for the capacity region in a state-dependent multiaccess channel with asymmetric state knowledge, including explicit capacity characterizations in special cases.

Findings

Strictly causal state knowledge can enlarge capacity region.

Explicit capacity characterization for common message transmission.

Strictly causal state knowledge does not increase capacity when the other encoder knows states non-causally.

Abstract

We consider a two-user state-dependent multiaccess channel in which the states of the channel are known non-causally to one of the encoders and only strictly causally to the other encoder. Both encoders transmit a common message and, in addition, the encoder that knows the states non-causally transmits an individual message. We study the capacity region of this communication model. In the discrete memoryless case, we establish inner and outer bounds on the capacity region. Although the encoder that sends both messages knows the states fully, we show that the strictly causal knowledge of these states at the other encoder can be beneficial for this encoder, and in general enlarges the capacity region. Furthermore, we find an explicit characterization of the capacity in the case in which the two encoders transmit only the common message. In the Gaussian case, we characterize the capacity region for the model with individual message as well. Our converse proof in this case shows that, for this model, strictly causal knowledge of the state at one of the encoders does not increase capacity if the other is informed non-causally, a result which sheds more light on the utility of conveying a compressed version of the state to the decoder in recent results by Lapidoth and Steinberg on a multiacess model with only strictly causal state at both encoders and independent messages.