Cooperative Binning for Semi-deterministic Channels with Non-causal State Information

The capacity of two semi-deterministic channels with the presence of non-causal channel state information (CSI) is characterized. The first channel is a state-dependent semi deterministic relay channel. The CSI is available only at the transmitter and receiver, but not at the relay. The second channel is a state-dependent multiple access channel (MAC) with partial cribbing and CSI only at one transmitter and the receiver. In the semi-deterministic relay channel without states, the capacity can be achieved using partial-decode-forward scheme. The transmission is split to blocks; in each block, the relay decodes a part of the message and cooperation is established using those bits. When the channel depends on a state, the decoding procedure at the relay reduces the transmission rate. Recently, a cooperative bin forward scheme has been proposed which establishes cooperation without requiring the relay to decode a part of the message. In this scheme, the relay maps its received sequence, which is a deterministic function of the transmitted sequence, into bins. The transmitter coordinates its transmission with the bin index that is chosen by the relay. This scheme achieves the capacity when the CSI is available causally. In this work, we present a variation of the cooperative-bin forward scheme that achieves capacity for non-causal CSI. The bin index corresponding to the deterministic output of the relay is selected by the transmitter in such a way that the relay's transmission is coordinated with the states. This coding scheme also applies for the MAC with partial cribbing and non-causal CSI at one transmitter and receiver. The capacity is achieved by the new variation of cooperative bin-forward. On top of that, we show an example in which the capacity with non-causal CSI is strictly greater than with causal CSI.