Multiple Access Channels with States Causally Known at Transmitters

TL;DR

This paper generalizes strategies for two-user multiple access channels with causally known states, proposing a new encoding scheme that improves capacity regions and extends to multiple users and feedback scenarios.

Contribution

It introduces a novel encoding scheme combining past state and codeword compression, enhancing capacity results for multi-user channels with causal state information.

Findings

Capacity region enlargement with the new scheme

Extension to multi-user MACs

Impact of feedback on capacity enhancement

Abstract

It has been recently shown by Lapidoth and Steinberg that strictly causal state information can be beneficial in multiple access channels (MACs). Specifically, it was proved that the capacity region of a two-user MAC with independent states, each known strictly causally to one encoder, can be enlarged by letting the encoders send compressed past state information to the decoder. In this work, a generalization of the said strategy is proposed whereby the encoders compress also the past transmitted codewords along with the past state sequences. The proposed scheme uses a combination of long-message encoding, compression of the past state sequences and codewords without binning, and joint decoding over all transmission blocks. The proposed strategy has been recently shown by Lapidoth and Steinberg to strictly improve upon the original one. Capacity results are then derived for a class of channels that include two-user modulo-additive state-dependent MACs. Moreover, the proposed scheme is extended to state-dependent MACs with an arbitrary number of users. Finally, output feedback is introduced and an example is provided to illustrate the interplay between feedback and availability of strictly causal state information in enlarging the capacity region.