Multiple Access Channels With States Causally Known at Transmitters

Abstract

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.Index Terms-Multiple access channels, state-dependent channels, strictly causal state information, long-message encoding, quantize-forward, output feedback.

A note on multiple-access channels with strictly-causal state information

“…By adapting this example to the double-state scenario, we provide an example showing that-as conjectured in [3]-the inner bound proposed by Li et al in [3] can be strictly larger than that in [2].…”

“…For the single-state scenario, an inner bound on C com s-c was derived in [1] and later extended to many-transmitters in [3]. In the absence of cost constraints this bound can be described as follows: Let P com s-c be the collection of all random variables (U, V, X 1 , X 2 , W, Y ) whose joint distribution satisfies…”

“…An improved inner bound was proposed by Li et al in [3]. There it was shown that the improved inner bound always contains the inner bound of [2], and it was conjectured that there are cases where the inclusion is strict.…”

“…For the single-state scenario, we present a new inner bound on the capacity region. This bound contains the inner bound of [1] (which was extended to the many-transmitters scenario in [3]). We also provide an example showing that the inclusion can be strict.…”

On the capacity region of the Gaussian MAC with batteryless energy harvesting transmitters

“…Single-user and multiple access state-dependent channels have been well investigated [12]- [17]. Specifically, when causal state information at the transmitters is available, Shannon strategies are capacity achieving for the single-user state-dependent channels and provide an achievable region for the state-dependent MAC [13]- [17].…”