Capacity with Causal and Non-Causal Side Information - A Unified View

TL;DR

This paper unifies the capacity analysis for channels with causal and non-causal side information, showing their capacity equivalence under certain conditions and establishing bounds on capacity gains from side information.

Contribution

It introduces a common capacity expression for both causal and non-causal side information, and derives bounds on capacity improvements, with applications to various multi-user channels.

Findings

Sum capacities are identical when all transmitter side info is known to receivers.

A genie-aided bound limits capacity gains to the number of bits provided.

One bit of side information can lead to unbounded capacity improvement.

Abstract

We identify the common underlying form of the capacity expression that is applicable to both cases where causal or non-causal side information is made available to the transmitter. Using this common form we find that for the single user channel, the multiple access channel, the degraded broadcast channel, and the degraded relay channel, the sum capacity with causal and non-causal side information are identical when all the transmitter side information is also made available to all the receivers. A genie-aided outerbound is developed that states that when a genie provides $n$ bits of side information to a receiver the resulting capacity improvement can not be more than $n$ bits. Combining these two results we are able to bound the relative capacity advantage of non-causal side information over causal side information for both single user as well as various multiple user communication scenarios. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement. As a side, we obtain the sum capacity for a multiple access channel when the side information available to the transmitter is causal and possibly correlated to the side information available to the receiver.