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

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

2005-10-31

arxiv.org/abs/cs/0511001v2

Computer Science

Information Theory

This work was presented in part at the IEEE Communication Theory Workshop, June 12-15, 2005 and at the Forty-third Annual Alle

Scientific paper

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.

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