Posted by: atri | August 29, 2007

## Project 8: Arbitrary Varying Channel

We saw two “extreme” ways of modeling the channel noise in class today. In particular Hamming modeled noise adversarially, where the channel can choose the locations as well as nature of errors arbitrarily subject to a bound on the total number of errors. Shannon on the other hand modeled the noise as a stochastic process. In today’s lecture we saw a special case called Binary Symmetric Channel or $BSC_p$, where $0\le p\le\frac{1}{2}$ is the cross over probability. In $BSC_p$, every bit is flipped with probability $p$ (also the probability of flipping is independent for each bit that is transmitted over the channel).

The two noise models above have been arguably studied the most in coding theory. The Hamming noise model is valid when we have no idea about the channel where as Shannon’s noise model assumes complete knowledge about the channel. Needless to say, in practice the truth is somewhere in between. The goal of this project is to review the literature for channels that lie “in between” the two extremes.

A good starting point is the survey by Amos Lapidoth and Prakash Narayan titled Reliable communication under channel uncertainty (IEEE IT 44(6), 1998). Note that since this is a survey you already have a good head start. For your report you are expected to focus (and expand) on one or two sub-topics in the above survey.