Using an Unreliable Channel

Abstract

In this chapter, we assume that we are given an unreliable channel Γ, such as a BSC with P < 1, and that our task is to transmit information through Γ as accurately as possible. Shannon’s Fundamental Theorem, which is perhaps the most important result in Information Theory, states that the capacity C of Γ is the least upper bound for the rates at which one can transmit information accurately through Γ. After first explaining some of the concepts involved, we will look at a simple example of how this accurate transmission might be achieved. A full proof of Shannon’s Theorem is technically quite difficult, so for simplicity we will restrict the proof to the case where Γ is the BSC; we will give an outline proof for this channel in §5.4, postponing a more detailed proof to Appendix C.