Coding for noisy channels

Abstract

In the treatment of source coding the communication channel was assumed to be noiseless. If the channel is noisy, then the coding strategy must be different. Now some form of error control is required to undo the damage caused by the channel. The overall communication problem is usually broken into two pieces: A source coder is designed for a noiseless channel with a given resolution or rate and an error correction code is designed for the actual noisy channel in order to make it appear almost noiseless. The combination of the two codes then provides the desired overall code or joint source and channel code. This division is natural in the sense that optimizing a code for a particular source may suggest quite different structure than optimizing it for a channel. The structures must be compatible at some point, however, so that they can be used together.