Coding for Noisy Channels
Reliable communication over a noisy channel is the focus of this chapter. The chapter begins with a development of the classic fundamental results of Feinstein regarding reliable communication of block codes and the relation of operational channel capacity to Shannon capacity for discrete channels. A technique of Dobrushin is used to extend Feinstein’s results for channels with no input memory or anticipation by making codes robust to small changes in the conditional distributions describing channels. This leads in turn to the extension of block coding theorems to d-bar continuous channels, discrete noisy channels where the noise distribution within a block can be well approximated in a d-bar sense with only finite knowledge of past and future inputs. Traditional channel coding theorems for block codes assume knowledge of synchronization – when the blocks begin. Another technique of Doburshin is used to synchronize block codes through noisy channels. Combining synchronized block codes with the Rohlin-Kakutani theorem yields a coding theorem for sliding-block channel coding. Finally, combining the source coding theorems with channel coding theorems yields joint-source and channel coding theorems.
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