Let

Summary: Describes the Noisy Channel Coding Theorem.

As the block length becomes larger, more error correction will
be needed. Do codes exist that can correct
*all* errors? Perhaps the crowning
achievement of Claude
Shannon's creation of information theory answers this
question. His result comes in two complementary forms: the
Noisy Channel Coding Theorem and its converse.

Let

If

This result astounded communication engineers when Shannon published it in 1948. Analog communication always yields a noisy version of the transmitted signal; in digital communication, error correction can be powerful enough to correct all errors as the block length increases. The key for this capability to exist is that the code's efficiency be less than the channel's capacity. For a binary symmetric channel, the capacity is given by

capacity of a channel |
---|

Comments:"Electrical Engineering Digital Processing Systems in Braille."