Noisy-channel coding theorem: Difference between revisions

Revision as of 20:49, 17 April 2006

Revision as of 23:11, 25 April 2006

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The converse is also important. If

:<math> R \ge> C </math>

the probability of error at the receiver increases without bound as the transmission rate is increased. NoSo no useful information can be transmitted beyond the channel capacity. The theorem does not address the rare situation in which rate and capacity are equal.

Simple schemes such as "send the message 3 times and use at best 2 out of 3 voting scheme if the copies differ" are inefficient error-correction methods, unable to asymptotically guarantee that a block of data can be communicated free of error. Advanced techniques such as [[Reed-Solomon code]]s and, more recently, [[Turbo code]]s come much closer to reaching the theoretical Shannon limit, but at a cost of high computational complexity. With Turbo codes and the computing power in today's [[digital signal processors]], it is now possible to reach within 1/10 of one [[decibel]] of the Shannon limit.