Noisy-channel coding theorem: Difference between revisions

Revision as of 23:36, 18 May 2006

Revision as of 23:38, 18 May 2006

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

thean arbitrarily small probability of error atis thenot receiverachievable. increasesSo withoutinformation boundcannot asbe theguaranteed rateto isbe increased.transmitted Soreliably noacross usefula informationchannel canat be transmittedrates 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.