The Noisy-Channel Coding Theorem
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چکیده
This is an exposition of two important theorems of information theory often singularly referred to as The Noisy-Channel Coding Theorem. Given a few assumptions about a channel and a source, the coding theorem demonstrates that information can be communicated over a noisy channel at a non-zero rate approximating the channel’s capacity with an arbitrarily small probability of error. It originally appeared in C.E. Shannon’s seminal paper, A Mathematical Theory of Communication, and was subsequently rigorously reformulated and proved by A.I. Khinchin. We first introduce the concept of entropy as a measure of information, and discuss its essential properties. We then state McMillan’s Theorem and attempt to provide a detailed sketch of the proof of what Khinchin calls Feinstein’s Fundamental Lemma, both crucial results used in the proof of the coding theorem. Finally, keeping in view some stringent assumptions and Khinchin’s delicate arguments, we attempt to frame the proof of The Noisy-Channel Coding Theorem.
منابع مشابه
Lecture 3 : Shannon ’ s theorem and some upper and lower bounds
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تاریخ انتشار 2015