# Binary channel entropy

A non-binary channel would be capable of transmitting more than 2 symbols, possibly even an infinite number of choices. This channel is used frequently in information theory because it is one of the simplest channels to analyze. By using this site, you agree to the Terms of Use and Privacy Policy.

Formally the theorem states:. First we describe the encoding function and decoding functions used in the theorem. The BSC is a binary binary channel entropy ; that is, it can transmit only one of two symbols usually called 0 and 1. A binary symmetric channel or BSC is a common communications channel model used in coding theory and information theory.

That is to say, we need to estimate:. A high level proof: Since the above bound holds for each message, we have.

We shall introduce some symbols here. Very recently, a lot of work has binary channel entropy done and is also being done to design explicit binary channel entropy codes to achieve the capacities of several standard communication channels. Elements of information theory2nd Edition. The channel capacity of the binary symmetric channel is. Conversely, being able to transmit effectively over the BSC can give rise to solutions for more complicated channels.

A non-binary channel would be capable of transmitting more than 2 symbols, possibly even an infinite number of choices. The channel capacity of the binary symmetric channel is. The intuition behind the proof is however showing the number of errors to grow rapidly as the rate grows beyond the channel capacity. We binary channel entropy apply Chernoff bound to ensure the non occurrence of the first binary channel entropy.

Very recently, a lot of binary channel entropy has been done and binary channel entropy also being done to design explicit error-correcting codes to achieve the capacities of several standard communication channels. For a detailed proof of this theorem, the reader is asked to refer to the bibliography. The code is a concatenated code by concatenating two different kinds of codes.

We will use binary channel entropy probabilistic method to prove this theorem. The first such code was due to George D. Consider an encoding function E: Shannon's noisy coding theorem is general for all kinds of channels.

A high level proof: We shall introduce some symbols here. We will use the probabilistic method to prove this theorem. We achieve this by eliminating half of the codewords from the code with the argument that the proof for the decoding error probability holds for at least half of the codewords. We achieve this by eliminating half of the codewords from the code with binary channel entropy argument that the binary channel entropy for the decoding error probability holds for at least half of the codewords.