Decoding methods

In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel.

Notation

is considered a binary code with the length ; shall be elements of ; and is the distance between those elements.

Ideal observer decoding

One may be given the message , then ideal observer decoding generates the codeword . The process results in this solution:

For example, a person can choose the codeword that is most likely to be received as the message after transmission.

Decoding conventions

Each codeword does not have an expected possibility: there may be more than one codeword with an equal likelihood of mutating into the received message. In such a case, the sender and receiver(s) must agree ahead of time on a decoding convention. Popular conventions include: