Information Theory and Coding > Channel Capacity > What is Channel Coding and why channel coding is important?
What is Channel Coding and why channel coding is important?
The mutual information I(A;B) of a channel with input A and output B measures the amount of information a channel is able to convey about the source. If the channel is noiseless then this is equal to the information content of the source A, that is
I(A;B) = H(A).
However in the presence of noise there is an uncertainty, H(A/B), that reduces the mutual information to
I(A;B) = H(A)- H(A/B)
The presence of noise manifests itself as random errors in the transmission of the symbols. Depending on the information being transmitted and its use, random errors may be tolerable. When the errors introduced by the information channel are unacceptable then channel coding is needed to reduce the error rate and improve the reliability of the transmission.
How Channel Coding works?
The channel encoder separates or segments the incoming bit stream (the output of the source encoder) into equal length blocks of L binary digits and maps each L-bit message block into an N-bit code word where N>L and the extra N-L check bits provide the required error protection.
There are M=2^L messages and 2^L code words of length N bits. The channel decoder maps the received N-bit word to the most likely code word and inversely maps the N-bit code word to the corresponding L-bit messages.
Since N > L , then that means there are 2^N -2^L received words of length N bits that are not code words (where 2^N is the space of all words of length N bits and 2^L is the subset corresponding to the code words). The key idea is that a bit error will change the code word to a non-code word which can then be detected. It should be obvious that this is only possible if N>L.
The task of a channel decoder is to detect that there has been a bit error and, if possible, correcting the bit error. The channel decoder can resolve bit errors by two different systems for error-control:
Automatic-Repeat-Request (ARQ): If the channel decoder performs error detection then errors can be detected and a feedback channel from the channel decoder to the channel encoder can be used to control the retransmission of the code word until the code word is received without detected errors.
Forward Error Correction (FEC): If the channel decoder performs error correction then errors are not only detected but the bits in error can be identified and corrected by bit inversion.
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