For a error free channel conditional probability should be zero, because having received Y there is complete certainty about the message X.

There exists a limiting value for EB/N0 below which they can be no error free communication at any information rate. This EB/N0 is called as Shannon limit.

Shannon uses a correction factor called equivocation to account for uncertainty in the received signal. It is defined as the conditional entropy of the message X given Y.

The capacity relationship from Shannon-hartley capacity theorem is given by C = W log2 ( 1+S/N ).

Entropy is defined as the average amount of information per source output.

Turbo codes are a class of high performance forward error correction codes.

Theoretical minimum nyquist bandwidth needed for the baseband transmission of Rs symbols per second without ISI is Rs/2.

According to Shannon the average effective information is obtained by subtracting the equivocation from the entropy of the source.

There are many instances of turbo codes, using different component encoders, input/output ratios, inter leavers, punching patterns.

Two elementary decoders are connected in serial connection for decoding the turbo codes.