Transmission of noisy information to a noisy receiver with minimum distortion

This paper is concerned with the transmission of information with a fidelity criterion where the source output may be distorted prior to encoding and, furthermore, where the output of the decoder may be distorted prior to its delivery to the final destination. The criterion for optimality is that the normalized average of the squared norm of the difference between the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> - second undistorted source sample and the corresponding <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> -second sample delivered to the final destination be minimum. The optimal structure of the encoder and decoder is derived for any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> .