A source coding problem for sources with additional outputs to keep secret from the receiver or wiretappers (Corresp.)

Abstract

A new source coding problem is considered for a one-way communication system with correlated source outputs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{XY\}</tex> . One of the source outputs, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X\}</tex> , must be transmitted to the receiver within a prescribed distortion tolerance as in ordinary source coding. On the other hand, the other source output, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Y\}</tex> , has to be kept as secret as possible from the receiver or wiretappers. For this case the equivocation-distortion function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma \ast(d)</tex> and the rate-distortion-equivocation function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R\ast (d,e)</tex> are defined and evaluated. The former is the maximum achievable equivocation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Y\}</tex> under the distortion tolerance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X\}</tex> , and the latter is the minimum rate necessary to attain both the equivocation tolerance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Y\}</tex> and the distortion tolerance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X\}</tex> . Some examples are included.