Two results on the coding of stationary nonergodic sources are presented. The first is a source coding theorem stating that there exist variable-rate codes with performance arbitrarily close to the rate-distortion function of the stationary nonergodic source. The second is a converse information transmission theorem. It is shown that the distortion which results when the source is transmitted across a channel with capacity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> is no less than the least distortion achievable by fixed-rate codes with rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> .
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Leon‐Garcia et al. (1979) studied this question.
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