The Strong Converse for Source Coding with a Fidelity Criterion

A source coding problem with a fidelity criterion, where the sources are stationary discrete and memoryless, is considered at low rates. The reliability function for the source coding without a fidelity criterion has been determined by Jelinek and by Csiszár and Longo for rates which are either higher or lower than the source entropy. On the other hand, the reliability function for the source coding with a fidelity criterion at rates which are higher than the rate-distortion function has been determined by Marton. The present paper determines the reliability function for the source coding with a fidelity criterion at lower rates, thereby establishing the strong converse. It is also shown that this reliability function can be attained by using a universal encoder.