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If the block-length is permitted to grow without limit, the rate-distortion function characterizes the minimal source coding rate compatible with a given distortion level, either in average or excess distortion sense. However, as relatively short block-lengths are common in some applications due to both delay and coding complexity constraints, it is of critical practical interest to assess the unavoidable overhead over the rate-distortion function required to sustain the desired fidelity at a given fixed block-length. Neither the strong version of Shannon's source coding theorem nor the reliability function, which gives the asymptotic exponential decay of the probability of exceeding a given distortion level when compressing at a fixed rate, supply an answer to that question.
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