43 research outputs found
Cumulant Generating Function of Codeword Lengths in Variable-Length Lossy Compression Allowing Positive Excess Distortion Probability
This paper considers the problem of variable-length lossy source coding. The
performance criteria are the excess distortion probability and the cumulant
generating function of codeword lengths. We derive a non-asymptotic fundamental
limit of the cumulant generating function of codeword lengths allowing positive
excess distortion probability. It is shown that the achievability and converse
bounds are characterized by the R\'enyi entropy-based quantity. In the proof of
the achievability result, the explicit code construction is provided. Further,
we investigate an asymptotic single-letter characterization of the fundamental
limit for a stationary memoryless source.Comment: arXiv admin note: text overlap with arXiv:1701.0180
Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance
This paper considers the problem of variable-length intrinsic randomness. We
propose the average variational distance as the performance criterion from the
viewpoint of a dual relationship with the problem formulation of
variable-length resolvability. Previous study has derived the general formula
of the -variable-length resolvability. We derive the general formula
of the -variable-length intrinsic randomness. Namely, we characterize
the supremum of the mean length under the constraint that the value of the
average variational distance is smaller than or equal to a constant .
Our result clarifies a dual relationship between the general formula of
-variable-length resolvability and that of -variable-length
intrinsic randomness. We also derive a lower bound of the quantity
characterizing our general formula