1 research outputs found
Third-Order Asymptotics of Variable-Length Compression Allowing Errors
This study investigates the fundamental limits of variable-length compression
in which prefix-free constraints are not imposed (i.e., one-to-one codes are
studied) and non-vanishing error probabilities are permitted. Due in part to a
crucial relation between the variable-length and fixed-length compression
problems, our analysis requires a careful and refined analysis of the
fundamental limits of fixed-length compression in the setting where the error
probabilities are allowed to approach either zero or one polynomially in the
blocklength. To obtain the refinements, we employ tools from moderate
deviations and strong large deviations. Finally, we provide the third-order
asymptotics for the problem of variable-length compression with non-vanishing
error probabilities. We show that unlike several other information-theoretic
problems in which the third-order asymptotics are known, for the problem of
interest here, the third-order term depends on the permissible error
probability.Comment: 20 pages. Some references were added and some parts of proofs were
revised (v2); a few typos were fixed (v3). To be presented in part at the
International Symposium on Information Theory and Its Applications (ISITA) in
Kapolei, Hawaii, USA in October 202