@inproceedings{79c8eb79e9ff4899b08d7ce7a8c82955,
title = "Cumulant generating function of codeword lengths in optimal lossless compression",
abstract = "This paper analyzes the distribution of the codeword lengths of the optimal lossless compression code without prefix constraints both in the non-asymptotic regime and in the asymptotic regime. The technique we use is based on upper and lower bounding the cumulant generating function of the optimum codeword lengths. In the context of prefix codes, the normalized version of this quantity was proposed by Campbell in 1965 as a generalized average length. We then use the one-shot bounds to analyze the large deviations (reliability function) and small deviations (normal approximation) of the asymptotic fundamental limit in the case of memoryless sources. In contrast to other approaches based on the method of types or the Berry-Ess{\'e}en inequality, we are able to deal with sources with infinite alphabets.",
author = "Courtade, {Thomas A.} and Sergio Verd{\'u}",
year = "2014",
doi = "10.1109/ISIT.2014.6875283",
language = "English (US)",
isbn = "9781479951864",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "2494--2498",
booktitle = "2014 IEEE International Symposium on Information Theory, ISIT 2014",
address = "United States",
note = "2014 IEEE International Symposium on Information Theory, ISIT 2014 ; Conference date: 29-06-2014 Through 04-07-2014",
}