Asymptotics and Non-Asymptotics for Universal Fixed-to-Variable Source Coding

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24 Scopus citations


Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher order asymptotic regimes. Optimal three-term fixed-error asymptotic expressions are derived for general fixed-to-variable codes and for prefix codes. It is shown that the non-prefix Type Size code, in which codeword lengths are chosen in ascending order of type class size, achieves the optimal third-order term, and outperforms classical two-stage codes. Converse results are proved making use of a result on the distribution of the empirical entropy and Laplace's approximation. Finally, the fixed-to-variable coding problem without a prefix constraint is shown to be essentially the same as the universal guessing problem.

Original languageEnglish (US)
Article number7885514
Pages (from-to)3757-3772
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2017


  • Data compression
  • finite blocklength
  • universal source coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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