Abstract
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 language | English (US) |
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Article number | 7885514 |
Pages (from-to) | 3757-3772 |
Number of pages | 16 |
Journal | IEEE Transactions on Information Theory |
Volume | 63 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2017 |
Keywords
- Data compression
- finite blocklength
- universal source coding
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences