Abstract
The minimum expected length for fixed-to-variable length encoding of an n -block memoryless source with entropy H grows as n H + O(1), where the term O(1) lies between 0 and 1. However, this well-known performance is obtained under the implicit constraint that the code assigned to the whole n-block is a prefix code. Dropping the prefix constraint, which is rarely necessary at the block level, we show that the minimum expected length for a finite-alphabet memoryless source with known distribution grows as n H - 1\2 log n +O(1) unless the source is equiprobable. We also refine this result up to o(1) for those memoryless sources whose log probabilities do not reside on a lattice.
Original language | English (US) |
---|---|
Article number | 5895099 |
Pages (from-to) | 4017-4025 |
Number of pages | 9 |
Journal | IEEE Transactions on Information Theory |
Volume | 57 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2011 |
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
Keywords
- Analytic information theory
- Shannon theory
- fixed-to-variable lossless compression
- memoryless sources
- one-to-one codes
- source coding