On the average redundancy rate of the Lempel-Ziv code
IEEE Transactions on Information Theory
Redundancy of the Lempel-Ziv incremental parsing rule
IEEE Transactions on Information Theory
On Finite Memory Universal Data Compression and Classification of Individual Sequences
IEEE Transactions on Information Theory
Quasi-distinct parsing and optimal compression methods
Theoretical Computer Science
| Hi-index | 754.84 |
Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite alphabet are being compressed into binary sequences by some one-to-one mapping. No a priori information about X is available at the encoder, which must therefore adopt a universal data-compression algorithm. It is known that there exist a number of asymptotically optimal universal data compression algorithms (e.g., the Lempel-Ziv (LZ) algorithm, Context tree algorithm and an adaptive Hufmann algorithm) such that when successively applied to N -blocks then, the best error-free compression for the particular individual sequence X is achieved as N tends to infinity. The best possible compression that may be achieved by any universal data compression algorithm for finite N -blocks is discussed. Essential optimality for the compression of finite-length sequences is defined. It is shown that the LZ77 universal compression of N -blocks is essentially optimal for finite N -blocks. Previously, it has been demonstrated that a universal context tree compression of N blocks is essentially optimal as well.