Redundancy of unbounded memory Markov classes with continuity conditions

02/01/2018
by   Changlong Wu, et al.
0

We study the redundancy of universally compressing strings X_1,..., X_n generated by a binary Markov source p without any bound on the memory. To better understand the connection between compression and estimation in the Markov regime, we consider a class of Markov sources restricted by a continuity condition. In the absence of an upper bound on memory, the continuity condition implies that p(X_0|X^-1_-m) gets closer to the true probability p(X_0|X_-∞^-1) as m increases, rather than vary around arbitrarily. For such sources, we prove asymptotically matching upper and lower bounds on the redundancy. In the process, we identify what sources in the class matter the most from a redundancy perspective.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/01/2018

Redundancy of Markov Family with Unbounded Memory

We study the redundancy of universally compressing strings X_1,..., X_n ...
research
05/02/2018

Lower bounds on the minimax redundancy for Markov chains with large state space

For any Markov source, there exist universal codes whose normalized code...
research
05/02/2018

Minimax redundancy for Markov chains with large state space

For any Markov source, there exist universal codes whose normalized code...
research
11/08/2022

Asymptotically Optimal Stochastic Lossy Coding of Markov Sources

An effective 'on-the-fly' mechanism for stochastic lossy coding of Marko...
research
01/29/2015

Sequential Probability Assignment with Binary Alphabets and Large Classes of Experts

We analyze the problem of sequential probability assignment for binary o...
research
02/28/2018

Redundancy allocation in finite-length nested codes for nonvolatile memories

In this paper, we investigate the optimum way to allocate redundancy of ...

Please sign up or login with your details

Forgot password? Click here to reset