Multiterminal Estimation - Extensions and a Geometric Interpretation
Abstract
In multiterminal estimation the basic theoretical question is to prove the existence of encoding and decoding schemes that can achieve a certain rate of compression, while resulting in a particular statistical estimation efficiency. This is by comparison a much less studied field than multiterminal source coding. Essentially, only two approaches have been reported. Zhang and Berger established an upper bound on the asymptotic estimation efficiency under certain rate-compatibility constraints, and a test channel constraint referred to as the solvability condition. Han and Amari tightened the upper bound under weaker constraints on both the rates and the test channel distributions. However, their bound is in most cases prohibitively complex to compute. Here we unify the two approaches. We are able to construct an upper bound that is asymptotically equal to Han and Amari's bound, under the same rate compatibility conditions. Our bound is valid under weaker constraints on the test channels than those of Zhang and Berger. Moreover, the bound is easily computed for most source distributions. We also present a new geometric interpretation of the upper bound on asymptotic estimation efficiency.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA406764
Entities
People
- Bin Yu
- Rebecka Jornsten
Organizations
- University of California, Berkeley