Probability of error for the fixed-length lossy coding of general sources

In this correspondence, we are interested in the error exponent of fixed-length lossy source coding, where the sources are general sources, in the sense of Han and Verduacute, including all nonstationary and/or nonergodic sources. The aim of the correspondence is to establish a unified formula for t...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 51; no. 4; pp. 1498 - 1507
Main Author: Iriyama, K.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2005
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Asymptotic properties
Codes
Coding
Coding, codes
Continuous alphabet
Decoding
Distortion
Entropy
Error correction
error exponent
Errors
Exact sciences and technology
Exponents
fixed-length source coding
Gaussian
general source
information spectrum
Information theory
Information, signal and communications theory
large-deviation
Mathematical analysis
Probability
Rate-distortion
rate-distortion theory
reliability function
Reliability theory
Signal and communications theory
Source coding
Telecommunications and information theory
Error probability
Source coding
large-deviation
rate-distortion theory
fixed-length source coding
general source
error exponent
Rate distortion theory
Continuous alphabet
information spectrum
reliability function
Reliability
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:In this correspondence, we are interested in the error exponent of fixed-length lossy source coding, where the sources are general sources, in the sense of Han and Verduacute, including all nonstationary and/or nonergodic sources. The aim of the correspondence is to establish a unified formula for the minimum (D, r)-achievable rate which is the minimum achievable coding rate under asymptotic constraints of the form epsiv n (D) ~ e -nr (n rarr infin), where r is the prescribed error exponent, epsiv n (D) is the probability of the distortion exceeding a level D, and n is the code-length. For the stationary memoryless source with finite alphabet, Marton (1974) obtained a formula for the reliability function which is expressed in terms of the minimum (D,r)- achievable rate. Recently, Ihara and Kubo proved that the Marton's formula remains true for the stationary memoryless Gaussian source under a mean-squared fidelity criterion. In this correspondence, it is shown that a formula similar to Marton's formula holds for the general sources. The error exponent of correct decoding is also investigated and a formula for the minimum achievable rate of correct decoding in lossy coding is established
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2004.842777