Lossy Compression of Discrete Sources via the Viterbi Algorithm

We present a new lossy compressor for finite-alphabet sources. For coding a sequence x n , the encoder starts by assigning a certain cost to each possible reconstruction sequence. It then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compr...

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Veröffentlicht in:IEEE transactions on information theory Jg. 58; H. 4; S. 2475 - 2489
Hauptverfasser: Jalali, S., Montanari, A., Weissman, T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.04.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithm design and analysis
Algorithms
Applied sciences
Approximation
Approximation algorithms
Approximation methods
Codes
Coding, codes
Compression algorithms
Entropy
Exact sciences and technology
Information theory
Information, signal and communications theory
Rate-distortion coding
Signal and communications theory
Telecommunications and information theory
universal compression
Vectors
Viterbi algorithm
Alphabet
Lossy compression
Performance evaluation
Cost minimization
Lossless circuit
Coding circuit
Rate distortion theory
Ergodicity
Lossy medium
Iterative method
universal compression
Decoding
Algorithm
Viterbi code
Viterbi algorithm
Linear combination
Coding
Rate-distortion coding
Cost function
ISSN:0018-9448, 1557-9654
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Beschreibung
Zusammenfassung:We present a new lossy compressor for finite-alphabet sources. For coding a sequence x n , the encoder starts by assigning a certain cost to each possible reconstruction sequence. It then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of each sequence is a linear combination of its distance from the sequence x n and a linear function of its k th order empirical distribution. The structure of the cost function allows the encoder to employ the Viterbi algorithm to find the sequence with minimum cost. We identify a choice of the coefficients used in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance for any stationary ergodic source, in the limit of large , provided that increases as o(log n). Iterative techniques for approximating the coefficients, which alleviate the computational burden of finding the optimal coefficients, are proposed and studied.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2178059