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Lossy Compression of Individual Sequences Revisited: Fundamental Limits of Finite-State Encoders
Version 1
: Received: 4 January 2024 / Approved: 4 January 2024 / Online: 4 January 2024 (16:05:12 CET)
A peer-reviewed article of this Preprint also exists.
Merhav, N. Lossy Compression of Individual Sequences Revisited: Fundamental Limits of Finite-State Encoders. Entropy 2024, 26, 116. Merhav, N. Lossy Compression of Individual Sequences Revisited: Fundamental Limits of Finite-State Encoders. Entropy 2024, 26, 116.
Abstract
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless finite-state encoder that compresses the
reconstruction codeword with no additional distortion. We first derive two different lower bounds to the compression ratio that depend on the number of states of the lossless encoder. Both bounds are asymptotically achievable by conceptually simple coding schemes. We then show that when the number of states of the lossless encoder is large enough in terms of the reconstruction
block-length, the performance can be improved, sometimes significantly so.
In particular, the improved performance is achievable using a random-coding ensemble
that is universal, not only in terms of the source sequence, but also in terms
of the distortion measure.
Keywords
rate-distortion; source coding; finite-state encoders; random coding; code ensemble; lossy compression; universal coding; universal distribution; LZ algorithm
Subject
Engineering, Electrical and Electronic Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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