Fixed-rate encoding of nonstationary information sources
IEEE Transactions on Information Theory
Elements of information theory
Elements of information theory
Universal Lossy Coding for Individual Sequences Based on Complexity Functions
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Simple universal lossy data compression schemes derived from the Lempel-Ziv algorithm
IEEE Transactions on Information Theory
Fixed-slope universal lossy data compression
IEEE Transactions on Information Theory
Variable-rate trellis source encoding
IEEE Transactions on Information Theory
Grammar-based codes: a new class of universal lossless source codes
IEEE Transactions on Information Theory
Universal coding of nonstationary sources
IEEE Transactions on Information Theory
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This paper investigates the fixed-slope lossy coding of individual sequences and nonstationary sources. We clarify that, for a given individual sequence, the optimal cost attainable by the blockwise lossy encoders is equal to the optimal average cost with respect to the empirical distribution of the given sequence. Moreover, we show that, for a given nonstationary source, the optimal cost attainable by the blockwise encoders is equal to the supremum of the optimal average cost over all the stationary sources in the stationary hull of the given source. In addition, we show that the universal lossy coding algorithm based on Lempel-Ziv 78 code attains the optimal cost for any individual sequence and any nonstationary source.