In this paper, we give a new variable-rate and variable-distortion coding scheme and show a coding theorem for time-discrete stationary sources with abstract alphabets and a single-letter fidelitycriterion without as...
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In this paper, we give a new variable-rate and variable-distortion coding scheme and show a coding theorem for time-discrete stationary sources with abstract alphabets and a single-letter fidelitycriterion without assuming reference letters. The approach used to prove the coding theorem is then specialized to maximum-distortion coding and to fixed-rate coding and the corresponding coding theorems are proved for stationary sources. We also consider the possibility of extending the results to time-continuous sources. We still need a reference letter for fixed-rate coding.
The problem of redundancy of sourcecoding with respect to a fidelitycriterion is considered, For any fixed rate R > 0 and any memoryless source with finite source and reproduction alphabets and a common distribut...
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The problem of redundancy of sourcecoding with respect to a fidelitycriterion is considered, For any fixed rate R > 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p, the nth-order distortion redundancy D-n(R) of fixed-rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate R and the distortion rate function d(p, R) of the source p. It is demonstrated that for sufficiently large n, D-n(R) is equal to -(partial derivative/partial derivative R)d(p, R) 1n n/2n + o(1n n/n), where (partial derivative/partial derivative)d(p, R) is the partial derivative of d(p, R) evaluated at R and assumed to exist. For any fixed distortion level d > 0 and any memoryless source p, the nth-order rate redundancy R(n)(d) of coding at fixed distortion level d (or by using d-semifaithful codes) is defined as the minimum of the difference between the expected rate per symbol of any d-semifaithful code of length n and the rate-distortion function R(p, d) of p evaluated at d, It is proved that for sufficiently large n, R(n)(d) is upper-bounded by In nln + o(ln n/n) and lower-bounded by In n/2n + o(ln n/n). As a by-product, the lower bound of R(n)(d) derived in this paper gives a positive answer to a recent conjecture proposed by Yu and Speed.
Lossy coding of speech, high-quality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of sourcecoding w...
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Lossy coding of speech, high-quality audio, still images, and video is commonplace today. However, in 1948, few lossy compression systems were in service. Shannon introduced and developed the theory of source coding with a fidelity criterion, also called rate-distortion theory. For the first 25 gears of its existence, rate-distortion theory had relatively little impact on the methods and systems actually used to compress real sources. Today, however, rate-distortion theoretic concepts are an important component of many lossy compression techniques and standards, me chronicle the development of rate-distortion theory and provide an overview of its influence on the practice of lossy sourcecoding.
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