Adaptive update algorithms for fixed dictionary lossless data compressors

Shamoon, T.; Heegard, C.

doi:10.1109/isit.1994.394957

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…In this correspondence, we present an algorithm for which this regret is at most A 2 ln(n) and also demonstrate that there is a lower bound of A 2 ln(n) 0 G for any sequential algorithm, and for some constant G. This algorithm was first shown by Vovk [4], and later by Azoury and Warmuth [2]. Our approach is based on sequential probability assignment, and is motivated by recent results in the universal source coding literature [5]- [11].…”

Section: Introductionmentioning

confidence: 89%

Universal linear least squares prediction: upper and lower bounds

Singer

Kozat

Feder

2002

IEEE Trans. Inform. Theory

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We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated [1]-[3] whose accumulated squared prediction error, for every bounded sequence, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order. The redundancy, or excess prediction error above that of the best predictor for that sequence, is upper-bounded by ln() , where is the data length and the sequence is assumed to be bounded by some. In this correspondence, we provide an alternative proof of this result by connecting it with universal probability assignment. We then show that this predictor is optimal in a min-max sense, by deriving a corresponding lower bound, such that no sequential predictor can ever do better than a redundancy of ln() .

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Section: Introductionmentioning

confidence: 89%

Universal linear least squares prediction: upper and lower bounds

Singer

Kozat

Feder

2002

IEEE Trans. Inform. Theory

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A rapidly adaptive lossless compression algorithm for high fidelity audio coding

Shamoon

Heegard

Proceedings of IEEE Data Compression Conference (DCC'94)

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1 Abstract Audio DataA new adaptive algorithm for lossless compression of digital audio is presented. The algorithm is derived from ideas from both dictionary coding and source-modeling. An adaptive Lempel-Ziv style k e d dictionary coder is used to build a source model that fuels an arithmetic coder. As a result, variable length strings drawn from the source alphabet are mapped onto variable length strings that are on average shorter. We show that this algorithm outperforms arithmetic coding or Lempel-Ziv coding working alone on the same source (in our experiments our source is an ADPCM quantizer). Adaptation heuristics for the Lempel-Ziv coder, relevant data structures, and a discussion of audio source modeling (entropy estimation) experiments are described. While the algorithm presented herein is designed to be used as a post-compressor in a lossy audio transform coding system, it is well suited for any instance where non-stationary source outputs must be compressed.

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Universal linear least-squares prediction

Singer

Feder

2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)

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An approach to the problem of linear prediction is discussed that is based on recent developments in the universal coding and computational learning theory literature. This development provides a novel perspective on the adaptive filtering problem, and represents a significant departure from traditional adaptive filtering methodologies. In this context, we demonstrate a sequential algorithm for linear prediction whose accumulated squared prediction error, for every possible sequence, is asymptotically as small as the best fixed linear predictor for that sequence.

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Adaptive update algorithms for fixed dictionary lossless data compressors

Cited by 3 publications

References 3 publications

Universal linear least squares prediction: upper and lower bounds

Universal linear least squares prediction: upper and lower bounds

A rapidly adaptive lossless compression algorithm for high fidelity audio coding

Universal linear least-squares prediction

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