Source coding for general penalties

Baer, Michael B.

doi:10.1109/isit.2003.1228266

Cited by 5 publications

(11 citation statements)

References 4 publications

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“…The infinite sequence of optimal codes obtained when k→∞ (q→0) stabilizes in the limit, as stated in the following proposition, which follows from Proposition 1 (the fact is also mentioned in [14,Ch. 5…”

Section: The Family Of Parameters Q = 2 −Kmentioning

confidence: 61%

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Optimal prefix codes for pairs of geometrically-distributed random variables

Bassino

Clément

Seroussi

et al. 2006

2006 IEEE International Symposium on Information Theory

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Abstract-Lossless compression is studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter q, 0 < q < 1. Optimal prefix codes are described for q = 1/2. These codes retain some of the low-complexity and low-latency advantage of symbol by symbol coding of geometric distributions, which is widely used in practice, while improving on the inherent redundancy of the approach. From a combinatorial standpoint, the codes described differ from previously characterized cases related to the geometric distribution in that their corresponding trees are of unbounded width, and in that an infinite set of distinct optimal codes is required to cover any interval (0, ε), ε > 0, of values of q.

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Section: The Family Of Parameters Q = 2 −Kmentioning

confidence: 61%

“…A matching decoding procedure is easily derived. Encoding and decoding procedures for all the codes in this section are presented in [12] [14]. Kraft functions.…”

Section: ])mentioning

confidence: 99%

Optimal prefix codes for pairs of geometrically-distributed random variables

Bassino

Clément

Seroussi

et al. 2006

2006 IEEE International Symposium on Information Theory

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“…Remark 2: (a) Note that if we formally substitute α = 0 in (3), it reduces to (1). Since inf M f > 0 (and thus M is bounded) the right hand side of (4) is finite.…”

Section: Resultsmentioning

confidence: 99%

“…From an operational point of view, the use of Rényi entropy as quantizer rate is supported by Campbell's work [4] and showed that Rényi's entropy plays an analogous role to Shannon entropy in this more general setting. An overview of related results can be found in [1].…”

Section: Introductionmentioning

confidence: 99%

Scalar quantization with Rényi entropy constraint

Kreitmeier

Linder

2011

2011 IEEE International Symposium on Information Theory Proceedings

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We consider optimal scalar quantization with rth power distortion and constrained Rényi entropy of order α. For sources with absolutely continuous distributions the high rate asymptotics of the quantizer distortion has long been known for α = 0 (fixed-rate quantization) and α = 1 (entropy-constrained quantization). For a large class of absolutely continuous source distributions we determine the sharp asymptotics of the optimal quantization distortion for Rényi entropy constraints of order α ∈ [−∞, 0) ∪ (0, 1). The proof of achievability is based on companding quantization and is thus constructive.

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“…This approach was first suggested in [13] as an alternative to the Lagrangian rate definition considered there which simultaneously controls codebook size and output (Shannon) entropy. Further motivation for using Rényi entropy as quantization rate can be obtained from axiomatic considerations [27,1], as well as from the operational role of the Rényi entropy in variable-length lossless coding [8,17,2].…”

Section: Introductionmentioning

confidence: 99%

Entropy Density and Mismatch in High-Rate Scalar Quantization With Rényi Entropy Constraint

Kreitmeier

Linder

2012

IEEE Trans. Inform. Theory

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Properties of scalar quantization with rth power distortion and constrained Rényi entropy of order α ∈ (0, 1) are investigated. For an asymptotically (high-rate) optimal sequence of quantizers, the contribution to the Rényi entropy due to source values in a fixed interval is identified in terms of the "entropy density" of the quantizer sequence. This extends results related to the well-known point density concept in optimal fixed-rate quantization. A dual of the entropy density result quantifies the distortion contribution of a given interval to the overall distortion. The distortion loss resulting from a mismatch of source densities in the design of an asymptotically optimal sequence of quantizers is also determined. This extends Bucklew's fixed-rate (α = 0) and Gray et al.'s variable-rate (α = 1) mismatch results to general values of the entropy order parameter α.

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Source coding for general penalties

Cited by 5 publications

References 4 publications

Optimal prefix codes for pairs of geometrically-distributed random variables

Optimal prefix codes for pairs of geometrically-distributed random variables

Scalar quantization with Rényi entropy constraint

Entropy Density and Mismatch in High-Rate Scalar Quantization With Rényi Entropy Constraint

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Source coding for general penalties

Cited by 5 publications

References 4 publications

Optimal prefix codes for pairs of geometrically-distributed random variables

Optimal prefix codes for pairs of geometrically-distributed random variables

Scalar quantization with R&#x00E9;nyi entropy constraint

Entropy Density and Mismatch in High-Rate Scalar Quantization With Rényi Entropy Constraint

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Scalar quantization with Rényi entropy constraint