Error exponent for source coding with a fidelity criterion

Marton, Katalin

doi:10.1109/tit.1974.1055204

Cited by 153 publications

(183 citation statements)

References 3 publications

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“…It immediately follows from Lemma 2 that (12) Taking expectation on both sides of (11) with respect to the random choice of the codebooks we have (13) where and is the set of all possible codes for type . For , each code is generated according to the distribution (14) We recall that each subcode is generated according to distribution , where and .…”

Section: Code Constructionmentioning

confidence: 99%

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Random-Coding Lower Bounds for the Error Exponent of Joint Quantization and Watermarking Systems

Zhong

Alajaji

Linder

2009

IEEE Trans. Inform. Theory

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Abstract-We establish random-coding lower bounds to the error exponent of discrete and Gaussian joint quantization and private watermarking systems. In the discrete system, both the covertext and the attack channel are memoryless and have finite alphabets. In the Gaussian system, the covertext is memoryless Gaussian and the attack channel has additive memoryless Gaussian noise. In both cases, our bounds on the error exponent are positive in the interior of the achievable quantization and watermarking rate region.Index Terms-Capacity region, error exponent, Gaussian-type class, information hiding, joint quantization and watermarking, private watermarking, random-coding lower bound.

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Section: Code Constructionmentioning

confidence: 99%

“…The distortion for a fixed code with rate parameters and is given by (32) where in (32) we used the bound of (31), the definition of the set in (30), and the bound (12). Now taking the expectation of with respect to the random choice of , we have…”

Section: Define (30)mentioning

confidence: 99%

Random-Coding Lower Bounds for the Error Exponent of Joint Quantization and Watermarking Systems

Zhong

Alajaji

Linder

2009

IEEE Trans. Inform. Theory

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“…Accordingly, the rate-function R(D; P ; M ) reduces to Shannon's rate-distortion function R(D; P ), and the theorem yields Marton's error-exponents result. [7] Let D ≥ 0 be a given distortion level, and R(D; P ) < R < log |A|. Among all sequences of codebooks {C n } with asymptotic rate no greater than R bits/symbol, lim sup n→∞ 1 n log |C n | ≤ R, the fastest achievable asymptotic rate of decay of the probability of error is…”

Section: Example 2: Lossy Data Compressionmentioning

confidence: 99%

A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration

Kontoyiannis

Sezer

2003

Stochastic Inequalities and Applications

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Let A be finite set equipped with a probability distribution P , and let M be a "mass" function on A. A characterization is given for the most efficient way in which A n can be covered using spheres of a fixed radius. A covering is a subset C n of A n with the property that most of the elements of A n are within some fixed distance from at least one element of C n , and "most of the elements" means a set whose probability is exponentially close to one (with respect to the product distribution P n ). An efficient covering is one with small mass M n (C n ). With different choices for the geometry on A, this characterization gives various corollaries as special cases, including Marton's error-exponents theorem in lossy data compression, Hoeffding's optimal hypothesis testing exponents, and a new sharp converse to some measure concentration inequalities on discrete spaces.

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“…where HA is the Rknyi entropy [2] given by log n (14) Therefore, without loss in asymptotic performance, the optimal length function can be assumed to depend on x only through Q,. Let T, be the type of x, namely,…”

Section: S € S X € Xmentioning

confidence: 99%

Universal coding with minimum probability of codeword length overflow

Merhav

1991

IEEE Trans. Inform. Theory

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--Lossless block-to-variable length source coding is studied for finite-state, finite-alphabet sources. We aim to minimize the probability that the normalized length of the codeword will exceed a given threshold B, subject to the Kraft inequality. It is shown that the Lempel-Ziv (LZ) algorithm asymptotically attains the optimal performance in the sense just defined, independently of the source and the value of B. For the subclass of unifilar Markov sources, faster convergence to the asymptotic optimum performance can be accomplished by using the minimum description length (MDL) universal code for this subclass. It is demonstrated that these universal codes are also nearly optimal in the sense of minimizing buffer overflow probability, and asymptotically optimal in a competitive sense.Index T e m -Universal noiseless coding, Lempel-Ziv algorithm, length overflow, buffer overflow, finite-state sources, large deviations, competitive optimality.

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Error exponent for source coding with a fidelity criterion

Cited by 153 publications

References 3 publications

Random-Coding Lower Bounds for the Error Exponent of Joint Quantization and Watermarking Systems

Random-Coding Lower Bounds for the Error Exponent of Joint Quantization and Watermarking Systems

A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration

Universal coding with minimum probability of codeword length overflow

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