Transmission of noisy information to a noisy receiver with minimum distortion

Wolf, J.K.; Ziv, J.

doi:10.1109/tit.1970.1054469

Cited by 200 publications

(204 citation statements)

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“…4. The following theorem extends the main result of [41,42] to entropy-constrained quantization, valid for any rate R = H(Q), not necessarily high. Definē…”

Section: Nondistributed Casesupporting

confidence: 62%

“…The nondistributed case was studied in [40][41][42], and [7,[43][44][45]8] analyzed the distributed case from an information-theoretic point of view. Using Gaussian statistics and Mean-Squared Error (MSE) as a distortion measure, [13] proved that distributed coding of two noisy observations without side information can be carried out with a performance close to that of joint coding and denoising, in the limit of small distortion and large dimension.…”

Section: Introductionmentioning

confidence: 99%

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High-rate quantization and transform coding with side information at the decoder

et al. 2006

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“…4. The following theorem extends the main result of [41,42] to entropy-constrained quantization, valid for any rate R = H(Q), not necessarily high. Definē…”

Section: Nondistributed Casesupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

High-rate quantization and transform coding with side information at the decoder

et al. 2006

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“…Proof: The fact that D W ( f s , R) converges to D W (R) no faster than 1/ f s follows from (11). From (6) it follows that the 1/ f s term of D W ( f s , R) is σ 2 /(6 f s ), as there are no 1/ f s terms in DW (R/ f s ).…”

Section: Convergence Ratementioning

confidence: 94%

“…The representation (11) implies that D( f s , R) can be found by evaluating the function D W (R). However, the lack of stationarity or other structure on the process W (·) makes such an evaluation a challenging task.…”

Section: Indirect Distortion-ratementioning

confidence: 99%

Information rates of sampled Wiener processes

Kipnis

Eldar

Goldsmith

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-The minimal distortion attainable in recovering the waveform of a continuous-time Wiener process from an encoded version of its uniform samples is considered. We first introduce a combined sampling and source coding problem and prove an associated source coding theorem. We then derive an upper bound on the minimal distortion attainable under any sampling rate and a prescribed number of bits to encode the samples. We show that this bound is accurate to within a second order term in the sampling rate, and converges to the true distortionrate function of the Wiener process as the sampling rate goes to infinity. For example, this bound implies that by providing a single bit per sample it is possible to achieve the optimal distortion-rate performance of the Wiener process, given by its distortion-rate function, to within a factor of 1.5. We conclude the distortion-rate function of the Wiener process is strictly smaller than the indirect distortion-rate function from its uniform samples obtained at any finite sampling rate. This is in contrast to stationary infinite bandwidth processes.

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“…The design of optimal quantizers of noisy observations of unseen sources without side information was studied in [10], and extended to the case of distributed quantization of many observations with joint reconstruction for fixed-rate coding in [11,12]. The problem of optimal noisy WZ (NWZ) quantization design with side information at the decoder and ideal Slepian-Wolf coding has only been studied under the assumptions of high rates and particular statistical conditions [13].…”

Section: Introductionmentioning

confidence: 99%

Design of Optimal Quantizers for Distributed Coding of Noisy Sources

Rebollo-Monedero

Girod

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.

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We investigate the design of optimal quantizers for individual encoding of several noisy observations of an unseen source, which is jointly decoded with the help of side information available at the decoder only. The joint statistics of the source data, the noisy observations and the side information are known, and exploited in the design. A variety of lossless coders for the quantization indices, including ideal Slepian-Wolf coders, are allowed. We present the optimality conditions such quantizers must satisfy, together with an extension of the Lloyd algorithm for a locally optimal design. Experimental results for Wyner-Ziv quantization of noisy Gaussian sources confirm the high-rate quantization theory established in our previous work.

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Transmission of noisy information to a noisy receiver with minimum distortion

Cited by 200 publications

References 1 publication

High-rate quantization and transform coding with side information at the decoder

High-rate quantization and transform coding with side information at the decoder

Information rates of sampled Wiener processes

Design of Optimal Quantizers for Distributed Coding of Noisy Sources

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