Strong Functional Representation Lemma and Applications to Coding Theorems

Li, Cheuk Ting; Gamal, Abbas El

doi:10.1109/tit.2018.2865570

Cited by 50 publications

(24 citation statements)

References 35 publications

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“…bits to communicate an exact sample. On the other hand, Li and El Gamal (2018) showed that distributions exist for which the coding cost is at least…”

Section: Related Workmentioning

confidence: 99%

“…As in RS, the index N * PFR picks one of infinitely many candidates and we obtain an exact sample from the target distribution. However, Li and El Gamal (2018) provided much stronger guarantees for the coding cost of the N * PFR . In particular,…”

Section: Poisson Functional Representationmentioning

confidence: 99%

“…29). Nevertheless, a coding cost corresponding to the bound above can be achieved by entropy encoding N * PFR while assuming a Zipf distribution p λ (n) ∝ n −λ with (Li and El Gamal, 2018)…”

Section: Poisson Functional Representationmentioning

confidence: 99%

“…The significance of these results is as follows. Li and El Gamal (2018) showed that the PFR is nearoptimal in the sense that the entropy of N * PFR is close to the worst-case coding cost needed for communicating a perfect sample. However, the construction of the PFR relies on an infinite number of candidates and all theoretical guarantees are lost if we naively limit the number of candidates to N .…”

Section: A Unifying Viewmentioning

confidence: 99%

“…The present article aims to provide an overview of several useful algorithms for reverse channel coding and to compare them. For instance, we describe a practical algorithm based on the Poisson functional representation Li and El Gamal (2018). We then introduce new algorithms along with practical advantages and provide results on their theoretical properties.…”

Section: Introductionmentioning

confidence: 99%

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Algorithms for the Communication of Samples

Theis¹,

Yosri²

2021

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We consider the problem of reverse channel coding, that is, how to simulate a noisy channel over a digital channel efficiently. We propose two new coding schemes with practical advantages over previous approaches. First, we introduce ordered random coding (ORC) which uses a simple trick to reduce the coding cost of previous approaches based on importance sampling. Our derivation also illuminates a connection between these schemes and the so-called Poisson functional representation. Second, we describe a hybrid coding scheme which uses dithered quantization to efficiently communicate samples from distributions with bounded support.

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“…bits to communicate an exact sample. On the other hand, Li and El Gamal (2018) showed that distributions exist for which the coding cost is at least…”

Section: Related Workmentioning

confidence: 99%

Section: Poisson Functional Representationmentioning

confidence: 99%

Section: Poisson Functional Representationmentioning

confidence: 99%

Section: A Unifying Viewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Algorithms for the Communication of Samples

Theis¹,

Yosri²

2021

Preprint

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Rate-Distortion-Perception Tradeoff Based on the Conditional Perception Measure

Salehkalaibar,

Phan,

Khisti

et al. 2023

2023 Biennial Symposium on Communications (BSC)

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We study the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large blocklengths. Our perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, which was first proposed in [1], [2]. We consider the case when there is no shared randomness between the encoder and the decoder. For the case of discrete memoryless sources we derive a single-letter characterization of the RDP function, thus settling a problem that remains open for the marginal metric introduced in Blau and Michaeli [3] (with no shared randomness). Our achievability scheme is based on lossy source coding with a posterior reference map proposed in [4]. For the case of continuous valued sources under squared error distortion measure and squared quadratic Wasserstein perception measure we also derive a single-letter characterization and show that a noise-adding mechanism at the decoder suffices to achieve the optimal representation. For the case of zero perception loss, we show that our characterization interestingly coincides with the results for the marginal metric derived in [5], [6] and again demonstrate that zero perception loss can be achieved with a 3-dB penalty in the minimum distortion. Finally we specialize our results to the case of Gaussian sources. We derive the RDP function for vector Gaussian sources and propose a waterfilling type solution. We also partially characterize the RDP function for a mixture of vector Gaussians.

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In-network Learning for Distributed Training and Inference in Networks

Moldoveanu

Zaidi

2021

2021 IEEE Globecom Workshops (GC Wkshps)

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Strong Functional Representation Lemma and Applications to Coding Theorems

Cited by 50 publications

References 35 publications

Algorithms for the Communication of Samples

Algorithms for the Communication of Samples

Rate-Distortion-Perception Tradeoff Based on the Conditional Perception Measure

In-network Learning for Distributed Training and Inference in Networks

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