The Impacts of Additive Noise and 1-bit Quantization on the Correlation Coefficient in the Low-SNR Regime

Williamson, Adam R.

doi:10.1109/allerton.2019.8919805

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…A similar setting with a maximal correlation criterion between the reconstructed random variables has been considered in [11], [12]. Furthermore, it is sometimes the case that the optimal biclustering problem is easier to solve then the standard single-sided clustering problem.…”

Section: Introductionmentioning

confidence: 99%

The Double-Sided Information-Bottleneck Function

Dikshtein

Ordentlich

Shitz

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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We consider a two-terminal variant (double-sided) of the information bottleneck problem, which is related to biclustering. In our setup, X and Y are dependent random variables and the problem is to find two independent channels P U|X and P V|Y (setting the Markovian structure U → X → Y → V) that maximize I(U; V) subject to constraints on the relevant mutual information expressions: I(U; X) and I(V; Y). For jointly Gaussian X and Y, we show that Gaussian channels are optimal in the low-SNR regime, but not for general SNR. Similarly, it is shown that for a doubly symmetric binary source, binary symmetric channels are optimal when the correlation is low, and are suboptimal for high correlation. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., X = Y), and provide supporting numerical evidence.

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Section: Introductionmentioning

confidence: 99%

The Double-Sided Information-Bottleneck Function

Dikshtein

Ordentlich

Shitz

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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show abstract

“…We show that while OOK is sub-optimal in terms of the single-receiver second-order coefficient, the second-order CMI coefficient of fixed-amplitude OOK surpasses those of Gaussian signaling and BPSK. This is notable, given that for the same received SNRs, all source distributions have the same linear correlation coefficient [13]. This indicates that the dependence between Y 1 and Y 2 is non-linear for OOK.…”

mentioning

confidence: 78%

“…In [13], Williamson studied the impacts of additive Gaussian noise and 2-level quantization on the correlation coefficient of correlated sources, considering both Gaussian sources and binary sources. In contrast to a classic analysis by Van Vleck [43], [13] considered the effects of noise and quantization separately, showing that as source power tends to zero, symmetric-threshold quantization of Gaussian sources and of equiprobable, antipodal binary sources degrades the correlation by 2 π . However, flash OOK sources and receivers with asymmetric quantization can avoid the 2 π correlation penalty: in the limit of zero SNR, the quantized signals' correlation approaches the sources' correlation.…”

Section: A Related Literaturementioning

confidence: 99%

Low-SNR Asymptotics of Cross-Receiver Mutual Information in Gaussian Channels

Williamson¹

2021

Preprint

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<div>In this paper, we analyze the low-SNR behavior of the cross-receiver mutual information (CMI) between two received signals corrupted by uncorrelated, additive Gaussian noise. This framework has use in distributed, passive sensor applications, such as passive radar and collaborative opportunistic navigation. For Gaussian and BPSK signaling, the CMI can be expressed in terms of the effective SNR between the receivers. On-off keying (OOK), while not optimal in terms of spectral efficiency for a single-receiver channel, is shown to have greater CMI than Gaussian or BPSK signaling. This is in spite of the fact that, given the same received SNRs, all three source distributions have the same linear correlation coefficient. This indicates that for OOK sources, effective SNR and correlation coefficient are not meaningful descriptors for passive receivers.<br></div><div><br></div><div>Full-length version of conference paper submission.</div>

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“…Moreover, if the Markov condition

is imposed on the multi-letter variant, then those problems are equivalent. A similar setting, but with a maximal correlation criterion between the reconstructed random variables, has been considered in [ 11 , 12 ]. Furthermore, it is sometimes the case that the optimal biclustering problem is more straightforward to solve than its standard, single-sided, clustering counterpart.…”

Section: Introductionmentioning

confidence: 99%

The Double-Sided Information Bottleneck Function

Dikshtein

Ordentlich

Shamai

2022

Entropy

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A double-sided variant of the information bottleneck method is considered. Let (X,Y) be a bivariate source characterized by a joint pmf PXY. The problem is to find two independent channels PU|X and PV|Y (setting the Markovian structure U→X→Y→V), that maximize I(U;V) subject to constraints on the relevant mutual information expressions: I(U;X) and I(V;Y). For jointly Gaussian X and Y, we show that Gaussian channels are optimal in the low-SNR regime but not for general SNR. Similarly, it is shown that for a doubly symmetric binary source, binary symmetric channels are optimal when the correlation is low and are suboptimal for high correlations. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., X=Y) and provide supporting numerical evidence. Furthermore, we present a Blahut–Arimoto type alternating maximization algorithm and demonstrate its performance for a representative setting. This problem is closely related to the domain of biclustering.

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The Impacts of Additive Noise and 1-bit Quantization on the Correlation Coefficient in the Low-SNR Regime

Cited by 3 publications

References 21 publications

The Double-Sided Information-Bottleneck Function

The Double-Sided Information-Bottleneck Function

Low-SNR Asymptotics of Cross-Receiver Mutual Information in Gaussian Channels

The Double-Sided Information Bottleneck Function

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