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Minimum MS. E. Gerber's Lemma
[article]

2015
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arXiv
*
pre-print

*Gerber's*

*Lemma*lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. ...

*Gerber's*

*Lemma*. As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate. ...

*Gerber's*

*Lemma*in certain scenarios. ...

##
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Minimum MS. E. Gerber's Lemma

2015
*
IEEE Transactions on Information Theory
*

*Gerber's*

*Lemma*lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. ...

*Gerber's*

*Lemma*. As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate. ...

*Gerber's*

*Lemma*in certain scenarios. ...

##
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Secret rate - Privacy leakage in biometric systems

2009
*
2009 IEEE International Symposium on Information Theory
*

*Gerber's*

*Lemma*[13) tells us that if H(X IU) = v, then 2N8 2 :>- 2 1(X N ;H) + 1(S;H) 2: 1(X N ;H) = 1(X N , S , P ;H) -1(P, S ;H IX N) = H(H) -H(P IX N) -H(S IP, X N) + H(P, S IX N , H) > H(H) -H(P) ... For binary symmetric (U, X) with crossover probability p the

*minimum*H(Y IU) is achieved. ...

##
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The efficiency of investment information

1998
*
IEEE Transactions on Information Theory
*

*E*. Erkip is with the Department of Electrical and Computer Engineering,

*MS*-366, Rice University, Houston, TX 77005-1892 USA. T. M. ...

*Lemma*1 ( 1 Corollary to "Mrs.

*Gerber's*

*Lemma*"): Suppose and are two binary random variables connected through a as in Fig. 5. Then for any satisfying . Fig. 6 . 6 Ṽ and V binary. ...

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Privacy-Aware Distributed Hypothesis Testing

2020
*
Entropy
*

Proof of

doi:10.3390/e22060665
pmid:33286437
fatcat:5ixjnkadbbcdvfrjuhxddl6uda
*Lemma*2 LetP (C n ,0) S n U n V n*MŜ*n = P S n U n V n M ∏ n i=1PŜ i |M,V n ,S i−1 andP (C n ,1) S n U n V n*MŜ*n = Q S n U n V n M ∏ n i=1PŜ i |M,V n ,S i−1 denote the joint distribution of the ... Here, the inequality in (64) and (65) follows by an application of Mrs*Gerber's**lemma*[68] , since V = U ⊕ N p under the null hypothesis and N p ∼ Ber(p) is independent of U and W. ...##
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Key Agreement with Physical Unclonable Functions and Biometric Identifiers
[article]

2021
*
IACR Cryptology ePrint Archive
*

*Gerber's*

*lemma*[79] , which gives the optimal auxiliary random variable U in (3.6) when P Y |X is a BSC. ...

*Gerber's*

*lemma*(MGL) [79] . The analysis differs from [56] and [57] because we need to apply MGL twice in different directions to a Markov chain rather than once. ... s , R , R w , C) that satisfies (6.12)-(6.14) for some P A| X , P V | XA , and P U |V such that

*E*[Γ(A)] ≤ C is achievable. ...

##
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Privacy-aware Distributed Hypothesis Testing
[article]

2020
*
arXiv
*
pre-print

*Gerber's*

*lemma*[53], since V = U ⊕ N p under the null hypothesis and N p ∼ Ber(p) is independent of U and W . Also, Λ min = 0 since S = U . ... Now, suppose (α U n V n

*MŜ*n = P S n U n V n M n i=1PŜ i|M,V n ,S i−1 andP (Cn,1) S n U n V n

*MŜ*n = Q S n U n V n M n i=1PŜi|M,V n ,S i−1 denote the joint distribution of the r.v.' ...

##
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Distributed Binary Detection with Lossy Data Compression
[article]

2017
*
arXiv
*
pre-print

In addition, A ≥ H 2 H −1 2 (H(X|U )) p , (60) which stems from

arXiv:1601.01152v2
fatcat:pmdyke3yczaazbk2qye5vjl5ua
*Ms*.*Gerber's**Lemma*(see e.g. [28] ). ... R) satisfies [7,*Lemma*1.a]:*E*(R) = sup n≥1*E*n (R) , (3) where*E*n (R) = sup fn 1 n I (f n (X n ); Y n ) log f n ≤ nR . (4) This asymptotic equivalence implies a strong converse property that, much like ...##
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Distributed Binary Detection With Lossy Data Compression

2017
*
IEEE Transactions on Information Theory
*

In addition, A ≥ H 2 H −1 2 (H(X|U )) p , (60) which stems from

doi:10.1109/tit.2017.2688348
fatcat:qzkewjb3pzgvnm4hq2sravetju
*Ms*.*Gerber's**Lemma*(see e.g. [28] ). ... R) satisfies [7,*Lemma*1.a]:*E*(R) = sup n≥1*E*n (R) , (3) where*E*n (R) = sup fn 1 n I (f n (X n ); Y n ) log f n ≤ nR . (4) This asymptotic equivalence implies a strong converse property that, much like ...##
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Coding for Communications and Secrecy

2017

The secrecy capacity of the wiretap channel W : X → Y × Z is given by
C

doi:10.5075/epfl-thesis-7751
fatcat:hjjgntnf35astazoouuwg6lgh4
*Ms*= x n*Ms*,1 x n*Ms*,2 . . . x n*Ms*,M . (5.10)To communicate a message s ∈ {1, 2, . . . , M s }, the encoder transmits a uniformly ...*Gerber's**Lemma*[119] , it is shown in [97,*Lemma*2.1] that if I(W ) ∈ (a, b) (for any 0 < a < b < 1) then I(W + ) − I(W − ) ≥ η(a, b) > 0 (2.53) Therefore, for all s m ∈ {−, +} m such that I(W s m ) ∈ ... Proof of*Lemma*C.3. By the virtue of*Lemma*C.1, there exist a sequence of n-types (P (n) ∈ P n (X × Y), n ∈ N) that converge to P as n grows large. ...##
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Information-theoretic analysis of identification systems in large-scale databases

2014

*Gerber's*

*Lemma*shown by Wyner and Ziv (1973) that if H(Y |U ) = v then H(X|U ) ≥ H 2 (q H −1 2 (v)). ...

*Gerber's*

*Lemma*(Wyner and Ziv 1973) , if H(X|U ) = v then H(Y |U ) ≥ H 2 (q H −1 2 (v )). If now 0 ≤ p ≤ 1/2 is such that H 2 (p ) = v then H(X|U ) = H 2 (p ) and H(Y |U ) ≥ H 2 (q p ). ... Consequently, p * is a local

*minimum*. Then, the Second-Order-Sucient-Condition (see for example Boyd and Vandenberghe 2004) shows that p * is a strict local

*minimum*. ...

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Compressed Sensing of Memoryless Sources:A Deterministic Hadamard Construction

2014

*Gerber's*

*Lemma*(MGL) proved in [92] by Wyner and Ziv for binary alphabets. ... Applying Fatou's

*lemma*[31] to I n , it results that I 1 (1) I 1 (2) I 2 (1) I 2 (2) I 2 (3) I 2 (4)

*E*(I ∞ ) =

*E*(lim inf n→∞ I n ) ≤ lim inf n→∞

*E*(I n ) =

*E*(I 0 ) = H(X), where we used the martingale ... For a, b ∈ R, we will use a ∨ b and a ∧ b for the maximum and

*minimum*of a and b. Also, a + = a ∨ 0 denotes the positive part of a. ...

##
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Rowing performance monitoring system development
[article]

2012

The

doi:10.26021/3009
fatcat:hbfmvb2livc2ro3zpwrc3ttati
*minimum*mean square estimate of ~ conditioned on correlated random vector y is given by (A3.27)where obviously Pyy is as before, and l)~y and*E*[~] are given byE[~] = AE[*e*] +*E*[d]P~y =*E*[(~ -*E*[~])(y-*E*... Following from the definition of the linear*minimum*mean square estimator:*E**[x(k+ 1)Ie z (k+ Ilk)] = cov[x(k+ l),ezClc+ 1)]cov[*e*z (k+ l),ez(k+ 1)r 1 (ez(k+ 1) -*E*[ez(k+ 1)]) +*E*[x(k+ 1)] (A3.53) where ... A3.2 Kalnlan Filter Problen1 Staten1ent The Kalman Filter is a recursive algorithm that calculates the linear*minimum*mean square estimate of the state of a dynamic system driven by white noise, based ...