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

Or Ordentlich, Ofer Shayevitz
2015 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.  ... 
arXiv:1506.00253v1 fatcat:b3dpbwcjinhmzczlxl7zxqyhou

Minimum MS. E. Gerber's Lemma

Or Ordentlich, Ofer Shayevitz
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.  ... 
doi:10.1109/tit.2015.2479641 fatcat:ymyv3sbisvfnnebjt4ilvwvdaq

Secret rate - Privacy leakage in biometric systems

Tanya Ignatenko, Frans Willems
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.  ... 
doi:10.1109/isit.2009.5205878 dblp:conf/isit/IgnatenkoW09 fatcat:ryacbcjyknhzxf5fh27vylch7i

The efficiency of investment information

E. Erkip, T.M. Cover
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.  ... 
doi:10.1109/18.669153 fatcat:mzruyncrazaihefasonsdr225a

Privacy-Aware Distributed Hypothesis Testing

Sreejith Sreekumar, Asaf Cohen, Deniz Gündüz
2020 Entropy  
Proof of Lemma 2 LetP (C n ,0) S n U n V n 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 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.  ... 
doi:10.3390/e22060665 pmid:33286437 fatcat:5ixjnkadbbcdvfrjuhxddl6uda

Key Agreement with Physical Unclonable Functions and Biometric Identifiers [article]

Onur Günlü
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.  ... 
dblp:journals/iacr/Gunlu21 fatcat:uuode2mzpfb2hcszi2o3f2jytu

Privacy-aware Distributed Hypothesis Testing [article]

Sreejith Sreekumar, Asaf Cohen, Deniz Gündüz
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 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 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.'  ... 
arXiv:1807.02764v6 fatcat:pzjbxrbvb5bvlnu7cmtoyq7sh4

Distributed Binary Detection with Lossy Data Compression [article]

Gil Katz, Pablo Piantanida, Mérouane Debbah
2017 arXiv   pre-print
In addition, A ≥ H 2 H −1 2 (H(X|U )) p , (60) which stems from 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  ... 
arXiv:1601.01152v2 fatcat:pmdyke3yczaazbk2qye5vjl5ua

Distributed Binary Detection With Lossy Data Compression

Gil Katz, Pablo Piantanida, Merouane Debbah
2017 IEEE Transactions on Information Theory  
In addition, A ≥ H 2 H −1 2 (H(X|U )) p , (60) which stems from 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  ... 
doi:10.1109/tit.2017.2688348 fatcat:qzkewjb3pzgvnm4hq2sravetju

Coding for Communications and Secrecy

Mani Bastaniparizi
2017
The secrecy capacity of the wiretap channel W : X → Y × Z is given by C 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.  ... 
doi:10.5075/epfl-thesis-7751 fatcat:hjjgntnf35astazoouuwg6lgh4

Information-theoretic analysis of identification systems in large-scale databases

Farzad Farhadzadeh, Svyatoslav Voloshynovskyy
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.  ... 
doi:10.13097/archive-ouverte/unige:34300 fatcat:3wi5lwyt4bajdgcw444xovqaq4

Compressed Sensing of Memoryless Sources:A Deterministic Hadamard Construction

Saeid Haghighatshoar
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.  ... 
doi:10.5075/epfl-thesis-6356 fatcat:rmrtepg5uzb35bmhotbhehwbn4

Rowing performance monitoring system development [article]

Thomas Williams, University Of Canterbury
2012
The 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  ... 
doi:10.26021/3009 fatcat:hbfmvb2livc2ro3zpwrc3ttati