Abstract

We analyze the unique statistics of complex amplitude noise in holographic data storage and determine the corresponding bit-error rate. Explicit expressions of the signal-to-noise ratio, the threshold value that distinguishes binary bits, and the bit-error rate are obtained analytically. Comparison between the analytical approximations and the direct numerical evaluations shows that the analytical expressions have excellent accuracy.

© 1996 Optical Society of America

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References

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1996

1995

1994

J. F. Heanue, M. C. Bashaw, L. Hesselink, Science 265, 749 (1994).
[CrossRef] [PubMed]

X. Yi, P. Yeh, C. Gu, Opt. Lett. 19, 1580 (1994).
[CrossRef] [PubMed]

1993

1992

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt.Soc. Am. A 9, 1978 (1992).
[CrossRef]

Asthana, P.

Bashaw, M. C.

Campbell, S.

Curtis, K.

Gu, C.

Heanue, J. F.

Hesselink, L.

Hong, J.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt.Soc. Am. A 9, 1978 (1992).
[CrossRef]

McMichael, I.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt.Soc. Am. A 9, 1978 (1992).
[CrossRef]

Mok, F.

D. Psaltis, F. Mok, Sci. Am. 273, 70 (1995).
[CrossRef]

Mok, F. H.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt.Soc. Am. A 9, 1978 (1992).
[CrossRef]

Nordin, G. P.

Psaltis, D.

Pu, A.

Saxena, R.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt.Soc. Am. A 9, 1978 (1992).
[CrossRef]

Yeh, P.

Yi, X.

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Figures (2)

Fig. 1
Fig. 1

PDF's as functions of the output pixel value. Each plot has two PDF's, one for the on pixel (centered at 1) and another for the off pixel (centered at |aoff|2).

Fig. 2
Fig. 2

BER as a function of the SNR, showing the analytical results (curves) and the numerical integration results (data points). CR, intensity contrast ratio.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

P u ( u r , u i | a ) = 1 2 π σ 2 exp { 1 2 σ 2 [ ( u r a ) 2 + u i 2 ] } .
p ν ( ν | a ) = { 1 2 σ 2 exp [ 1 2 σ 2 ( ν + a 2 ) ] I 0 ( a ν σ 2 ) for ν 0 0 for ν < 0 ,
p ν ( ν | a = 0 ) = 1 2 σ 2 exp ( ν 2 σ 2 ) .
ν = a 2 + 2 σ 2 ,
σ ν 2 = ν 2 ν 2 = 4 σ 2 ( a 2 + σ 2 ) .
SNR = ν σ ν = 1 + 2 σ 2 2 σ 1 + σ 2 1 2 σ ,
BER = P ( a = 1 ) P ( ν < ν th | a = 1 ) + P ( a = ɛ ) P ( ν > ν th | a = ɛ ) ,
P ( ν < ν t h | a = 1 ) = 0 ν t h p ν ( ν | a = 1 ) d ν , P ( ν > ν t h | a = ɛ ) = ν t h p ν ( ν | a = ɛ ) d ν .
p ν ( ν t h | a = 1 ) = p ν ( ν t h | a = ɛ ) .
I 0 ( x ) 1 / 2 π x exp ( x ) for x 1 .
ν th a off + a on 2 = ɛ + 1 2 for ɛ 2 σ 2 ,
ν t h = 1 / 2 [ 1 + σ 2 ln ( π / σ 2 ) ] for ɛ 0 ,
ν th = ( 1 + δ ) / 2 ,
δ = max [ ɛ , σ 2 ln ( π / σ 2 ) ] .
p ν ( ν | a 0 ) 1 2 σ [ 2 π a ( ν ) 1 / 2 ] 1 / 2 exp [ ( a ν ) 2 2 σ 2 ] ν th 1 / 4 2 σ 2 π a ν exp [ ( a ν ) 2 2 σ 2 ] ,
BER ɛ + 1 4 2 [ erfc ( 1 ɛ 2 2 σ ) erfc ( 1 2 σ ) ] + ɛ + 1 4 2 ɛ [ erfc ( 1 ɛ 2 2 σ ) ] for ɛ > σ 2 ln ( π / σ 2 ) ,
BER = [ 1 + σ 2 ln ( π / σ 2 ) ] 1 / 2 4 2 { erfc [ 1 σ 2 ln ( π / σ 2 ) 2 2 σ ] erfc ( 1 2 σ ) } + 1 2 exp { [ 1 + σ 2 ln ( π / σ 2 ) ] 2 8 σ 2 } for ɛ < σ 2 ln ( π / σ 2 ) ,

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