Abstract

Despite the fact that the channel in a holographic data-storage system is nonlinear, most of the existing approaches use linear equalization for data recovery. We present a novel and simple to implement nonlinear equalization approach based on a minimum mean-square-error criterion. We use a quadratic equalizer whose complexity is comparable to that of a linear equalizer. We also explore the effectiveness of a nonlinear equalization target as compared with the conventional linear target. Bit-error-rate (BER) performance is studied for channels having electronics noise, optical noise, and a different span of intersymbol interference. With a linear target, whereas the linear equalizer exhibits an error floor in the BER performance, the quadratic equalizer significantly improves the performance with no sign of error floor even up to 107. With a nonlinear target, whereas the quadratic equalizer provides an additional performance gain of 12  dB, the error-floor problem of the linear equalizer has been considerably alleviated, thereby significantly improving the latter's performance. A theoretical performance analysis of the nonlinear receiver with non-Gaussian noise is also presented. A simplified approach is developed to compute the underlying probability density functions, optimum detector threshold, and BER using the theoretical analysis. Numerical results show that the theoretical predictions agree well with simulations.

© 2006 Optical Society of America

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References

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  1. T. H. Chao, H. Zhou, and G. F. Reyes, " Compact holographic data storage system," in Proceedings of the 18th IEEE Symposium on Mass Storage Systems and Technologies (IEEE Press, 2001), pp. 237- 247.
    [CrossRef]
  2. S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
    [CrossRef]
  3. V. Vadde and B. V. K. V. Kumar, " Channel modeling and estimation for intrapage equalization in pixel-matched volume holographic data storage," Appl. Opt. 38, 4374- 4386 ( 1999).
    [CrossRef]
  4. B. M. King and M. A. Neifeld, " Parallel detection algorithm for page-oriented optical memories," Appl. Opt. 37, 6275- 6298 ( 1998).
    [CrossRef]
  5. M. Keskinoz and B. V. K. V. Kumar, " Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels," Appl. Opt. 43, 1368- 1378 ( 2004).
    [CrossRef] [PubMed]
  6. M. Keskinoz and B. V. K. V. Kumar, " Application of linear minimum mean-squared-error equalization for volume holographic data storage," Appl. Opt. 38, 4387- 4393 ( 1999).
    [CrossRef]
  7. K. M. Chugg, X. Chen, and M. A. Neifeld, " Two-dimensional equalization in coherent and incoherent page-oriented optical memory," J. Opt. Soc. Am. A 16, 549- 561 ( 1999).
    [CrossRef]
  8. S. Nabavi and B. V. K. V. Kumar, " Comparative evaluation of equalization methods for holographic data storage channel," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).
  9. A. He and G. Mathew, " Application of nonlinear minimum mean square error equalization for holographic data storage," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).
  10. C. Gu, F. Dai, and J. Hong, " Statistics of both optical and electrical noise in digital volume holographic data storage," Electron. Lett. 32, 1400- 1402 ( 1996).
    [CrossRef]
  11. L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.
  12. S. Gupta, " Performance evaluation of an adaptive Volterra/hybrid equalizer for nonlinear ISI in a magneto-optic storage channel," in Proceedings of the 36th Southeastern Symposium System Theory (IEEE, 2004), pp. 314- 317.
  13. B. Farhang-Boronjeny, Adaptive Filters: Theory and Applications (Wiley, 1998), Chap. 3.
  14. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, 1996), Chap. 2.
  15. M. -P. Bernal, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, and G. Wittmann, " A precision tester for studies of holographic optical storage materials and recording physics," Appl. Opt. 35, 2360- 2374 ( 1996).
    [CrossRef] [PubMed]
  16. M. -P. Bernal, G. W. Burr, H. Coufal, and M. Quintanilla, " Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems," Appl. Opt. 37, 5377- 5385 ( 1998).
    [CrossRef]
  17. H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
    [CrossRef]

2005 (1)

H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
[CrossRef]

2004 (1)

1999 (3)

1998 (2)

1996 (2)

Agarossi, L.

L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.

Bellini, S.

L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.

Bernal, M. -P.

Bjornson, E.

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

Bregoil, F.

L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.

Burr, G. W.

Chao, T. H.

T. H. Chao, H. Zhou, and G. F. Reyes, " Compact holographic data storage system," in Proceedings of the 18th IEEE Symposium on Mass Storage Systems and Technologies (IEEE Press, 2001), pp. 237- 247.
[CrossRef]

Chen, X.

Chugg, K. M.

Coufal, H.

Dai, F.

C. Gu, F. Dai, and J. Hong, " Statistics of both optical and electrical noise in digital volume holographic data storage," Electron. Lett. 32, 1400- 1402 ( 1996).
[CrossRef]

Farhang-Boronjeny, B.

H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
[CrossRef]

B. Farhang-Boronjeny, Adaptive Filters: Theory and Applications (Wiley, 1998), Chap. 3.

Grygier, R. K.

Gu, C.

C. Gu, F. Dai, and J. Hong, " Statistics of both optical and electrical noise in digital volume holographic data storage," Electron. Lett. 32, 1400- 1402 ( 1996).
[CrossRef]

Gupta, S.

S. Gupta, " Performance evaluation of an adaptive Volterra/hybrid equalizer for nonlinear ISI in a magneto-optic storage channel," in Proceedings of the 36th Southeastern Symposium System Theory (IEEE, 2004), pp. 314- 317.

He, A.

A. He and G. Mathew, " Application of nonlinear minimum mean square error equalization for holographic data storage," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).

Hesselink, L.

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

Hoffnagle, J. A.

Hong, J.

C. Gu, F. Dai, and J. Hong, " Statistics of both optical and electrical noise in digital volume holographic data storage," Electron. Lett. 32, 1400- 1402 ( 1996).
[CrossRef]

Jefferson, C. M.

Keskinoz, M.

King, B. M.

Kumar, B. V. K. V.

Macfarlane, R. M.

Mathew, G.

H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
[CrossRef]

A. He and G. Mathew, " Application of nonlinear minimum mean square error equalization for holographic data storage," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).

Migliorati, P.

L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.

Nabavi, S.

S. Nabavi and B. V. K. V. Kumar, " Comparative evaluation of equalization methods for holographic data storage channel," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).

Neifeld, M. A.

Okas, R.

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

Orlov, S. S.

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

Philips, W.

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

Proakis, J. G.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, 1996), Chap. 2.

Quintanilla, M.

Reyes, G. F.

T. H. Chao, H. Zhou, and G. F. Reyes, " Compact holographic data storage system," in Proceedings of the 18th IEEE Symposium on Mass Storage Systems and Technologies (IEEE Press, 2001), pp. 237- 247.
[CrossRef]

Shelby, R. M.

Sincerbox, G. T.

Sun, H.

H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
[CrossRef]

Vadde, V.

Wimmer, P.

Wittmann, G.

Zhou, H.

T. H. Chao, H. Zhou, and G. F. Reyes, " Compact holographic data storage system," in Proceedings of the 18th IEEE Symposium on Mass Storage Systems and Technologies (IEEE Press, 2001), pp. 237- 247.
[CrossRef]

Appl. Opt. (6)

Electron. Lett. (1)

C. Gu, F. Dai, and J. Hong, " Statistics of both optical and electrical noise in digital volume holographic data storage," Electron. Lett. 32, 1400- 1402 ( 1996).
[CrossRef]

IEEE Trans. Magn. (1)

H. Sun, G. Mathew, and B. Farhang-Boronjeny, " Detection techniques for high-density magnetic recording," IEEE Trans. Magn. 41, 1193- 1199 ( 2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (8)

S. Nabavi and B. V. K. V. Kumar, " Comparative evaluation of equalization methods for holographic data storage channel," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).

A. He and G. Mathew, " Application of nonlinear minimum mean square error equalization for holographic data storage," in Proceedings of the International Symposium on Optical Memory and Optical Data Storage (SPIE, 2005).

L. Agarossi, S. Bellini, F. Bregoil, and P. Migliorati, " Equalization for nonlinear optical channels," in Proceedings of the IEEE International Conference on Communication (IEEE Press, 1998), Vol. 2, pp. 662- 667.

S. Gupta, " Performance evaluation of an adaptive Volterra/hybrid equalizer for nonlinear ISI in a magneto-optic storage channel," in Proceedings of the 36th Southeastern Symposium System Theory (IEEE, 2004), pp. 314- 317.

B. Farhang-Boronjeny, Adaptive Filters: Theory and Applications (Wiley, 1998), Chap. 3.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, 1996), Chap. 2.

T. H. Chao, H. Zhou, and G. F. Reyes, " Compact holographic data storage system," in Proceedings of the 18th IEEE Symposium on Mass Storage Systems and Technologies (IEEE Press, 2001), pp. 237- 247.
[CrossRef]

S. S. Orlov, W. Philips, E. Bjornson, L. Hesselink, and R. Okas, " Ultra-high transfer rate high capacity holographic disk digital data storage system," in Proceedings of the 29th IEEE Workshop on Applied Imagery Pattern Recognition, (IEEE Press, 2000), pp. 71- 77.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Schematic of the 4fL HDSS.

Fig. 2
Fig. 2

Conditional PDFs of equalizer output y given di,j .

Fig. 3
Fig. 3

Comparison of BER performances obtained using analysis and simulation for a 3 × 3 channel with equal amounts of electronics noise and optical noise (QE, linear target). The simulation results correspond to optimum and nonoptimum slicer thresholds. Noise ratio r = 1.

Fig. 4
Fig. 4

(a) MMSE and (b) BER performances with linear and quadratic equalizers for 3 × 3 electronics noise channel with linear target.

Fig. 5
Fig. 5

(a) MMSE and (b) BER performances with linear and quadratic equalizers for 5 × 5 electronics noise channel with linear target.

Fig. 6
Fig. 6

Comparison of MMSE (left) and BER (right) performances with linear and quadratic equalizers for 3 × 3 electronics noise channel with linear and nonlinear targets.

Fig. 7
Fig. 7

Comparison of MMSE (left) and BER (right) performances with linear and quadratic equalizers for 5 × 5 electronics noise channel with linear and nonlinear targets.

Fig. 8
Fig. 8

Comparison of BER performances obtained using analysis and simulation with a QE for a 3 × 3 electronics noise channel with a linear target.

Fig. 9
Fig. 9

BER performances with linear and quadratic equalizers and a linear target for (a) 3 × 3 and (b) 5 × 5 channels with optical noise.

Fig. 10
Fig. 10

Comparison of BER performances with linear and quadratic equalizers and linear and nonlinear targets for (a) 3 × 3 and (b) 5 × 5 channels with optical noise.

Fig. 11
Fig. 11

Comparison of BER performances obtained using analysis and simulation with a QE for a 3 × 3 optical noise channel with a linear target.

Fig. 12
Fig. 12

BER performances with linear and quadratic equalizers and linear target for (a) 3 × 3 and (b) 5 × 5 channels that have equal amounts of electronics noise and optical noise.

Fig. 13
Fig. 13

Comparison of BER performances with linear and quadratic equalizers and linear and nonlinear targets for (a) 3 × 3 and (b) 5 × 5 channels that have equal amounts of electronics noise and optical noise.

Fig. 14
Fig. 14

BER performance (analytically obtained) comparison for the 3 × 3 channel with a QE and linear target under the three different noise conditions: electronics noise only, optical noise only, and electronics noise and optical noise in equal proportion.

Equations (47)

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

I i , j = β Δ / 2 β Δ / 2 β Δ / 2 β Δ / 2 | k , l = i ( N 1 ) / 2 i + ( N 1 ) / 2 d i k , j l h ( x + k Δ , y + l Δ ) + n o ( x , y ) | 2 d y d x + n i , j e ,
I i , j = k , l , m , n = L L d i k , j l d i m , j n G k , m G l , n + n i , j e ,
G k , m = w 2 Δ β / 2 β / 2 [ u + k α / 2 u + k + α / 2 sinc ( w u ) d u ] × [ u + m α / 2 u + m + α / 2 sinc ( wu ) d u ] d u ,
G k , m   λ v k v m ,
I i , j k , l , m , n = L L d i k , j l d i m , j n λ 2 v k v l v m v n + n i , j e = | d i , j h i , j | 2 + n i , j e ,
h i , j   =   λ v i v j .
I i , j | d i , j h i , j + n i , j           o | 2 + n i , j e ,
y i , j = n 1 = Q Q n 2 = Q Q c n 1 , n 2 ( 1 ) I i n 1 , j n 2 + c 0 , 0         ( 2 ) I i , j 2 ,
e i , j = d ̃ i , j y i , j ,
i = [ I i + Q , j + Q , , I i Q , j Q , I i , j 2 ] T = [ i 1 T , I i , j 2 ] T ,
c = [ c Q , Q ( 1 ) , , c Q , Q ( 1 ) , c 0 , 0 ( 2 ) ] T ,
y i , j = k = 1 ( 2 Q + 1 ) 2 + 1 c k i k = c T i .
d ̃ i , j = d i , j ,
e i , j = d i , j y i , j = d i , j c T i .
ξ = E [ e i , j 2 ] = E [ d i , j 2 ] 2 c T p + c T R c ,
p = E [ i d i , j ] = [ p 1 T p 2 ] T ,
R = E [ i i T ] = [ R 1 r r T r 0 ] ,
E [ e i , j o i ] = p R c o = 0 ,
c o = R 1 p .
ξ min = E [ d i , j 2 ] c o T p = E [ d i , j 2 ] c o T R c o .
d ̃ i , j = d i , j 2 ,
e ̄ i , j = d i , j 2 y i , j = d i , j 2 c T i .
ξ ¯ = E [ e ̄ i , j 2 ] = E [ d i , j 4 ] 2 c T p ̄ + c T R c ,
p ̄ = E [ i d i , j 2 ] = [ p ̄ 1 T , p ̄ 2 ] T ,
c ̄ o = R 1 p ̄ ,
ξ ̄ min = E [ d i , j 4 ] c ̄ o    T p ̄ = E [ d i , j 4 ] c ̄ o T R c ̄ o .
d ^ i , j = 1 , y i , j > v th ,
d ^ i , j = 1 / ϵ ,   if       y i , j v th ,
s i , j = d i , j h i , j = s ̃ i , j + j s i , j ,
u i , j = s i , j + n i , j o = u ̃ i , j + j u i , j ,
v i , j = | u i , j | 2 = u ̃ i , j 2 + u i , j 2 ,
u ̃ i , j = s ̃ i , j + n ̃ i , j o , u i , j = s i , j + n i , j o ,
I i , j = v i , j + n i , j e .
p v ( v | s i , j ) = { 1 2 σ o 2 exp ( v + | s i , j | 2 2 σ o 2 ) I 0 ( | s i , j | v σ o     2 ) v 0 0                                                                                                               v < 0 ,
p I ( I | s i , j ) = p v p n e = 0 p v ( v | s i , j ) p n e ( I v ) d v ,
p n e ( n ) = 1 2 π σ e exp ( n 2 2 σ e 2 ) .
y i , j = n 1 , n 2 = Q Q x n 1 , n 2 ,
x n 1 , n 2 = { c 0 , 0 ( 1 ) I i , j + c 0 , 0 2 I i , j 2       if       n 1 = 0 , n 2 = 0 c n 1 , n 2 ( 1 ) I i - n 1 , j - n 2       otherwise .
p x n 1 , n 2 ( x | s i , j ) = { 1 α ( x ) p I ( c 0 , 0 ( 1 ) + α ( x ) 2 c 0 , 0 ( 2 ) ) + 1 α ( x ) p I ( c 0 , 0 ( 1 ) α ( x ) 2 c 0 , 0 ( 2 ) ) ,       n 1 = 0      and      n 2 = 0 1 | c n 1 , n 2 ( 1 ) | p I ( x c n 1 , n 2 ( 1 ) ) ,                              otherwise ,
p y ( y | s i , j ) = p 0 , 0 p Q , Q p Q , Q + 1 p Q , Q ,
P e = Pr ( 1 / ϵ | 1 ) Pr ( d i , j = 1 ) + Pr ( 1 | 1 / ϵ ) Pr ( d i , j = 1 / ϵ ) ,
Pr ( 1 / ϵ | 1 ) = Pr ( y i , j < v th | d i , j = 1 ) ,
Pr ( 1 | 1 / ϵ ) = Pr ( y i , j v th | d i , j = 1 / ϵ ) ,
P e = 1 2 [ Pr ( 1 / ϵ | 1 ) + Pr ( 1 | 1 / ϵ ) ] .
P e = 1 2 D J [ P D J ( 1 / ϵ | 1 ) + P D J ( 1 | 1 / ϵ ) ] Pr ( D J ) ,
P D J ( 1 / ϵ | 1 ) = Pr ( y i , j < v th | D J , d i , j = 1 ) ,
P D J ( 1 | 1 / ϵ ) = Pr ( y i , j v th | D J , d i , j = 1 / ϵ ) .

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