Abstract

In page-oriented memories, data pages commonly consist of comparable numbers of on and off pixels. Data-page sparsity is defined by reduction of the number of on pixels per page, leading to an increased diffracted power into each pixel. When page retrieval is dominated by a fixed noise floor, the number of pages in the memory is limited by the pixel diffraction efficiency. Sparsity increases the number of storable pages while reducing the amount of user information per page. A detailed analysis of sparsity in volume holographic memories shows that the total memory capacity can be increased by 15% by use of data pages that contain on average 25% on pixels. Sparsity also helps to reduce the effects of interpixel cross talk by strongly reducing the probability that worst-case pixel patterns (e.g., blocks of on pixels with a center off pixel) will occur in the data page. Enumeration block coding techniques provide construction of sparse-data pages with minimal overhead. In addition, enumeration coding offers maximum-likelihood detection with low encoding–decoding latency. We discuss the theoretical advantages of data-page sparsity. We also present experimental results that demonstrate the proposed capacity gain. The experiment verifies that it is practical to construct and use sparse-data pages that result in an overall user capacity gain of 16% subject to a page retrieval bit-error rate of 10-4.

© 2000 Optical Society of America

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References

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  1. R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
    [CrossRef]
  2. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  3. S. Campbell, X. Yi, P. Yeh, “Hybrid sparse-wavelength angle-multiplexed optical data storage system,” Opt. Lett. 19, 2161–2163 (1994).
    [CrossRef] [PubMed]
  4. J. Heanue, M. Bashaw, L. Hesselink, “Recall of linear combinations of stored data pages based on phase-code multiplexing in volume holography,” Opt. Lett. 19, 1079–1081 (1994).
    [CrossRef] [PubMed]
  5. E. Chuang, D. Psaltis, “Storage of 1000 holograms with use of a dual-wavelength method,” Appl. Opt. 36, 8445–8454 (1997).
    [CrossRef]
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    [CrossRef]
  7. V. Markov, J. Millerd, J. Trolinger, M. Norrie, J. Dowaie, D. Timucin, “Multilayer volume holographic optical memory,” Opt. Lett. 24, 265–267 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed., (IEEE Computer Soc. Press, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.
  15. M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).
    [CrossRef]
  16. T. N. Garrett, P. A. Mitkas, “Three-dimensional error correcting codes for volumetric optical memories,” in Advanced Optical Memories and Interfaces to Computer Storage, Z. U. Hasan, P. A. Mitkas, eds., Proc. SPIE3468, 116–124 (1998).
    [CrossRef]
  17. M. E. Schaffer, P. A. Mitkas, “Requirements and constraints for the design of smart photodetector arrays for page-oriented optical memories,” IEEE. J. Sel. Top. Quantum Electron. 4, 856–865 (1998).
    [CrossRef]
  18. B. M. King, M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275–6298 (1998).
    [CrossRef]
  19. G. W. Burr, W.-C. Chou, M. A. Neifeld, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “Experimental evaluation of user capacity in holographic data-storage systems,” Appl. Opt. 37, 5431–5443 (1998).
    [CrossRef]
  20. G. W. Burr, B. Marcus, “Coding tradeoffs for high-density holographic data storage,” in Advanced Optical Data Storage: Materials, Systems, and Interfaces to Computers, P. A. Mitkas, Z. U. Hasan, H. J. Coufal, G. T. Sincerbox, eds., Proc. SPIE3802, 18–29 (1999).
  21. Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  22. F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
    [CrossRef] [PubMed]
  23. A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
    [CrossRef]
  24. D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
    [CrossRef]
  25. T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
    [CrossRef]
  26. M. A. Neifeld, W.-C. Chou, “Information theoretic limits to the capacity of volume holographic optical memory,” Appl. Opt. 36, 514–517 (1997).
    [CrossRef] [PubMed]
  27. T. S. Cover, “Enumerative source encoding,” IEEE Trans. Inf. Theory 19, 73–77 (1973).
    [CrossRef]
  28. D. Slepian, “Permutation modulation,” Proc. IEEE 53, 228–236 (1965).
    [CrossRef]
  29. B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun., Special Issue on Signal Processing for High Density Storage Channels (to be published).
  30. M. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998).
    [CrossRef]
  31. G. W. Burr, G. Barking, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. A. Neifeld, “Gray-scale data pages for digital holographic data storage,” Opt. Lett. 23, 1218–1220 (1998).
    [CrossRef]

1999 (1)

1998 (5)

1997 (6)

1996 (4)

J. F. Heanue, K. Gũrkan, L. Hesselink, “Signal detection for page-access optical memories with intersymbol interference,” Appl. Opt. 35, 2431–2438 (1996).
[CrossRef] [PubMed]

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
[CrossRef] [PubMed]

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

1995 (2)

1994 (2)

1993 (1)

1992 (2)

1991 (1)

1973 (1)

T. S. Cover, “Enumerative source encoding,” IEEE Trans. Inf. Theory 19, 73–77 (1973).
[CrossRef]

1965 (1)

D. Slepian, “Permutation modulation,” Proc. IEEE 53, 228–236 (1965).
[CrossRef]

Aguilar, M.

Agulló-López, F.

Ashley, J.

Barking, G.

Bashaw, M.

Bashaw, M. C.

Bernal, M.

Bernal, M.-P.

Blaum, M.

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

Brady, D.

Burr, G. W.

M. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998).
[CrossRef]

G. W. Burr, G. Barking, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. A. Neifeld, “Gray-scale data pages for digital holographic data storage,” Opt. Lett. 23, 1218–1220 (1998).
[CrossRef]

G. W. Burr, W.-C. Chou, M. A. Neifeld, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “Experimental evaluation of user capacity in holographic data-storage systems,” Appl. Opt. 37, 5431–5443 (1998).
[CrossRef]

G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639–641 (1997).
[CrossRef] [PubMed]

R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
[CrossRef]

F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
[CrossRef] [PubMed]

G. W. Burr, B. Marcus, “Coding tradeoffs for high-density holographic data storage,” in Advanced Optical Data Storage: Materials, Systems, and Interfaces to Computers, P. A. Mitkas, Z. U. Hasan, H. J. Coufal, G. T. Sincerbox, eds., Proc. SPIE3802, 18–29 (1999).

Campbell, S.

Carrascosa, M.

Chou, W.-C.

Chuang, E.

Chugg, K. M.

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed., (IEEE Computer Soc. Press, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.

Coufal, H.

Cover, T. M.

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

Cover, T. S.

T. S. Cover, “Enumerative source encoding,” IEEE Trans. Inf. Theory 19, 73–77 (1973).
[CrossRef]

Curtis, K.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

Dowaie, J.

Fainman, Y.

Ford, J. E.

Garrett, T. N.

T. N. Garrett, P. A. Mitkas, “Three-dimensional error correcting codes for volumetric optical memories,” in Advanced Optical Memories and Interfaces to Computer Storage, Z. U. Hasan, P. A. Mitkas, eds., Proc. SPIE3468, 116–124 (1998).
[CrossRef]

Grygier, R. K.

Günther, H.

Gurkan, K.

Hayes, J. D.

Heanue, J.

Heanue, J. F.

Hesselink, L.

Hoffnagle, J. A.

Jefferson, C. M.

King, B. M.

B. M. King, M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275–6298 (1998).
[CrossRef]

B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun., Special Issue on Signal Processing for High Density Storage Channels (to be published).

Lee, S. H.

Leyva, V.

Ma, J.

Macfarlane, R. M.

Marcus, B.

G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639–641 (1997).
[CrossRef] [PubMed]

G. W. Burr, B. Marcus, “Coding tradeoffs for high-density holographic data storage,” in Advanced Optical Data Storage: Materials, Systems, and Interfaces to Computers, P. A. Mitkas, Z. U. Hasan, H. J. Coufal, G. T. Sincerbox, eds., Proc. SPIE3802, 18–29 (1999).

Markov, V.

Millerd, J.

Mitkas, P. A.

M. E. Schaffer, P. A. Mitkas, “Requirements and constraints for the design of smart photodetector arrays for page-oriented optical memories,” IEEE. J. Sel. Top. Quantum Electron. 4, 856–865 (1998).
[CrossRef]

T. N. Garrett, P. A. Mitkas, “Three-dimensional error correcting codes for volumetric optical memories,” in Advanced Optical Memories and Interfaces to Computer Storage, Z. U. Hasan, P. A. Mitkas, eds., Proc. SPIE3468, 116–124 (1998).
[CrossRef]

Mok, F. H.

Neifeld, M. A.

Norrie, M.

Psaltis, D.

Pu, A.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

Quintanilla, M.

Rakuljic, G. A.

Sasaki, H.

Schaffer, M. E.

M. E. Schaffer, P. A. Mitkas, “Requirements and constraints for the design of smart photodetector arrays for page-oriented optical memories,” IEEE. J. Sel. Top. Quantum Electron. 4, 856–865 (1998).
[CrossRef]

Shelby, R. M.

Siegel, P. H.

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

Sincerbox, G. T.

R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
[CrossRef]

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

Slepian, D.

D. Slepian, “Permutation modulation,” Proc. IEEE 53, 228–236 (1965).
[CrossRef]

Sridharan, S. K.

M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).
[CrossRef]

Taketomi, Y.

Thomas, J. A.

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

Timucin, D.

Trolinger, J.

Vardy, A.

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

Yariv, A.

Yeh, P.

Yi, X.

Appl. Opt. (7)

IEEE Trans. Inf. Theory (2)

T. S. Cover, “Enumerative source encoding,” IEEE Trans. Inf. Theory 19, 73–77 (1973).
[CrossRef]

A. Vardy, M. Blaum, P. H. Siegel, G. T. Sincerbox, “Conservative arrays: multidimensional modulation codes for holographic recording,” IEEE Trans. Inf. Theory 42, 227–230 (1996).
[CrossRef]

IEEE. J. Sel. Top. Quantum Electron. (1)

M. E. Schaffer, P. A. Mitkas, “Requirements and constraints for the design of smart photodetector arrays for page-oriented optical memories,” IEEE. J. Sel. Top. Quantum Electron. 4, 856–865 (1998).
[CrossRef]

J. Opt. Commun. (1)

M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Eng. (1)

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

Opt. Lett. (10)

G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639–641 (1997).
[CrossRef] [PubMed]

R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
[CrossRef]

G. W. Burr, G. Barking, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, M. A. Neifeld, “Gray-scale data pages for digital holographic data storage,” Opt. Lett. 23, 1218–1220 (1998).
[CrossRef]

V. Markov, J. Millerd, J. Trolinger, M. Norrie, J. Dowaie, D. Timucin, “Multilayer volume holographic optical memory,” Opt. Lett. 24, 265–267 (1999).
[CrossRef]

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef]

F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
[CrossRef] [PubMed]

J. Heanue, M. Bashaw, L. Hesselink, “Recall of linear combinations of stored data pages based on phase-code multiplexing in volume holography,” Opt. Lett. 19, 1079–1081 (1994).
[CrossRef] [PubMed]

S. Campbell, X. Yi, P. Yeh, “Hybrid sparse-wavelength angle-multiplexed optical data storage system,” Opt. Lett. 19, 2161–2163 (1994).
[CrossRef] [PubMed]

F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
[CrossRef] [PubMed]

Proc. IEEE (1)

D. Slepian, “Permutation modulation,” Proc. IEEE 53, 228–236 (1965).
[CrossRef]

Other (5)

B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun., Special Issue on Signal Processing for High Density Storage Channels (to be published).

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

G. W. Burr, B. Marcus, “Coding tradeoffs for high-density holographic data storage,” in Advanced Optical Data Storage: Materials, Systems, and Interfaces to Computers, P. A. Mitkas, Z. U. Hasan, H. J. Coufal, G. T. Sincerbox, eds., Proc. SPIE3802, 18–29 (1999).

T. N. Garrett, P. A. Mitkas, “Three-dimensional error correcting codes for volumetric optical memories,” in Advanced Optical Memories and Interfaces to Computer Storage, Z. U. Hasan, P. A. Mitkas, eds., Proc. SPIE3468, 116–124 (1998).
[CrossRef]

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed., (IEEE Computer Soc. Press, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.

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Figures (5)

Fig. 1
Fig. 1

Capacity of a VHM with on pixel a priori probability π1. Capacity is relative to an equal-priors (π1 = 1/2) memory.

Fig. 2
Fig. 2

IT capacity of a VHM with M pages. The thicker solid curve shows the memory capacity with an on pixel a priori probability π1 that maximizes the capacity; the dashed curve shows the memory capacity when π1 is forced to be 0.5. The circle-symbol curve along with the right-hand vertical axis shows the maximizing value of π1 as a function of M.

Fig. 3
Fig. 3

Block diagram of the VHM experiment.

Fig. 4
Fig. 4

Retrieved holographic data pages for (a) π1 = 1/4 and (b) π1 = 1/2.

Fig. 5
Fig. 5

BER’s for different page readout exposures for the sparse and dense memories. Error bars on the data points indicate the 95% confidence interval.

Equations (25)

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

ηpage=M/#M2.
Ijx=Ir+Io+2 ReEoEr* expikoj-kr·x,
AGt=A01-exp-t/τR,
AGt  A0/τR.
PBR|Er|2/|Eo|2=Ir/Io,
A0/τR  ReEoEr*=Ir/PBR.
AGt=AG0exp-t/τe,
τe  1/Ir+NONIo,
M˜/#  PBRPBR+NON.
M˜/#  BRBR+11NON
=M/# 1NON.
η  M˜/#M2
=M/#M21NON.
PrNON=n=Nnπ1nπ0N-n.
Eη=M/#M21π1N,
η  M/#M21π1N.
SNR  M/#M21π1N.
η*=M/#M21N/2.
M*=M/#η*π1N.
Ipπ1R0π1=-π1 log2π1-π0 log2π0,
Cπ1=M*Ipπ1N
M*R0π1N.
CM, π1=MNIpM, π1R0π1,
CIT=maxM,π1 CM, π1.
Ip=-½ log2 2πe-- pylog2 pydy,

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