Abstract

We discuss experimental results of a versatile nonbinary modulation and channel code appropriate for two-dimensional page-oriented holographic memories. An enumerative permutation code is used to provide a modulation code that permits a simple maximum-likelihood detection scheme. Experimental results from the IBM Demon testbed are used to characterize the performance and feasibility of the proposed modulation and channel codes. A reverse coding technique is introduced to combat the effects of error propagation on the modulation-code performance.

We find experimentally that level-3 pixels achieve the best practical results, offering an 11–35% improvement in capacity and a 12% increase in readout rate as compared with local binary thresholding techniques.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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  7. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. T. N. Garrett, P. A. Mitkas, “Three-dimensional error correcting codes for volumetric optical memories,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 116–124 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  24. K. Immink, A. Janssen, “Error propagation assessment of enumerative coding schemes,” Proc. IEEE International Conference on Communications 2, 961–963 (1998).
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    [CrossRef]
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2001 (1)

B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun. 19, 783–790 (2001).
[CrossRef]

2000 (1)

1998 (8)

K. Immink, A. Janssen, “Error propagation assessment of enumerative coding schemes,” Proc. IEEE International Conference on Communications 2, 961–963 (1998).

J. L. Fan, A. Calderbank, “A modified concatenated coding scheme, with applications to magnetic data storage,” IEEE Trans. Inf. Theory 44, 1565–1574 (1998).
[CrossRef]

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. Ashley, B. Marcus, “Two-dimensional lowpass filtering codes for holographic storage,” IEEE Trans. Commun. 46, 724–727 (1998).
[CrossRef]

G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, “Noise reduction of page-oriented data storage by inverse filtering during recording,” Opt. Lett. 23, 289–291 (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]

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

1997 (2)

1996 (3)

1995 (2)

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Amer. A 12, 2432–2439 (1995).
[CrossRef]

G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

1994 (1)

1991 (1)

1981 (1)

W. Bliss, “Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation,” IBM Tech. Discl. Bull. 23, 4633–4634 (1981).

Ashley, J.

Barking, G.

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Amer. A 12, 2432–2439 (1995).
[CrossRef]

Bhagavatula, V.

V. Bhagavatula, M. Wong, “Crosstalk-limited signal-to-noise ratio resulting from phase errors in phase-multiplexed volume holographic storage,” in Optical Society of America 1996 Annual Meeting, p. 145 (Optical Society of America, Washington, D.C., 1996), session WZ6.

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]

Bliss, W.

W. Bliss, “Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation,” IBM Tech. Discl. Bull. 23, 4633–4634 (1981).

Burr, G. W.

Calderbank, A.

J. L. Fan, A. Calderbank, “A modified concatenated coding scheme, with applications to magnetic data storage,” IEEE Trans. Inf. Theory 44, 1565–1574 (1998).
[CrossRef]

Chou, W.-C.

Coufal, H.

Esener, S. C.

Fainman, Y.

Fan, J. L.

J. L. Fan, A. Calderbank, “A modified concatenated coding scheme, with applications to magnetic data storage,” IEEE Trans. Inf. Theory 44, 1565–1574 (1998).
[CrossRef]

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, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 116–124 (1998).
[CrossRef]

Grygier, R. K.

Gürkan, K.

Heanue, J. F.

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

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Amer. A 12, 2432–2439 (1995).
[CrossRef]

Hesselink, L.

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

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Amer. A 12, 2432–2439 (1995).
[CrossRef]

Hoffnagle, J. A.

Immink, K.

K. Immink, A. Janssen, “Error propagation assessment of enumerative coding schemes,” Proc. IEEE International Conference on Communications 2, 961–963 (1998).

Janssen, A.

K. Immink, A. Janssen, “Error propagation assessment of enumerative coding schemes,” Proc. IEEE International Conference on Communications 2, 961–963 (1998).

Jefferson, C. M.

King, B. M.

B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun. 19, 783–790 (2001).
[CrossRef]

B. M. King, M. A. Neifeld, “Sparse modulation coding for increased capacity in volume holographic storage,” Appl. Opt. 39, 6681–6688 (2000).
[CrossRef]

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, “Unequal a-priori probabilities for holographic 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, 40–45 (1999).

Lee, S. H.

Ma, J.

Mansuripur, M.

M. Mansuripur, “Enumerative modulation coding with arbitrary constraints and post-modulation error correction coding for data storage systems,” in Optical Data Storage 191, J. J. Burke, T. A. Shull, N. Imamura, eds., Proc. SPIE1499, 72–86 (1991).

Marcus, B.

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, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 116–124 (1998).
[CrossRef]

Mok, F. H.

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, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

Neifeld, M. A.

Olson, B. H.

Psaltis, D.

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, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

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]

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.

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]

Taketomi, Y.

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]

Wong, M.

V. Bhagavatula, M. Wong, “Crosstalk-limited signal-to-noise ratio resulting from phase errors in phase-multiplexed volume holographic storage,” in Optical Society of America 1996 Annual Meeting, p. 145 (Optical Society of America, Washington, D.C., 1996), session WZ6.

Appl. Opt. (5)

IBM Tech. Discl. Bull. (1)

W. Bliss, “Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation,” IBM Tech. Discl. Bull. 23, 4633–4634 (1981).

IEEE J. Sel. Areas Commun. (1)

B. M. King, M. A. Neifeld, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage,” IEEE J. Sel. Areas Commun. 19, 783–790 (2001).
[CrossRef]

IEEE Trans. Commun. (1)

J. Ashley, B. Marcus, “Two-dimensional lowpass filtering codes for holographic storage,” IEEE Trans. Commun. 46, 724–727 (1998).
[CrossRef]

IEEE Trans. Inf. Theory (2)

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]

J. L. Fan, A. Calderbank, “A modified concatenated coding scheme, with applications to magnetic data storage,” IEEE Trans. Inf. Theory 44, 1565–1574 (1998).
[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. Soc. Amer. A (1)

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Amer. A 12, 2432–2439 (1995).
[CrossRef]

Opt. Commun. (1)

G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

Opt. Lett. (6)

Proc. IEEE International Conference on Communications (1)

K. Immink, A. Janssen, “Error propagation assessment of enumerative coding schemes,” Proc. IEEE International Conference on Communications 2, 961–963 (1998).

Other (6)

S. B. Wicker, V. K. Bhargava, eds., Reed-Solomon Codes and Their Applications (IEEE Press, New York, 1994).

B. M. King, M. A. Neifeld, “Unequal a-priori probabilities for holographic 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, 40–45 (1999).

M. Mansuripur, “Enumerative modulation coding with arbitrary constraints and post-modulation error correction coding for data storage systems,” in Optical Data Storage 191, J. J. Burke, T. A. Shull, N. Imamura, eds., Proc. SPIE1499, 72–86 (1991).

V. Bhagavatula, M. Wong, “Crosstalk-limited signal-to-noise ratio resulting from phase errors in phase-multiplexed volume holographic storage,” in Optical Society of America 1996 Annual Meeting, p. 145 (Optical Society of America, Washington, D.C., 1996), session WZ6.

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

Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds., (Springer-Verlag, Berlin, 2000).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a) Example of an SLM image, (b) reconstructed hologram for a 3-ary valued pixel case.

Fig. 2
Fig. 2

Histogram of a 3-level hologram.

Fig. 3
Fig. 3

Experimental data and curve fit of gray-scale level 2 mean pixel value to bit-error-rate for the XA32 data set.

Fig. 4
Fig. 4

Experimental estimated VHM capacity. The lines connect symbols that differ only in the code block length parameter (all other code parameters remain the same).

Fig. 5
Fig. 5

Histogram of the number of bit errors incurred when decoding random codewords from code A46 with weight 2 error patterns.

Fig. 6
Fig. 6

Block diagram of reverse encoding scheme. (a) Type I: parity pixels violate sparse constraint. (b) Type II: parity pixels meet sparse constraint due to encoding with enumeration code E2.

Fig. 7
Fig. 7

Unprotected BER performance of the A4 set of codes (n = {12, 24, 48, 90}, L = 4). Error propagation limits the performance of the long codes.

Fig. 8
Fig. 8

Reverse coding on the A46 (n = 90, L = 4) code using an inner RS(255, K, t) code.

Fig. 9
Fig. 9

Comparison of theoretical and experimental input/output error-rates for data sets XA2, XA3, XA4, and XB4.

Fig. 10
Fig. 10

Extrapolated reverse code performance for XA3 data set. Triangle symbols mark the performance without reverse coding. Applying type I (circle symbols) and II (square symbols) reverse codes significantly improves the capacity. The lines connect symbols that differ only in the code block length parameter (all other code parameters remain the same).

Tables (5)

Tables Icon

Table 1 Experimental Data Sets and Key Parameters of Interest (Part I)

Tables Icon

Table 2 Experimental Data Sets and Key Parameters of Interest (Part II)

Tables Icon

Table 3 Experimental Capacity Parameters

Tables Icon

Table 4 Change in Capacity and Readout Ratea

Tables Icon

Table 5 Inner-Code Parameters

Equations (21)

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

ηp=M/#M2.
ηp=M/#M212π1,
η=M/#M21π1N,
ηi=M/#iM2.
BR=Pr/Po.
Po=i=0L-1 PiNi,
Ai  Pi/PL-1.
M/#i=PrPiPr+Po
=PrPoBR+1PL-1AiPo
=BRBR+1PL-1AiPL-1j=0L-1 AjNj
=BRBR+1AiN j=0L-1 Ajπj
=M/# AiN j=0L-1 Ajπj.
ηi=M/#M2AiN j=0L-1 Ajπj.
M=M/#N1ηL-11j=0L-1 Ajπj.
M*=M/#N1μL-1*1j=0L-1 Ajπj.
C=M*NR,
C=M*NR
=FMFBSRER0
=M/#2N1μL-1*12 j=0L-1 AjπjRER0.
Bj  j-1L-1,
γ=j=0L-1 Bjπjj=0L-1 Ajπj.

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