Abstract

We study the use of soft-decision array decoding in a volume holographic memory (VHM) system that is corrupted by interpixel interference (IPI) and detector noise. Soft-decision methods can unify equalization and error decoding. A highly parallel array decoder is presented in the context of two-dimensional low-pass channel mitigation and error correction. The new decoding algorithm is motivated by iterative turbo-decoding methods and is capable of incorporating a priori knowledge of the corrupting IPI channel during decoding. The resulting joint detection decoding algorithm is shown to offer VHM capacity and density performance superior to that of hard-decision n=255 Reed–Solomon codes in concatenation with a Wiener filter.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. J. van Heerden, “A new optical method of storing and retrieving information,” Appl. Opt. 2, 387–392 (1963).
    [CrossRef]
  2. K. Buse, A. Adibi, D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
    [CrossRef]
  3. H. Guenther, G. Wittmann, R. M. Macfarlane, R. R. Neurgaonkar, “Intensity dependence and white-light gating of two-color photorefractive gratings in LiNbO3,” Opt. Lett. 22, 1305–1307 (1997).
    [CrossRef]
  4. L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett. 24, 487–489 (1999).
    [CrossRef]
  5. W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
    [CrossRef]
  6. J. D. Downie, D. A. Timuçin, D. T. Smithey, M. Crew, “Long holographic lifetimes in bacteriorhodopsin films,” Opt. Lett. 23, 730–732 (1998).
    [CrossRef]
  7. J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).
  8. H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
    [CrossRef]
  9. L. Dhar, K. Curtis, M. Tackitt, M. Schilling, S. Campbell, W. Wilson, A. Hill, C. Boyd, N. Levinos, A. Harris, “Holographic storage of multiple high-capacity digital data pages in thick photopolymer systems,” Opt. Lett. 23, 1710–1712 (1998).
    [CrossRef]
  10. 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]
  11. I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
    [CrossRef] [PubMed]
  12. E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Recording of 6000 holograms by use of spectral hole burning,” Appl. Opt. 34, 4140–4148 (1995).
    [CrossRef] [PubMed]
  13. S. A. Domrovskii, “Effectiveness of using error-correcting codes in holographic storage systems,” Avtometriya 2, 57–61 (1989).
  14. M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
    [CrossRef] [PubMed]
  15. B. J. Goertzen, P. A. Mitkas, “Error-correcting codes for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
    [CrossRef] [PubMed]
  16. 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]
  17. G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.
  18. 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]
  19. V. Vadde, B. V. K. V. Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, J. Z. Kwiecien, eds., Proc. SPIE3109, 245–250 (1997).
    [CrossRef]
  20. B. M. King, M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275–6298 (1998).
    [CrossRef]
  21. X. Chen, K. M. Chugg, M. A. Neifeld, “Near-optimal parallel distributed data detection for page-oriented optical memories,” IEEE J. Sel. Top. Quantum Electron. 4, 866–879 (1998).
    [CrossRef]
  22. K. M. Chugg, X. Chen, M. A. Neifeld, “Two-dimensional equalization in coherent and incoherent page-oriented optical memory,” J. Opt. Soc. Am. A 16, 549–562 (1999).
    [CrossRef]
  23. S. Lin, C. Daniel J., Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).
  24. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  25. D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
    [CrossRef]
  26. F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
    [CrossRef] [PubMed]
  27. R. J. G. Smith, “Easily decodable efficient self-orthogonal block codes,” Electron. Lett. 13, 173–174 (1977).
    [CrossRef]
  28. J. Hagenauer, “Source-controlled channel decoding,” IEEE Trans. Commun. 43, 2449–2457 (1995).
    [CrossRef]
  29. J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
    [CrossRef]
  30. C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.
  31. C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
    [CrossRef]
  32. S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
    [CrossRef]
  33. S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
    [CrossRef]
  34. M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
    [CrossRef] [PubMed]
  35. H. L. V. Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).
  36. M.-P. 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]

1999 (2)

1998 (8)

M.-P. 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]

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

J. D. Downie, D. A. Timuçin, D. T. Smithey, M. Crew, “Long holographic lifetimes in bacteriorhodopsin films,” Opt. Lett. 23, 730–732 (1998).
[CrossRef]

L. Dhar, K. Curtis, M. Tackitt, M. Schilling, S. Campbell, W. Wilson, A. Hill, C. Boyd, N. Levinos, A. Harris, “Holographic storage of multiple high-capacity digital data pages in thick photopolymer systems,” Opt. Lett. 23, 1710–1712 (1998).
[CrossRef]

S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
[CrossRef]

K. Buse, A. Adibi, D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

X. Chen, K. M. Chugg, M. A. Neifeld, “Near-optimal parallel distributed data detection for page-oriented optical memories,” IEEE J. Sel. Top. Quantum Electron. 4, 866–879 (1998).
[CrossRef]

1997 (3)

1996 (7)

1995 (4)

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

J. Hagenauer, “Source-controlled channel decoding,” IEEE Trans. Commun. 43, 2449–2457 (1995).
[CrossRef]

B. J. Goertzen, P. A. Mitkas, “Error-correcting codes for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
[CrossRef] [PubMed]

E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, U. P. Wild, “Recording of 6000 holograms by use of spectral hole burning,” Appl. Opt. 34, 4140–4148 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

1989 (1)

S. A. Domrovskii, “Effectiveness of using error-correcting codes in holographic storage systems,” Avtometriya 2, 57–61 (1989).

1988 (1)

1977 (1)

R. J. G. Smith, “Easily decodable efficient self-orthogonal block codes,” Electron. Lett. 13, 173–174 (1977).
[CrossRef]

1963 (1)

Adibi, A.

K. Buse, A. Adibi, D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

Altner, S. B.

Ashley, J.

Benedetto, S.

S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
[CrossRef]

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

Bernal, M.-P.

Bernet, S.

Berrou, C.

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Betzos, G. A.

G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.

Boyd, C.

Brady, D.

Bratcher, M. S.

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

Burr, G. W.

Buse, K.

K. Buse, A. Adibi, D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

Campbell, S.

Chang, T. Y.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

Chen, X.

K. M. Chugg, X. Chen, M. A. Neifeld, “Two-dimensional equalization in coherent and incoherent page-oriented optical memory,” J. Opt. Soc. Am. A 16, 549–562 (1999).
[CrossRef]

X. Chen, K. M. Chugg, M. A. Neifeld, “Near-optimal parallel distributed data detection for page-oriented optical memories,” IEEE J. Sel. Top. Quantum Electron. 4, 866–879 (1998).
[CrossRef]

Christian, W.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

Chugg, K. M.

Coufal, H.

Crew, M.

Curtis, K.

Daniel J., C.

S. Lin, C. Daniel J., Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Dhar, L.

Divsalar, D.

S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
[CrossRef]

Domrovskii, S. A.

S. A. Domrovskii, “Effectiveness of using error-correcting codes in holographic storage systems,” Avtometriya 2, 57–61 (1989).

Downie, J. D.

Eichler, H. J.

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

Glavieux, A.

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Goertzen, B. J.

Graf, F. R.

Grunnet-Jepsen, A.

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

Grygier, R. K.

Guenther, H.

Günther, H.

Gürkan, K.

Hagenauer, J.

S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
[CrossRef]

J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

J. Hagenauer, “Source-controlled channel decoding,” IEEE Trans. Commun. 43, 2449–2457 (1995).
[CrossRef]

Hale, A.

Harris, A.

Heanue, J. F.

Hesselink, L.

Hill, A.

Hoffnagle, J. A.

Hong, J. H.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

Hutton, J. F.

G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.

Jefferson, C. M.

Katz, H. E.

King, B. M.

Kuemmel, P.

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

Kumar, B. V. K. V.

V. Vadde, B. V. K. V. Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, J. Z. Kwiecien, eds., Proc. SPIE3109, 245–250 (1997).
[CrossRef]

Levinos, N.

Lin, S.

S. Lin, C. Daniel J., Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Macfarlane, R. M.

Maniloff, E. S.

Marcus, B.

McDonald, M.

McMichael, I.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

Mitkas, P. A.

B. J. Goertzen, P. A. Mitkas, “Error-correcting codes for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
[CrossRef] [PubMed]

G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.

Moerner, W. E.

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

Mok, F. H.

Montorsi, G.

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

Neifeld, M. A.

Neurgaonkar, R. R.

Offer, E.

J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

Orlic, S.

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

Paek, E. G.

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Appl. Opt. 34, 2193–2203 (1995).

Papke, L.

J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

Pletcher, D.

Porter, M.

G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.

Psaltis, D.

Quintanilla, M.

Renn, A.

Schilling, F. C.

Schilling, M.

Schilling, M. L.

Schnoes, M. G.

Shelby, R. M.

Sincerbox, G. T.

Smith, R. J. G.

R. J. G. Smith, “Easily decodable efficient self-orthogonal block codes,” Electron. Lett. 13, 173–174 (1977).
[CrossRef]

Smithey, D. T.

Tackitt, M.

Thitimajshima, P.

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Thompson, C. L.

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

Timuçin, D. A.

Trees, H. L. V.

H. L. V. Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Twieg, R. J.

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

Vadde, V.

V. Vadde, B. V. K. V. Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, J. Z. Kwiecien, eds., Proc. SPIE3109, 245–250 (1997).
[CrossRef]

van Heerden, P. J.

Wagner, K.

Wappelt, A.

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

Wild, U. P.

Wilson, W.

Wittmann, G.

Appl. Opt. (8)

Avtometriya (1)

S. A. Domrovskii, “Effectiveness of using error-correcting codes in holographic storage systems,” Avtometriya 2, 57–61 (1989).

Electron. Lett. (1)

R. J. G. Smith, “Easily decodable efficient self-orthogonal block codes,” Electron. Lett. 13, 173–174 (1977).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

S. Benedetto, D. Divsalar, J. Hagenauer, “Guest editorial: Concatenated coding techniques and iterative decoding: sailing toward channel capacity,” IEEE J. Sel. Areas Commun. 16, 137–139 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

X. Chen, K. M. Chugg, M. A. Neifeld, “Near-optimal parallel distributed data detection for page-oriented optical memories,” IEEE J. Sel. Top. Quantum Electron. 4, 866–879 (1998).
[CrossRef]

H. J. Eichler, P. Kuemmel, S. Orlic, A. Wappelt, “High-density disk storage by multiplexed microholograms,” IEEE J. Sel. Top. Quantum Electron. 4, 840–848 (1998).
[CrossRef]

IEEE Trans. Commun. (2)

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

J. Hagenauer, “Source-controlled channel decoding,” IEEE Trans. Commun. 43, 2449–2457 (1995).
[CrossRef]

IEEE Trans. Inf. Theory (2)

J. Hagenauer, E. Offer, L. Papke, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

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

Nature (London) (1)

K. Buse, A. Adibi, D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
[CrossRef]

Opt. Lett. (10)

L. Dhar, K. Curtis, M. Tackitt, M. Schilling, S. Campbell, W. Wilson, A. Hill, C. Boyd, N. Levinos, A. Harris, “Holographic storage of multiple high-capacity digital data pages in thick photopolymer systems,” Opt. Lett. 23, 1710–1712 (1998).
[CrossRef]

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

M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
[CrossRef] [PubMed]

B. J. Goertzen, P. A. Mitkas, “Error-correcting codes for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
[CrossRef] [PubMed]

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]

H. Guenther, G. Wittmann, R. M. Macfarlane, R. R. Neurgaonkar, “Intensity dependence and white-light gating of two-color photorefractive gratings in LiNbO3,” Opt. Lett. 22, 1305–1307 (1997).
[CrossRef]

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]

J. D. Downie, D. A. Timuçin, D. T. Smithey, M. Crew, “Long holographic lifetimes in bacteriorhodopsin films,” Opt. Lett. 23, 730–732 (1998).
[CrossRef]

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett. 24, 487–489 (1999).
[CrossRef]

M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
[CrossRef] [PubMed]

Other (6)

W. E. Moerner, A. Grunnet-Jepsen, C. L. Thompson, M. S. Bratcher, R. J. Twieg, “Recent advances in photorefractive polymer materials,” in Nonlinear Optical Properties of Organic Materials X, M. G. Kuzyk, ed., Proc. SPIE3147, 84–94 (1997).
[CrossRef]

S. Lin, C. Daniel J., Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

G. A. Betzos, J. F. Hutton, M. Porter, P. A. Mitkas, “Evaluation of array codes for page-oriented optical memories,” in Optics in Computing, Vol. 8 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 204–206.

V. Vadde, B. V. K. V. Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, J. Z. Kwiecien, eds., Proc. SPIE3109, 245–250 (1997).
[CrossRef]

H. L. V. Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

The VHM system model used in this paper includes the 1/M2 volume holographic memory (VHM) diffraction efficiency signal scaling law, a low-pass filter, and additive white Gaussian noise (AWGN).

Fig. 2
Fig. 2

Storage capacity as a function of number of pages stored in a VHM. The five dashed curves represent the performance with the use of Reed–Solomon codes. The open- and closed-circle curves are for hard- and soft-decision row–column–diagonal (RCDS) array codes, respectively. The output bit-error rate (BER) is 10-12, and the VHM characteristic constant γVHM=2.3×108.

Fig. 3
Fig. 3

Example of RCDS(k=5) array codeword where 4×k parity bits are appended to the k×k information bits. R, C, D, and S indicate the row, column, (right-handed) diagonal and sinistral-diagonal parity columns. The associated code rate is k2/(k2+4k).

Fig. 4
Fig. 4

Output BER performance as a function of channel signal-to-noise ratio (SNR) while using hard-decision (solid curves) and soft-decision (dashed curves) RCDS decoding schemes. The symbols indicate the Monte Carlo simulation data points. Circles and diamonds represent the use of RCDS k=7 and k=71 array codes, respectively.

Fig. 5
Fig. 5

The soft-decision RCDS array decoding algorithm is an iterative decoding scheme operating on the soft-decision results. The initial value of LLRz(u=0) is based on the received analog value of pixel z. During succeeding iterations, the LLRz estimate is modified and updated by incorporating RCDS codeword constraints, i.e., the RCDS update rule.

Fig. 6
Fig. 6

Output BER performance while using the soft-decision RCDS(3) code during the first ten iterations. Different symbols correspond to different values of β, and the two groups of curves are for different SNR values.

Fig. 7
Fig. 7

Schematic of the Q-bit-flip likelihood-based detection algorithm. Instead of considering all the possible input patterns, this pseudo-maximum-likelihood detection scheme searches only the candidate set {nxΩ}Q for the (pseudo) maximum log-likelihood (LL) value.

Fig. 8
Fig. 8

Output BER performance while using the Q-bit-flip likelihood detection scheme during the first 20 iterations. Two different groups of curves correspond to different SNR values, and different symbols represent different values of Q.

Fig. 9
Fig. 9

Comparison of the output BER performance as a function of channel SNR between our likelihood-based detection scheme and the use of a Wiener filter. Solid and dashed curves represent systems with different system LPBW values, and different symbols correspond to the use of the Wiener filter and Q-bit-flip detection methods.

Fig. 10
Fig. 10

The joint detection soft-decision array (JDSA) decoding algorithm is an iterative algorithm with iteration index u. LL ratio updates are independently generated from the soft-decision RCDS decoding (LLRz|RCDSU) and the likelihood-based 2-D detection scheme (LLRz|2-DU).

Fig. 11
Fig. 11

The JDSA decoder is compared with two other conventional decoders that combine a Wiener filter in concatenation with (1) a RS(n=255) error-correction decoder and (2) a hard-decision RCDS decoder.

Fig. 12
Fig. 12

Optimum storage capacity performance for the use of JDSA(71), W-RS(255), and W-hard RCDS decoders.

Fig. 13
Fig. 13

Storage density performance for the use of JDSA(71), W-RS(255), and W-hard RCDS decoders.

Fig. 14
Fig. 14

Output BER performance of the soft-decision RCDS(71) code with β=0.4 and SNR=29 during the first seven iterations. Different curves correspond to the use of different soft-value resolutions.

Equations (30)

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

{x}R(i){x(i, j)|j=0, 1,, k-1}
{x}C(j){x(i,j)|i=0, 1,, k-1},
{x}D(j){x(i,j)|i=0, 1,, k-1; j=(j-i)mod k)},
{x}S(i){x(i,j)|j=0, 1,, k-1; i=(j+i)mod k)},
R(i)=XOR[{x}R(i)],
Rx(i, j)=R(i),
Cx(i, j)=C(j),
Dx(i, j)=D((j-i)mod k),
Sx(i, j)=S((j+i)mod k).
x(i,j)=XOR[{x}R-x(i, j)],
R(i)=XOR[{R}-R(i)]  XOR[{R¯}],
BERx(out)=t=3nAt[BER(raw)]t[1-BER(raw)]n-t,
A3=6k2+4k3,A4=-6k2 +7k4+4k5,A5=10k2-143k3-9k4-43 k5+4k6+2k7,A6=-10k2+6k3+403k4-236 k5-193k6-43k7+32 k8+23 k9.
LLR(X|yX)=LLR(yX|X)+LLR(X),
LLR(yX|X)=logP(yX|X=0)P(yX|X=1),
LLR(XOR[{Xi|i=0, 1,, k-1}])
i=0k-1sgn[LLR(Xi)] ×mini=0,, k-1[|LLR(Xi)|].
LLRx|R=x{x}R-xsgn[LLR(x)]×minx{x}R-x [|LLR(x)|],
(i)LLRR(i)|yR(i),
(ii)LLRR(i)|{x}R(i)=x{x}R(i)sgn[LLR(x)]×minx{x}R(i) |LLR(x)|,
(iiiv)LLRR(i)|R¯=x{R}-R(i){R¯}sgn[LLR(x)]×minx{R}-R(i){R¯}|LLR(x)|.
LLRxU(u)=LLRx|R(u)+LLRx|C(u)+LLRx|D(u)+LLRx|S(u).
LLRR(i)U(u)=LLRR(i)|{x}R(i)(u)+LLRR(i)|C(u)+LLRR(i)|D(u)+LLRR(i)|S(u).
LLRz(u+1)=(1-β)LLRz(u)+βLLRzU(u),
y(i, j)x(i, j)f(0, 0)+(l,m)NijΩx(i-l, j-m)f(l, m)+w(i, j)
=x(i, j)f(0, 0)+ybiasnijΩ+w(i, j),
LLx=Xˆ(u)=max{nxΩ}Q{log[Pw(y-Xˆf(0, 0)-ybiasnxΩ)]+log[P(nxΩ)]},
LLRxU(u)=LLx=0(u)-LLx=1(u),
LLRx(u)=(1-δ)LLRx(u-1)+δLLRxU(u).
LLRz(u+1)=(1-β-δ)LLRz(u)+βLLRz|RCDSU(u)+δLLRz|2-DU(u),

Metrics