OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 35 — Dec. 10, 2000
  • pp: 6681–6688

Sparse modulation coding for increased capacity in volume holographic storage

Brian M. King and Mark A. Neifeld  »View Author Affiliations

Applied Optics, Vol. 39, Issue 35, pp. 6681-6688 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (975 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(210.2860) Optical data storage : Holographic and volume memories

Original Manuscript: December 13, 1999
Revised Manuscript: August 28, 2000
Published: December 10, 2000

Brian M. King and Mark A. Neifeld, "Sparse modulation coding for increased capacity in volume holographic storage," Appl. Opt. 39, 6681-6688 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]
  6. G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992). [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]
  8. M. A. Neifeld, J. D. Hayes, “Error correction schemes for volume optical memories,” Appl. Opt. 34, 8183–8191 (1995). [CrossRef] [PubMed]
  9. J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Am. A 12, 2432–2439 (1995). [CrossRef]
  10. 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]
  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]
  12. M. Aguilar, M. Carrascosa, F. Agulló-López, “Optimization of selective erasure in photorefractive memories,” J. Opt. Soc. Am. B 14, 110–115 (1997). [CrossRef]
  13. 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]
  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited