Abstract

We derive the information theoretic limit to storage capacity in volume holographic optical memories for the limiting cases of dominant intensity noise (Gaussian noise) and dominant field noise (Rician noise). These capacity bounds are compared with the performance achievable using simple Reed–Solomon error-correcting codes.

© 1997 Optical Society of America

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References

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  1. G. Burr, F. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90 degree geometry,” Opt. Commun. 117, 49–55 (1995).
    [CrossRef]
  2. J. Hong, I. McMichael, T. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
    [CrossRef]
  3. J. Heanue, M. Bashaw, L. Hesselink, “Sparse selection of reference beams for wavelength- and angular-multiplexed volume holography,” J. Opt. Soc. Am. A 12, 1671–1676 (1995).
    [CrossRef]
  4. B. J. Goertzen, P. A. Mitkas, “Error-correcting code for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
    [CrossRef] [PubMed]
  5. M. A. Neifeld, J. D. Hayes, “Error-correction schemes for volume optical memories,” Appl. Opt. 34, 8183–8191 (1995).
    [CrossRef] [PubMed]
  6. M. A. Neifeld, M. McDonald, “Error-correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
    [CrossRef] [PubMed]
  7. J. Heanue, M. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Am. A 12, 2432–2439 (1995).
    [CrossRef]
  8. C. Gu, J. Hong, I. McMichael, R. Saxena, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  9. D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
    [CrossRef]

1995

1994

1992

Bashaw, M.

Brady, D.

Burr, G.

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

Chang, T.

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

Christian, W.

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

Goertzen, B. J.

Gu, C.

Hayes, J. D.

Heanue, J.

Hesselink, L.

Hong, J.

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

C. Gu, J. Hong, I. McMichael, R. Saxena, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
[CrossRef]

McDonald, M.

McMichael, I.

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

C. Gu, J. Hong, I. McMichael, R. Saxena, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
[CrossRef]

Mitkas, P. A.

Mok, F.

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

Neifeld, M. A.

Paek, E. G.

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

Psaltis, D.

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

D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
[CrossRef]

Saxena, R.

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Figures (3)

Fig. 1
Fig. 1

Mutual information versus the noise standard deviation for an optical memory channel characterized by Gaussian ( RmaxG ) and Rician ( RmaxR ) intensity probability density functions.

Fig. 2
Fig. 2

Capacity versus the number of pages for noise-free (C), Gaussian-dominated (C G ), and Rician-dominated (C R ) cases.

Fig. 3
Fig. 3

Capacity versus the number of pages in the information theoretic limit (C R and C G ) compared with the performance achievable by use of RS codes (CRRS and CGRS) required to achieve a decoded value of BER = 10-12.

Equations (4)

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p0/1RI=12σr2exp-I+S0/12σr2I0IS0/1σr2,
σI2=4σr2σr2+S0/1,
p0/1GI=12πσg2exp-I-S0/122σg2,
RmaxR/G=maxπ0,π1π0-p0R/GI×log2p0R/GIπ0p0R/GI+π1p1R/GIdI+π1-p1R/GI×log2p1R/GIπ0p0R/GI+π1p1R/GIdI,

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