Abstract

We present a parallel algorithm for the reliable detection of two-dimensional binary data in page-oriented memories. The development of the proposed pseudodecision-feedback equalization (PDFE) method is motivated by the classical decision-feedback equalization receiver. The technique takes advantage of the known or the estimated optical system characteristics to mitigate space-variant blur and additive thermal noise. We extend the method to correct for fixed-pattern errors including magnification, rotation, and transverse shift. Advantages of the PDFE algorithm include its parallel design, low computational complexity, and local connectivity. A system-capacity metric is used to compare the performance of the PDFE receiver with other conventional approaches, including the simple threshold, the 1:2 modulation code, and the Wiener filter. Results show the PDFE to outperform all the above techniques over a variety of channels for both incoherent and coherent systems. Implementation issues are discussed, and a MOSIS (Metal-Oxide Semiconductor Implementation Service) 2-μm design is presented.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. 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]
  3. M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).
  4. M. Aguilar, M. Carrascosa, F. Agulló-López, “Optimization of selective erasure in photorefractive memories,” J. Opt. Soc. Am. B 14, 110–115 (1997).
    [CrossRef]
  5. M. A. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
    [CrossRef] [PubMed]
  6. M. A. Neifeld, M. McDonald, “Optical design for page access to volume optical media,” Appl. Opt. 35, 2418–2430 (1996).
    [CrossRef] [PubMed]
  7. 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]
  8. M. A. Neifeld, J. D. Hayes, “Error-correction schemes for volume optical memories,” Appl. Opt. 34, 8183–8191 (1995).
    [CrossRef] [PubMed]
  9. F. Dai, C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
    [CrossRef]
  10. M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
    [CrossRef] [PubMed]
  11. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  12. G. D. Forney, “The Viterbi algorithm,” Proc. IEEE 61, 268–278 (1973).
    [CrossRef]
  13. K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 956–962.
  14. 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]
  15. C. L. Miller, B. R. Hunt, M. A. Neifeld, M. W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 1, pp. 181–184.
    [CrossRef]
  16. D. Messerschmitt, “A geometric theory of intersymbol interference: part I,” Bell Sys. Tech. J. 52, 1483–1519 (1973).
  17. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. E. A. Lee, D. G. Messerschmitt, Digital Communications (Kluwer, Dordrecht, The Netherlands, 1988).
  23. D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
    [CrossRef]
  24. S. S. Haykin, Neural Networks: A Comprehensive Foundation (Macmillan, New York, 1994).

1997

1996

1995

1994

1993

1992

1973

G. D. Forney, “The Viterbi algorithm,” Proc. IEEE 61, 268–278 (1973).
[CrossRef]

D. Messerschmitt, “A geometric theory of intersymbol interference: part I,” Bell Sys. Tech. J. 52, 1483–1519 (1973).

Aguilar, M.

Agulló-López, F.

Ashley, J.

Bashaw, M. C.

Bernal, M.-P.

Brady, D.

Burr, G. W.

Carrascosa, M.

Chang, T. Y.

Chou, W.-C.

Christian, W.

Chugg, K. M.

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]

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 956–962.

Coufal, H.

Dai, F.

Forney, G. D.

G. D. Forney, “The Viterbi algorithm,” Proc. IEEE 61, 268–278 (1973).
[CrossRef]

Grygier, R. K.

Gu, C.

Günther, H.

Gürkan, K.

Hayes, J. D.

Haykin, S. S.

S. S. Haykin, Neural Networks: A Comprehensive Foundation (Macmillan, New York, 1994).

Heanue, J. F.

Hesselink, L.

Hoffnagle, J. A.

Hong, J. H.

Hunt, B. R.

C. L. Miller, B. R. Hunt, M. A. Neifeld, M. W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 1, pp. 181–184.
[CrossRef]

Jefferson, C. M.

King, B. M.

Lee, E. A.

E. A. Lee, D. G. Messerschmitt, Digital Communications (Kluwer, Dordrecht, The Netherlands, 1988).

Macfarlane, R. M.

Marcellin, M. W.

C. L. Miller, B. R. Hunt, M. A. Neifeld, M. W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 1, pp. 181–184.
[CrossRef]

Marcus, B.

McDonald, M.

McMichael, I.

Messerschmitt, D.

D. Messerschmitt, “A geometric theory of intersymbol interference: part I,” Bell Sys. Tech. J. 52, 1483–1519 (1973).

Messerschmitt, D. G.

E. A. Lee, D. G. Messerschmitt, Digital Communications (Kluwer, Dordrecht, The Netherlands, 1988).

Miller, C. L.

C. L. Miller, B. R. Hunt, M. A. Neifeld, M. W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 1, pp. 181–184.
[CrossRef]

Mok, F. H.

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]

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

Neifeld, M. A.

Pletcher, D.

Proakis, J. G.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

Psaltis, D.

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]

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

Shelby, R. M.

Sincerbox, G. T.

Sridharan, S. K.

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

Appl. Opt.

Bell Sys. Tech. J.

D. Messerschmitt, “A geometric theory of intersymbol interference: part I,” Bell Sys. Tech. J. 52, 1483–1519 (1973).

J. Opt. Commun.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

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.

Proc. IEEE

G. D. Forney, “The Viterbi algorithm,” Proc. IEEE 61, 268–278 (1973).
[CrossRef]

Other

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 956–962.

C. L. Miller, B. R. Hunt, M. A. Neifeld, M. W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 1, pp. 181–184.
[CrossRef]

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

E. A. Lee, D. G. Messerschmitt, Digital Communications (Kluwer, Dordrecht, The Netherlands, 1988).

S. S. Haykin, Neural Networks: A Comprehensive Foundation (Macmillan, New York, 1994).

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 (25)

Fig. 1
Fig. 1

Parallel optical binary detection system: (a) system architecture and (b) system model. L1 and L2 are Fourier transform lenses, XTAL is a photorefractive crystal, and REF represents the reference beam.

Fig. 2
Fig. 2

Incoherent pixel profiles at the detection plane: (a) Sparrow criterion Gaussian resolved, (b) Sparrow criterion sinc2 resolved, (c) Gaussian 25% beyond resolution, and (d) sinc2 25% beyond resolution.

Fig. 3
Fig. 3

Superposition of incoherent pixel profiles at the detection plane: (a) Sparrow criterion Gaussian resolved, (b) Sparrow criterion sinc2 resolved, (c) Gaussian 25% beyond resolution, and (d) sinc2 25% beyond resolution.

Fig. 4
Fig. 4

Histograms (0 and 1 levels) for incoherent (a) sinc2 and (b) Gaussian channels with no noise.

Fig. 5
Fig. 5

BER’s of the detection schemes on the sinc2-resolved channel.

Fig. 6
Fig. 6

BER’s of the detection schemes on the Gaussian-resolved channel.

Fig. 7
Fig. 7

BER’s of the detection schemes on the sinc2 beyond-resolution channel.

Fig. 8
Fig. 8

BER’s of the detection schemes on the Gaussian beyond-resolution channel.

Fig. 9
Fig. 9

System capacity in the presence of magnification error: (a) Sinc2-resolved channel, (b) Gaussian-resolved channel, (c) sinc2 beyond-resolution channel, and (d) Gaussian beyond-resolution channel.

Fig. 10
Fig. 10

System capacity in the presence of rotation error: (a) sinc2-resolved channel, (b) Gaussian-resolved channel, (c) sinc2 beyond-resolution channel, and (d) Gaussian beyond-resolution channel.

Fig. 11
Fig. 11

System capacity in the presence of shift error: (a) sinc2-resolved channel, (b) Gaussian-resolved channel, (c) sinc2 beyond-resolution channel, and (d) Gaussian beyond-resolution channel.

Fig. 12
Fig. 12

Tolerance of the decision schemes to knowledge of the system blur width.

Fig. 13
Fig. 13

Tolerance of the decision schemes to knowledge of the system magnification.

Fig. 14
Fig. 14

Tolerance of the decision schemes to knowledge of system rotation.

Fig. 15
Fig. 15

Tolerance of the decision schemes to knowledge of shift.

Fig. 16
Fig. 16

Coherent sinc Rayleigh-resolved pixel profile at the detection plane.

Fig. 17
Fig. 17

Intensity histograms (0 and 1 levels) for the coherent sinc channel.

Fig. 18
Fig. 18

BER’s of the detection schemes on the coherent sinc channel.

Fig. 19
Fig. 19

Coherent sinc system capacity in the presence of magnification error.

Fig. 20
Fig. 20

Coherent sinc system capacity in the presence of rotation error.

Fig. 21
Fig. 21

Coherent sinc system capacity in the presence of shift error.

Fig. 22
Fig. 22

PDFE implementational block diagram: (a) digital and (b) analog.

Fig. 23
Fig. 23

PDFE VLSI transistor scaling law. Fab, fabrication.

Fig. 24
Fig. 24

PDFE VLSI clock-rate scaling law.

Fig. 25
Fig. 25

Proof-of-concept fabricated PDFE chip plot.

Tables (11)

Tables Icon

Table 1 Channel Capacities of Decision Schemes for the Gaussian Noise-Dominated Case

Tables Icon

Table 2 Magnification 90% Tolerance Width

Tables Icon

Table 3 Rotation 90% Tolerance Width

Tables Icon

Table 4 Shift 90% Tolerance Width

Tables Icon

Table 5 90% Tolerance Values in Prior Knowledge Study

Tables Icon

Table 6 Coherent Sinc Channel Capacities for the Gaussian Noise-Dominated Case

Tables Icon

Table 7 Coherent Magnification 90% Tolerance Width

Tables Icon

Table 8 Coherent Rotation 90% Tolerance Width

Tables Icon

Table 9 Coherent Shift 90% Tolerance Width

Tables Icon

Table 10 Coherent 90% Tolerance Values in Prior Knowledge Study

Tables Icon

Table 11 PDFE Design Options

Equations (31)

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

h x ,   y     p x ,   y h chan x ,   y ,
sinc 2 x ,   y = sin π x / σ b π x / σ b sin π y / σ b π y / σ b 2 , Gaussian x ,   y ;   σ b 2 = 1 2 π σ b 2 exp - x 2 + y 2 2 σ b 2 .
r ij = kl = -   a ij - kl h kl + n ij ,
h kl   = x l - , y k - x l + , y k +   h x ,   y d x d y ,
h x ,   y = 1 Δ 2 rect x / Δ ,   y / Δ Gaussian x ,   y ;   σ b 2 ,
h x ,   y = 1 Δ 2 rect x / Δ ,   y / Δ 1 σ b 2 sinc 2 x / σ b ,   y / σ b .
h kl = 0.00033 0.0027 0.011 0.0027 0.00033 0.0027 0.022 0.091 0.022 0.0027 0.011 0.091 0.39 0.091 0.011 0.0027 0.022 0.091 0.022 0.0027 0.00033 0.0027 0.011 0.0027 0.00033 .
E a ij - a ˆ ij r ij - kl 0 ,     k ,   l ,
m n   w mn E r ij - kl r ij - mn = E a ij r ij - kl ,     k ,   l .
K w = c .
e ˆ ij = k i l j   a ˆ ij - kl h kl ,
r ˆ ij | 0 = e ˆ ij + a ˆ ij | a ij = 0 h 00 ,
r ˆ ij | 1 = e ˆ ij + a ˆ ij | a ij = 1 h 00 .
P s σ n = Γ M 2 ,
M * = Γ σ n * 1 / 2 .
C = MN 2 R ,
C = N 2 R Γ σ n * 1 / 2 .
Γ = P 4 k B TN 3 r 2 ,
E o c x ,   y = ij   a ij p c x - jD ,   y - iD h chan c x ,   y
= ij   a ij h c x - jD ,   y - iD
= ij   a ij E ij c ,
I o c x ,   y = E o c x ,   y E o c * x ,   y
= ij kl   a ij a kl * E ij c E kl c *
= I o x ,   y + ij kl ij   a ij a kl * E ij c E kl c * .
y ij c =   I o x ,   y d x d y + ij kl ij   a ij a kl *     E ij c E kl c * d x d y
= y ij + ij kl ij   a ij a kl * x c ij ;   kl ,
y ij c = ij   a ij kl   a kl * x c ij ;   kl
= ij   a ij a ij * x c ij ;   ij + kl ij   a kl * x c ij ;   kl .
w ij c = w ˜ ij c
= a ij * x c ij ;   ij + kl ij   a kl * x c ij ;   kl
= x c ij ;   ij + 1 2 kl ij   x c ij ;   kl ,

Metrics