Abstract

We investigate the effect of data page misregistration, and its subsequent correction in postprocessing, on the storage density of holographic data storage systems. A numerical simulation is used to obtain the bit-error rate as a function of hologram aperture, page misregistration, pixel fill factors, and Gaussian additive intensity noise. Postprocessing of simulated data pages is performed by a nonlinear pixel shift compensation algorithm [Opt. Lett. 26, 542 (2001)]. The performance of this algorithm is analyzed in the presence of noise by determining the achievable areal density. The impact of inaccurate measurements of page misregistration is also investigated. Results show that the shift-compensation algorithm can provide almost complete immunity to page misregistration, although at some penalty to the baseline areal density offered by a system with zero tolerance to misalignment.

© 2003 Optical Society of America

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References

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    [CrossRef]
  3. S. S. Orlov, Volume holographic data storage. Communications of the ACM 43, 46–54 (2000).
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  4. G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
    [CrossRef]
  5. M.-P. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing inter-pixel crosstalk and thermal noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  28. G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).
  29. A. Papoulis, Probability, random variables, and stochastic processes, 2nd ed. (McGraw-Hill, New York, 1984).

2002 (1)

2001 (5)

2000 (4)

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).

R. M. Shelby, D. A. Waldman, R. T. Ingwall, “Distortions in pixel-matched holographic data storage due to lateral dimensional change of photopolymer storage media,” Opt. Lett. 25, 713–715 (2000).
[CrossRef]

S. S. Orlov, Volume holographic data storage. Communications of the ACM 43, 46–54 (2000).
[CrossRef]

1999 (3)

1998 (3)

1997 (2)

1996 (5)

1992 (1)

Ashley, J.

Baek, W. S.

A. S. Choi, W. S. Baek, “Equalization for digital holographic data storage,” Jpn. J. Appl. Phys. Part 1, 40, 1737–1740 (2001).
[CrossRef]

Bernal, M.-P.

Boopathi, V.

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Burr, G. W.

G. W. Burr, “Holographic data storage with arbitrarily misaligned data pages,” Opt. Lett. 27, 542–544 (2002).
[CrossRef]

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby. Volume holographic data storage at an areal density of 250 Gigapixels/in2. Opt. Lett. 26, 444–446 (2001).
[CrossRef]

G. W. Burr, T. Weiss, “Compensation of pixel misregistration in volume holographic data storage,” Opt. Lett. 26, 542–544 (2001).
[CrossRef]

G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).

M.-P. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing inter-pixel crosstalk and thermal noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (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]

M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel crosstalk in holographic data storage,” Appl. Opt. 36, 3107–3115 (1997).
[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]

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, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Campbell, S.

Chen, X. P.

Choi, A. S.

A. S. Choi, W. S. Baek, “Equalization for digital holographic data storage,” Jpn. J. Appl. Phys. Part 1, 40, 1737–1740 (2001).
[CrossRef]

Chong, T. C.

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Chou, W. C.

Chou, W.-C.

Chugg, K. M.

Coufal, H.

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby. Volume holographic data storage at an areal density of 250 Gigapixels/in2. Opt. Lett. 26, 444–446 (2001).
[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]

M.-P. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing inter-pixel crosstalk and thermal noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998).
[CrossRef]

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]

M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel crosstalk in holographic data storage,” Appl. Opt. 36, 3107–3115 (1997).
[CrossRef] [PubMed]

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Gallego, F.

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Grygier, R. K.

Gu, C.

Gurkan, K.

Hampp, N.

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Heanue, J. F.

Hesselink, L.

Hoffnagle, J. A.

Hong, J.

Ingwall, R. T.

Jefferson, C. M.

Juchem, T.

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Jurich, M.

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby. Volume holographic data storage at an areal density of 250 Gigapixels/in2. Opt. Lett. 26, 444–446 (2001).
[CrossRef]

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Keskinoz, M.

M. Keskinoz, B. V. K. Vijaya Kumar, “Application of linear minimum mean-squared-error equalization for volume holographic data storage,” Appl. Opt. 38, 4387–4390 (1999).
[CrossRef]

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling and iterative magnitude-squared decision feedback equalization (dfe) for volume holographic storage channels,” in International Conference on Communications (ICC2001), 9, 2696–2700 (2001).

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling of volume holographic storage channels (VHSC),” in Optical Data Storage 20004090, Proc. SPIE, 205–210 (2000).
[CrossRef]

King, B. M.

Li, Z. M.

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Lin, S. H.

Liu, J. F.

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Ma, J.

Macfarlane, R. M.

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby. Volume holographic data storage at an areal density of 250 Gigapixels/in2. Opt. Lett. 26, 444–446 (2001).
[CrossRef]

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Marcus, B.

McMichael, I.

Mecher, E.

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Meerholz, K.

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Mok, F. H.

Neifeld, A.

Neifeld, M. A.

Oesterschulze, E.

Orlov, S. S.

S. S. Orlov, Volume holographic data storage. Communications of the ACM 43, 46–54 (2000).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, random variables, and stochastic processes, 2nd ed. (McGraw-Hill, New York, 1984).

Psaltis, D.

Quintanilla, M.

Shelby, R. M.

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby. Volume holographic data storage at an areal density of 250 Gigapixels/in2. Opt. Lett. 26, 444–446 (2001).
[CrossRef]

G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).

R. M. Shelby, D. A. Waldman, R. T. Ingwall, “Distortions in pixel-matched holographic data storage due to lateral dimensional change of photopolymer storage media,” Opt. Lett. 25, 713–715 (2000).
[CrossRef]

M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel crosstalk in holographic data storage,” Appl. Opt. 36, 3107–3115 (1997).
[CrossRef] [PubMed]

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

Sincerbox, G. T.

Vadde, V.

Vijay Kumar, B. V. K.

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling and iterative magnitude-squared decision feedback equalization (dfe) for volume holographic storage channels,” in International Conference on Communications (ICC2001), 9, 2696–2700 (2001).

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling of volume holographic storage channels (VHSC),” in Optical Data Storage 20004090, Proc. SPIE, 205–210 (2000).
[CrossRef]

Vijaya Kumar, B. V. K.

Waldman, D. A.

Weiss, T.

G. W. Burr, T. Weiss, “Compensation of pixel misregistration in volume holographic data storage,” Opt. Lett. 26, 542–544 (2001).
[CrossRef]

G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).

Wu, Y. H.

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Yeh, P.

Yeh, P. C.

Yi, X. M.

Zhou, B. L.

M. A. Neifeld, B. L. Zhou, “Optimal pixel profiles for spatially discrete coherent imaging systems,” Opt. Commun. 193, 87–95 (2001).
[CrossRef]

Appl. Opt. (7)

Communications of the ACM (1)

S. S. Orlov, Volume holographic data storage. Communications of the ACM 43, 46–54 (2000).
[CrossRef]

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

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

Jpn. J. Appl. Phys. Part 1 (1)

A. S. Choi, W. S. Baek, “Equalization for digital holographic data storage,” Jpn. J. Appl. Phys. Part 1, 40, 1737–1740 (2001).
[CrossRef]

Opt. Commun. (1)

M. A. Neifeld, B. L. Zhou, “Optimal pixel profiles for spatially discrete coherent imaging systems,” Opt. Commun. 193, 87–95 (2001).
[CrossRef]

Opt. Eng. (1)

J. F. Liu, V. Boopathi, T. C. Chong, Y. H. Wu, Z. M. Li, “Space-invariant patches in diffraction-limited imaging,” Opt. Eng. 39, 396–400 (2000).
[CrossRef]

Opt. Lett. (8)

SPIE Holography newsletter (1)

G. W. Burr, T. Weiss, R. M. Shelby, “Post-processing to correct for optical distortion and material shrinkage in holographic data storage,” SPIE Holography newsletter 11, 4,8 (2000).

Other (5)

A. Papoulis, Probability, random variables, and stochastic processes, 2nd ed. (McGraw-Hill, New York, 1984).

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling and iterative magnitude-squared decision feedback equalization (dfe) for volume holographic storage channels,” in International Conference on Communications (ICC2001), 9, 2696–2700 (2001).

M. Keskinoz, B. V. K. Vijay Kumar, “Efficient modeling of volume holographic storage channels (VHSC),” in Optical Data Storage 20004090, Proc. SPIE, 205–210 (2000).
[CrossRef]

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

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, M. Jurich, R. M. Macfarlane, R. M. Shelby, “Progress in read-write, fast-access volume holographic data storage,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications VII, and Optical Data Storage, S. Yin, F. T. Ya, H. J. Coufal, eds., Proc. SPIE4459, 290–305 (2002).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Histograms for ON and OFF pixels after passing through a 4-F system containing a square aperture with sides 1.4× those of the Nyquist aperture, D N . The detector array is misaligned: (a) by 0.25 pixels, (b) by 0.5 pixels along x. To show the distributions clearly, the occurrences of OFF pixels are plotted along the negative vertical axis.

Fig. 2
Fig. 2

Simulated bit-error rate (BER) as a function of the page shift: (a) along the x axis (δ y = 0), (b) along the line y = x y = δ x ), for various bandlimiting apertures. Page shifts are in units of a pixel, aperture sizes in units of the Nyquist aperture. The device fill factors are large (g SLM = g CCD = 0.9), SLM contrast is high (c = 100) and a moderate amount of detector noise is present (σ d = 0.05).

Fig. 3
Fig. 3

Simulated areal density in arbitrary units as a function of the page shift: (a) along the x axis (δ y = 0), (b) along the line y = x y = δ x ), for various bandlimiting apertures. Page shifts are in units of a pixel, aperture sizes in units of the Nyquist aperture. The device fill factors are large (g SLM = g CCD = 0.9), SLM contrast is high (c = 100). Density is obtained by increasing random noise until a BER of 10-3 is achieved, zero density implies that interpixel crosstalk has already driven the BER over this target even without any random noise.

Fig. 4
Fig. 4

Spatially blurred images of three SLM pixels (p 0, p 1, p 2) are slightly shifted relative to three CCD pixels (r 0, r 1, r 2), reducing the signal in the desired target pixels and creating crosstalk in their neighbors.

Fig. 5
Fig. 5

Histograms for ON and OFF pixels for the same data page as Fig. 1 after shift-compensation postprocessing.

Fig. 6
Fig. 6

Simulated BER after shift compensation as a function of page shift: (a) along the x axis (δ y = 0), (b) along the line y = x y = δ x ), for various bandlimiting apertures. System parameters are identical to Fig. 2, enabling a direct before-and-after comparison.

Fig. 7
Fig. 7

Simulated areal density in arbitrary units as a function of the page shift: (a) along the x axis (δ y = 0), (b) along the line y = x y = δ x ), for various bandlimiting apertures. System parameters are identical to Fig. 3, enabling a direct before-and-after comparison.

Fig. 8
Fig. 8

BER after shift compensation as a function of the error in estimating the pixel shift, for various actual page shifts. System parameters are identical to Fig. 2.

Fig. 9
Fig. 9

Simulated BER after Wiener filtering as a function of page shift: (a) along the x axis (δ y = 0), (b) along the line y = x y = δ x ), for various bandlimiting apertures. System parameters are identical to Figs. 2 and 6.

Fig. 10
Fig. 10

Comparison of simulated BER for the Wiener filter (open circles and triangles) and for the shift-compensation algorithm (filled circles and triangles). Data are taken from Figs. 6 and 9. Note the truncation of both horizontal axes.

Tables (1)

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Table 1 Simulated Signal Valuesa

Equations (14)

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BERΘ=141d0i=1N w0ierfcΘ-μi2σd+1d1i=1N w1ierfcμi-Θ2σd.
D=NpMD2,
M  σd D  σdD2.
hxc -gSLM/2gSLM/2sincDDNx-xdx,
r2=-gCCD/2gCCD/2p2hx-δx+p1hx-δx+12dx.
r2=p2H00δx+2p1p2H01δx+p1H11δx,
H00δx-gCCD/2gCCD/2hx-δx2dx.
H01δx=rcal-H00δx-H11δx/2.
p2=1H00δx[-p1 H01δx+(p1H01δx2-H00δxH11δx+H00δxr2)1/2].
rs=psHss+phHhh+pvHvv+pdHdd+2psphHsh+2pspvHsv+2pspdHsd+2phpvHhv+2phpdHhd+2pvpdHvd.
D=M/#D DN22NpPrefhνσdnd+nf ηoptηetint1/2.
Ik=|dkhk2+nk|,
dˆk=j=-N+1N-1 wjIk-j,
w=FT-1FTRdIFTRII,

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