Abstract

This paper presents an efficient solution to recovering data pixels of images that have undergone optical and electrical channel impairments in holographic data storage systems. The channel impairments considered include interpixel interference, three types of misalignment, and noise. The proposed misalignment-compensation scheme, consisting of realignment and rate conversion, can effectively eliminate misalignment with more than 84% reduction in additions and 74% reduction in multiplications. In addition, several low-complexity techniques are introduced to reduce the complexity of a two-dimensional maximum a posteriori pixel detection method by up to 95% and do so with negligible degradation in detection performance.

© 2008 Optical Society of America

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  1. H. J. Coufal, G. T. Sincerbox, and D. Psaltis, eds., Holographic Data Storage (Springer-Verlag, 2000).
  2. L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” in Proceedings of the IEEE, Vol. 92, pp. 1231-1280 (2004).
    [CrossRef]
  3. H. Horimai and X. Tan, “Holographic information storage system: today and future,” IEEE Trans. Magn. 43, 943-947(2007).
    [CrossRef]
  4. L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
    [CrossRef]
  5. L. Menetrier and G. W. Burr, “Density implications of shift compensation postprocessing in holographic storage systems,” Appl. Opt. 42, 845-860 (2003).
    [CrossRef] [PubMed]
  6. S. G. Srinivasa and S. W. McLaughlin, “Signal recovery due to rotational pixel misalignment,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (2005), pp. IV-121-IV-124.
  7. M. Ayres, A. Hoskins, and K. Curtis, “Image oversampling for page-oriented optical data storage,” Appl. Opt. 45, 2459-2464 (2006).
    [CrossRef] [PubMed]
  8. M. Keskinoz and B. Kumar, “Application of linear minimum mean-squared-error equalization for volume holographic data storage,” Appl. Opt. 38, 4387-4393 (1999).
    [CrossRef]
  9. X. Chen, K. M. Chugg, and 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]
  10. B. M. King and M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275-6298(1998).
    [CrossRef]
  11. M. Keskinoz and B. Kumar, “Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels,” Appl. Opt. 43, 1368-1378(2004).
    [CrossRef] [PubMed]
  12. W. Chou and M. A. Neifeld, “Interleaving and error correction in volume holographic memory systems,” Appl. Opt. 37, 6951-6968 (1998).
    [CrossRef]
  13. C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
    [CrossRef]
  14. G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, and B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639-641 (1997).
    [CrossRef] [PubMed]
  15. M. Goldberg and H. Sun, “Image sequence coding using vector quantization,” IEEE Trans. Commun. 34, 703-710 (1986).
    [CrossRef]
  16. K. J. Pharris, “Methods and systems for holographic data recovery,” U.S. patent application 20050018263 (27 January, 2005).
  17. R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
    [CrossRef]
  18. M. R. Ayres, A. Hoskins, and K. R. Curtis, “Processing data pixels in a holographic data storage system,” WIPO patent WO/2006/093945 (8 September, 2006).

2008 (1)

L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
[CrossRef]

2007 (1)

H. Horimai and X. Tan, “Holographic information storage system: today and future,” IEEE Trans. Magn. 43, 943-947(2007).
[CrossRef]

2006 (1)

2004 (1)

2003 (1)

1999 (2)

M. Keskinoz and B. Kumar, “Application of linear minimum mean-squared-error equalization for volume holographic data storage,” Appl. Opt. 38, 4387-4393 (1999).
[CrossRef]

R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
[CrossRef]

1998 (3)

1997 (1)

1996 (1)

C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
[CrossRef]

1986 (1)

M. Goldberg and H. Sun, “Image sequence coding using vector quantization,” IEEE Trans. Commun. 34, 703-710 (1986).
[CrossRef]

Ashley, J.

Ayres, M.

Ayres, M. R.

M. R. Ayres, A. Hoskins, and K. R. Curtis, “Processing data pixels in a holographic data storage system,” WIPO patent WO/2006/093945 (8 September, 2006).

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” in Proceedings of the IEEE, Vol. 92, pp. 1231-1280 (2004).
[CrossRef]

Burr, G. W.

Chen, X.

X. Chen, K. M. Chugg, and 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]

Chou, W.

Chugg, K. M.

X. Chen, K. M. Chugg, and 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]

Coufal, H.

Curtis, K.

L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
[CrossRef]

M. Ayres, A. Hoskins, and K. Curtis, “Image oversampling for page-oriented optical data storage,” Appl. Opt. 45, 2459-2464 (2006).
[CrossRef] [PubMed]

Curtis, K. R.

M. R. Ayres, A. Hoskins, and K. R. Curtis, “Processing data pixels in a holographic data storage system,” WIPO patent WO/2006/093945 (8 September, 2006).

Dai, F.

C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
[CrossRef]

Dhar, L.

L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
[CrossRef]

Fäcke, T.

L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
[CrossRef]

Fossorier, M. P. C.

R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
[CrossRef]

Goldberg, M.

M. Goldberg and H. Sun, “Image sequence coding using vector quantization,” IEEE Trans. Commun. 34, 703-710 (1986).
[CrossRef]

Grygier, R. K.

Gu, C.

C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
[CrossRef]

Hesselink, L.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” in Proceedings of the IEEE, Vol. 92, pp. 1231-1280 (2004).
[CrossRef]

Hoffnagle, J. A.

Hong, J.

C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
[CrossRef]

Horimai, H.

H. Horimai and X. Tan, “Holographic information storage system: today and future,” IEEE Trans. Magn. 43, 943-947(2007).
[CrossRef]

Hoskins, A.

M. Ayres, A. Hoskins, and K. Curtis, “Image oversampling for page-oriented optical data storage,” Appl. Opt. 45, 2459-2464 (2006).
[CrossRef] [PubMed]

M. R. Ayres, A. Hoskins, and K. R. Curtis, “Processing data pixels in a holographic data storage system,” WIPO patent WO/2006/093945 (8 September, 2006).

Jefferson, C. M.

Keskinoz, M.

King, B. M.

Kumar, B.

Lin, S.

R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
[CrossRef]

Marcus, B.

McLaughlin, S. W.

S. G. Srinivasa and S. W. McLaughlin, “Signal recovery due to rotational pixel misalignment,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (2005), pp. IV-121-IV-124.

Menetrier, L.

Neifeld, M. A.

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” in Proceedings of the IEEE, Vol. 92, pp. 1231-1280 (2004).
[CrossRef]

Pharris, K. J.

K. J. Pharris, “Methods and systems for holographic data recovery,” U.S. patent application 20050018263 (27 January, 2005).

Shao, R. Y.

R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
[CrossRef]

Srinivasa, S. G.

S. G. Srinivasa and S. W. McLaughlin, “Signal recovery due to rotational pixel misalignment,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (2005), pp. IV-121-IV-124.

Sun, H.

M. Goldberg and H. Sun, “Image sequence coding using vector quantization,” IEEE Trans. Commun. 34, 703-710 (1986).
[CrossRef]

Tan, X.

H. Horimai and X. Tan, “Holographic information storage system: today and future,” IEEE Trans. Magn. 43, 943-947(2007).
[CrossRef]

Appl. Opt. (6)

IEEE Electron. Lett. (1)

C. Gu, F. Dai, and J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” IEEE Electron. Lett. 32, 1400-1402 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Chen, K. M. Chugg, and 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]

IEEE Trans. Commun. (2)

M. Goldberg and H. Sun, “Image sequence coding using vector quantization,” IEEE Trans. Commun. 34, 703-710 (1986).
[CrossRef]

R. Y. Shao, S. Lin, and M. P. C. Fossorier, “Two simple stopping criteria for turbo decoding,” IEEE Trans. Commun. 47, 1117-1120 (1999).
[CrossRef]

IEEE Trans. Magn. (1)

H. Horimai and X. Tan, “Holographic information storage system: today and future,” IEEE Trans. Magn. 43, 943-947(2007).
[CrossRef]

Nat. Photon. (1)

L. Dhar, K. Curtis, and T. Fäcke, “Holographic data storage: coming of age,” Nat. Photon. 2, 403-405 (2008).
[CrossRef]

Opt. Lett. (1)

Other (5)

M. R. Ayres, A. Hoskins, and K. R. Curtis, “Processing data pixels in a holographic data storage system,” WIPO patent WO/2006/093945 (8 September, 2006).

K. J. Pharris, “Methods and systems for holographic data recovery,” U.S. patent application 20050018263 (27 January, 2005).

H. J. Coufal, G. T. Sincerbox, and D. Psaltis, eds., Holographic Data Storage (Springer-Verlag, 2000).

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” in Proceedings of the IEEE, Vol. 92, pp. 1231-1280 (2004).
[CrossRef]

S. G. Srinivasa and S. W. McLaughlin, “Signal recovery due to rotational pixel misalignment,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (2005), pp. IV-121-IV-124.

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Figures (15)

Fig. 1
Fig. 1

Holographic data storage system: (a) recording process and (b) retrieving process.

Fig. 2
Fig. 2

Block diagram of a complete channel model.

Fig. 3
Fig. 3

Signal flows of pixels-detection blocks and related notations.

Fig. 4
Fig. 4

Two-dimensional frequency responses magnitude of (a) the bilinear interpolator, (b) the bicubic interpolator, (c) the 4 × 4 -tap sinc interpolator, and (d) the 4 × 4 -tap raised-cosine interpolator. ( μ x , μ y ) = ( 0.5 , 0.5 ) .

Fig. 5
Fig. 5

NMSE performance of four realignment interpolators under different translation and rotation effects using CH1.

Fig. 6
Fig. 6

Trade-off between complexity and NMSE performance using the truncated raised-cosine interpolators with different sizes. The NMSE range is due to different setting of σ x , σ y , and θ.

Fig. 7
Fig. 7

The NMSE performance of images that have undergone realignment only (Ra) and both realignment and rate conversion ( Ra + Rc ). “ Ra + Rc (LC)” refers to the low-complexity implementation that applies two complexity-reduction schemes.

Fig. 8
Fig. 8

Arithmetic operations involved in 2D-MAP with 3 × 3 neighborhood and illustration of the four proposed schemes for complexity reduction.

Fig. 9
Fig. 9

Flowchart of the iteration-reduction scheme.

Fig. 10
Fig. 10

(a) Candidate-reduction scheme based on the Hamming distance; (b) trade-off between the number of candidates and uncoded BER performance for images with different SNR values.

Fig. 11
Fig. 11

Examples of neighborhood reduction. (a)  Q max = 2 and (b)  Q max = 3 .

Fig. 12
Fig. 12

(a) Neighborhood pixel numbering. (b) Adder tree computes sum of LLRs more efficiently.

Fig. 13
Fig. 13

Performance after applying the neighborhood-reduction scheme: (a) average iteration number and average candidate number, (b) uncoded BER performance. INR = IR + NR . ICR = IR + CR . ICNR = IR + CR + NR . Q max = 2 for CR.

Fig. 14
Fig. 14

Uncoded BER performance of the 2D-MAP with four complexity-reduction schemes in two misalignment-free channels, CH1 and CH2. TH, adaptive threshold detection; 2D, 2D-MAP; 2D*, low-complexity 2D-MAP ( IR + CR + NR + AR ).

Fig. 15
Fig. 15

Performance of MMSE and 2D-MAP under IPI-only and misalignment-plus-IPI channel with oversampling ratio of 2. The misalignment parameters for this simulation are (0.98, 0.98, 0.5, 0.5, 0.5 ° ). 2D, 2D-MAP; 2D*, low-complexity 2D-MAP; MA, proposed low-complexity misalignemnt compensation on images with misalignment effects.

Tables (5)

Tables Icon

Table 1 Channel Parameters for Simulation

Tables Icon

Table 2 Summary of the Computational Complexity Needed by Misalignment-Compensation Methods

Tables Icon

Table 3 Examples of Required Computational Complexity

Tables Icon

Table 4 Additions Needed to Generate Sum of LLRs for Candidates of Different Q

Tables Icon

Table 5 Summary of Computational Complexity-Reduction Schemes a

Equations (17)

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

p ( x , y ) = Π ( x f f SLM Δ ) Π ( y f f SLM Δ ) ,
h A ( x , y ) = h A ( x ) h A ( y ) ,
h A ( x ) = ( D / λ f L ) sinc ( x D / λ f L ) .
C m ( k , l ) = Λ X Λ Y | [ a b A ( i + a , j + b ) h ( x a Δ , y b Δ ) ] + n o ( x , y ) | 2 d y d x + n e ( k , l ) ,
Λ X = [ ( k f f CCD / 2 M γ x + σ x ) Δ , ( k + f f CCD / 2 M γ x + σ x ) Δ ] , Λ Y = [ ( l f f CCD / 2 M γ y + σ y ) Δ , ( l + f f CCD / 2 M γ y + σ y ) Δ ] ,
x = x cos θ + y sin θ , y = x sin θ + y cos θ .
SNR e = 10 log 10 ( 0.5 / N 0 ) ,
a , b E ( Z ˜ ( a , b ) C ( a , b ) ) 2 a , b E C ( a , b ) 2 ,
Z ˜ ( a , b ) = { Z m ( a , b ) , realignment   ( Ra ) Z ( a , b ) , realignment + rate conversion   ( Ra + Rc ) .
Z m ( k , l ) = ( p , q ) S f ( μ x p ) f ( μ y q ) C m ( k + p , l + q ) ,
k ˜ = ( k cos θ l sin θ + σ x ) · M γ x , l ˜ = ( k sin θ + l cos θ + σ y ) · M γ y ,
k = k ˜ , μ x = k ˜ k , l = l ˜ , μ y = l ˜ l .
Z ( i , j ) = p = P min P max r = R min R max ν x ( p ) ν y ( r ) Z m ( k + p , l + r ) ,
ν x ( p ) = { ( ( k + p ) / M γ x ) mod 1 , p = P min ( 1 / M γ x ) mod 1 , P min < p < P max 1 a = P min P max 1 ν x ( a ) , p = P max ,
ν y ( r ) = { ( ( l + r ) / M γ y ) mod 1 , r = R min ( 1 / M γ y ) mod 1 , R min < r < R max 1 a = R min R max 1 ν y ( a ) , r = R max ,
LL 1 U ( k ) ( i , j ) = min N i j { 1 2 N 0 | Z ( i , j ) H ( 1 , n i j ) | 2 + d i j ( k 1 ) n i j } , LL 0 U ( k ) ( i , j ) = min N i j { 1 2 N 0 | Z ( i , j ) H ( 0 , n i j ) | 2 + d i j ( k 1 ) n i j } .
L ( k ) ( i , j ) = ( 1 β ) L ( k 1 ) ( i , j ) + β { LL 1 U ( k ) ( i , j ) LL 0 U ( k ) ( i , j ) } .

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