Abstract

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2001

T. J. Richardson, R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 638–656 (2001).
[CrossRef]

S. Y. Chung, T. J. Richardson, R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47, 657–670 (2001).
[CrossRef]

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

W. Chou, M. A. Neifeld, “Soft-decision array decoding for volume holographic memory systems,” J. Opt. Soc. Am. A 18, 185–194 (2001).
[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 areal density of 250 gigapixels/in.2,” Opt. Lett. 26, 444–446 (2001).
[CrossRef]

1999

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory 45, 399–431 (1999).
[CrossRef]

X. An, G. W. Burr, D. Psaltis, “Thermal fixing of 10,000 holograms in linbo3:Fe,” Appl. Opt. 38, 386–393 (1999).
[CrossRef]

1998

W. Chou, M. A. Neifeld, “Interleaving and error correction in volume holographic memory systems,” Appl. Opt. 37, 6951–6968 (1998).
[CrossRef]

X. Chen, K. M. Chugg, 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]

1997

1996

1995

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
[CrossRef]

1994

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

1993

1992

1981

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27, 533–547 (1981).
[CrossRef]

An, X.

Ashley, J.

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Bernal, M.-P.

Brady, D. J.

Burr, G. W.

Chang, T. Y.

Chen, X.

X. Chen, K. M. Chugg, 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.

Christian, W.

Chugg, K. M.

X. Chen, K. M. Chugg, 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]

Chung, S. Y.

S. Y. Chung, T. J. Richardson, R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47, 657–670 (2001).
[CrossRef]

S. Y. Chung, “On the construction of some capacity-approaching coding schemes,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 2000).

Coufal, H.

Galleger, R. G.

R. G. Galleger, Low-density Parity-Check Codes (MIT, Cambridge, Mass., 1963).

Grygier, R. K.

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Hoffnagle, J. A.

Hong, J. H.

Jefferson, C. M.

Jurich, M.

Luby, M.

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

Macfarlane, R. M.

MacKay, D. J. C.

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory 45, 399–431 (1999).
[CrossRef]

Marcus, B.

McMichael, I.

Mitzenmacher, M.

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

Mok, F.

Mok, G. B. F.

Neifeld, M. A.

Pletcher, D.

Psaltis, D.

Richardson, T. J.

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

S. Y. Chung, T. J. Richardson, R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47, 657–670 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 638–656 (2001).
[CrossRef]

Shelby, R. M.

Shokrollahi, M.

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

Shokrollahi, M. A.

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

Sincerbox, G. T.

Spielman, D.

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

Tanner, R. M.

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27, 533–547 (1981).
[CrossRef]

Unther, H. G.

Urbanke, R. L.

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 638–656 (2001).
[CrossRef]

S. Y. Chung, T. J. Richardson, R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47, 657–670 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

X. Chen, K. M. Chugg, 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. Inf. Theory

T. J. Richardson, R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inf. Theory 45, 399–431 (1999).
[CrossRef]

T. J. Richardson, M. A. Shokrollahi, R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

T. J. Richardson, R. L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 638–656 (2001).
[CrossRef]

S. Y. Chung, T. J. Richardson, R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47, 657–670 (2001).
[CrossRef]

M. Luby, M. Mitzenmacher, M. Shokrollahi, D. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47, 585–598 (2001).
[CrossRef]

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27, 533–547 (1981).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Sci. Am.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273, 70–76 (1995).
[CrossRef]

Science

J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Other

R. G. Galleger, Low-density Parity-Check Codes (MIT, Cambridge, Mass., 1963).

S. Y. Chung, “On the construction of some capacity-approaching coding schemes,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 2000).

H. Pishro-Nik, N. Rahnavard, F. Fekri, “Nonuniform error correction using low-density parity-check codes,” in Proceedings of Fortieth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Ill., Oct. (2002). http://www.csl.uiuc.edu/allerton/ .

A. Kavčić, X. Ma, M. Mitzenmacher, “Binary inersymbol interference channels: Gallager codes, density evolution, and code performance bounds,” IEEE Trans. Inf. Theory. http://www.eecs.harvard.edu/∼michaelm/NEWWORK/papers.html#CodesAn .

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Figures (9)

Fig. 1
Fig. 1

Capacity of the BSC and the BIWAGN channel versus the bit error probability.

Fig. 2
Fig. 2

Tanner graph for an LDPC code.

Fig. 3
Fig. 3

Different regions in a typical data page in holographic recording. Raw BER is almost constant in each region.

Fig. 4
Fig. 4

Comparison of different coding schemes for VHMs.

Fig. 5
Fig. 5

Performance of the irregular LDPC code of rate 0.85.

Fig. 6
Fig. 6

Comparison of the performance of irregular LDPC code with Shannon’s capacity of the channel.

Fig. 7
Fig. 7

Comparison of the performance of irregular and regular LDPC codes.

Fig. 8
Fig. 8

Performance of the irregular LDPC code for different iterations.

Fig. 9
Fig. 9

Performance of irregular LDPC codes with different block lengths.

Equations (8)

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

C=M i=1N2 Ci,
C=M i=1N2 Ci=M i=1N21-Hpi,
Hp=p log21p+ 1-plog211-p.
Ci=- ϕixlog2ϕixdx- 12log22πeσi2.
ϕix= 18πσi2e- x+122σi2+e- x-122σi2,
H=110100011010101001.
d1=3, d2=4, d3=7, d4=10, dc=40,
SNR2-SNR1=1.61dB, SNR3-SNR1=2.80dB, SNR4-SNR1=3.74dB.

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