Abstract

We consider the retrieval of data from a time-domain spectral hole-burning (SHB) memory system. A new iterative log-likelihood (ILL) algorithm is used to reliably detect corrupted retrieved data signals. It is a blockwise technique that takes advantage of the known SHB system characteristics to mitigate time-varying intersymbol interference and detector shot noise. We present bit-error-rate results obtained with the ILL algorithm and five other typical methods (i.e., precompensator, simple threshold, adaptive threshold, a simple Wiener filter, and an adaptive Wiener filter). Results show that the ILL algorithm outperforms all five techniques and hence offers improved SHB storage capacity. In a SHB system with typical material parameters, we find that ILL offers a storage capacity gain of 197% as compared with simple thresholding.

© 2001 Optical Society of America

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References

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2000

M. A. Neifeld, L. Zhang, “Limits on the bitwise information density of spectral storage,” Opt. Commun. 177, 171–179 (2000).
[CrossRef]

1999

1998

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]

B. M. King, M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275–6298 (1998).
[CrossRef]

1997

1996

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

K. D. Merkel, W. R. Babbitt, “Compensation for homogeneous dephasing in coherent transient optical memories and processors,” Opt. Commun. 128, 136–144 (1996).
[CrossRef]

J. Hagenauer, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

1995

J. H. Zhai, Y. Ruan, Z. G. Li, “Holographic technique for improving the performances of frequency-domain optical storage,” Opt. Commun. 118, 499–504 (1995).
[CrossRef]

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

1993

1992

1988

W. R. Babbitt, T. W. Mossberg, “Time-domain frequency-selective optical data storage in a solid-state material,” Opt. Commun. 65, 185–187 (1988).
[CrossRef]

1986

1982

Altner, S. B.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Babbitt, W. R.

K. D. Merkel, W. R. Babbitt, “Compensation for homogeneous dephasing in coherent transient optical memories and processors,” Opt. Commun. 128, 136–144 (1996).
[CrossRef]

W. R. Babbitt, T. W. Mossberg, “Time-domain frequency-selective optical data storage in a solid-state material,” Opt. Commun. 65, 185–187 (1988).
[CrossRef]

W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Convolution, correlation, and storage of optical data in inhomogeneously broadened absorbing materials,” in Optical Information Processing II, D. R. Pape, ed., Proc. SPIE639, 240–247 (1988).
[CrossRef]

Bai, Y. S.

W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Convolution, correlation, and storage of optical data in inhomogeneously broadened absorbing materials,” in Optical Information Processing II, D. R. Pape, ed., Proc. SPIE639, 240–247 (1988).
[CrossRef]

Benedetto, S.

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

S. Benedetto, D. Divsalar, G. Montorsi, F. J. Pollara, “Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes,” in 1995 IEEE International Conference on Communications (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 112–117.

Bernal, M. P.

Bernet, S.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Berrou, C.

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings, (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Burr, G. W.

Chen, X.

K. M. Chugg, X. Chen, M. A. Neifeld, “Two-dimensional equalization in coherent and incoherent page-oriented optical memory,” J. Opt. Soc. Am. A 16, 549–562 (1999).
[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]

Choi, J. Y.

J. Y. Choi, J. F. Walkup, T. F. Krile, D. J. Mehrl, “Bit error rates for a photon echo memory,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 248–257 (1998).
[CrossRef]

Chugg, K. M.

K. M. Chugg, X. Chen, M. A. Neifeld, “Two-dimensional equalization in coherent and incoherent page-oriented optical memory,” J. Opt. Soc. Am. A 16, 549–562 (1999).
[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]

Coufal, H.

Divsalar, D.

S. Benedetto, D. Divsalar, G. Montorsi, F. J. Pollara, “Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes,” in 1995 IEEE International Conference on Communications (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 112–117.

Glavieux, A.

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings, (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Graf, F. R.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Grygier, R. K.

Guenette, D. R.

D. R. Guenette, D. J. Parker, “CD, CD-ROM, CD-R, CD-RW, DVD, DVD-R, DVD-RAM: the family album,” EMedia Professional 10, 30–34 (1997).

Gunther, H.

Hagenauer, J.

J. Hagenauer, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

Hoffnagle, J. A.

Horie, K.

Jefferson, C. M.

Jiang, S.-S.

King, B. M.

Krile, T. F.

J. Y. Choi, J. F. Walkup, T. F. Krile, D. J. Mehrl, “Bit error rates for a photon echo memory,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 248–257 (1998).
[CrossRef]

Lenth, W.

W. Lenth, W. E. Moerner, “Gated spectral hole-burning for frequency domain optical recording,” Opt. Commun. 58, 249–254 (1986).
[CrossRef]

Li, Z. G.

J. H. Zhai, Y. Ruan, Z. G. Li, “Holographic technique for improving the performances of frequency-domain optical storage,” Opt. Commun. 118, 499–504 (1995).
[CrossRef]

Macfarlane, R. M.

Maniloff, E. S.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Mehrl, D. J.

J. Y. Choi, J. F. Walkup, T. F. Krile, D. J. Mehrl, “Bit error rates for a photon echo memory,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 248–257 (1998).
[CrossRef]

Merkel, K. D.

K. D. Merkel, W. R. Babbitt, “Compensation for homogeneous dephasing in coherent transient optical memories and processors,” Opt. Commun. 128, 136–144 (1996).
[CrossRef]

Moerner, W. E.

W. Lenth, W. E. Moerner, “Gated spectral hole-burning for frequency domain optical recording,” Opt. Commun. 58, 249–254 (1986).
[CrossRef]

W. E. Moerner, Persistent Hole Burning: Science and Application (Springer, Berlin, 1998).

Mok, F. H.

Montorsi, G.

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

S. Benedetto, D. Divsalar, G. Montorsi, F. J. Pollara, “Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes,” in 1995 IEEE International Conference on Communications (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 112–117.

Mossberg, T. W.

W. R. Babbitt, T. W. Mossberg, “Time-domain frequency-selective optical data storage in a solid-state material,” Opt. Commun. 65, 185–187 (1988).
[CrossRef]

T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
[CrossRef] [PubMed]

W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Convolution, correlation, and storage of optical data in inhomogeneously broadened absorbing materials,” in Optical Information Processing II, D. R. Pape, ed., Proc. SPIE639, 240–247 (1988).
[CrossRef]

Murase, N.

Neifeld, M. A.

M. A. Neifeld, L. Zhang, “Limits on the bitwise information density of spectral storage,” Opt. Commun. 177, 171–179 (2000).
[CrossRef]

K. M. Chugg, X. Chen, M. A. Neifeld, “Two-dimensional equalization in coherent and incoherent page-oriented optical memory,” J. Opt. Soc. Am. A 16, 549–562 (1999).
[CrossRef]

B. M. King, M. A. Neifeld, “Parallel detection algorithm for page-oriented optical memories,” Appl. Opt. 37, 6275–6298 (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]

Ojima, M.

Parker, D. J.

D. R. Guenette, D. J. Parker, “CD, CD-ROM, CD-R, CD-RW, DVD, DVD-R, DVD-RAM: the family album,” EMedia Professional 10, 30–34 (1997).

Pollara, F. J.

S. Benedetto, D. Divsalar, G. Montorsi, F. J. Pollara, “Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes,” in 1995 IEEE International Conference on Communications (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 112–117.

Renn, A.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Ruan, Y.

J. H. Zhai, Y. Ruan, Z. G. Li, “Holographic technique for improving the performances of frequency-domain optical storage,” Opt. Commun. 118, 499–504 (1995).
[CrossRef]

Sawchuk, A. A.

Shelby, R. M.

Sincerbox, G. T.

Terao, M.

Thitimajshima, P.

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings, (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

Walkup, J. F.

J. Y. Choi, J. F. Walkup, T. F. Krile, D. J. Mehrl, “Bit error rates for a photon echo memory,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 248–257 (1998).
[CrossRef]

Wild, U. P.

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

Zhai, J. H.

J. H. Zhai, Y. Ruan, Z. G. Li, “Holographic technique for improving the performances of frequency-domain optical storage,” Opt. Commun. 118, 499–504 (1995).
[CrossRef]

Zhang, L.

M. A. Neifeld, L. Zhang, “Limits on the bitwise information density of spectral storage,” Opt. Commun. 177, 171–179 (2000).
[CrossRef]

Appl. Opt.

EMedia Professional

D. R. Guenette, D. J. Parker, “CD, CD-ROM, CD-R, CD-RW, DVD, DVD-R, DVD-RAM: the family album,” EMedia Professional 10, 30–34 (1997).

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. Commun.

C. Berrou, A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Trans. Commun. 44, 1261–1271 (1996).
[CrossRef]

IEEE Trans. Inf. Theory

S. Benedetto, G. Montorsi, “Unveiling turbo codes: some results on parallel concatenated coding schemes,” IEEE Trans. Inf. Theory 42, 409–428 (1996).
[CrossRef]

J. Hagenauer, “Iterative decoding of binary block and convolutional codes,” IEEE Trans. Inf. Theory 42, 429–445 (1996).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

J. H. Zhai, Y. Ruan, Z. G. Li, “Holographic technique for improving the performances of frequency-domain optical storage,” Opt. Commun. 118, 499–504 (1995).
[CrossRef]

K. D. Merkel, W. R. Babbitt, “Compensation for homogeneous dephasing in coherent transient optical memories and processors,” Opt. Commun. 128, 136–144 (1996).
[CrossRef]

W. Lenth, W. E. Moerner, “Gated spectral hole-burning for frequency domain optical recording,” Opt. Commun. 58, 249–254 (1986).
[CrossRef]

W. R. Babbitt, T. W. Mossberg, “Time-domain frequency-selective optical data storage in a solid-state material,” Opt. Commun. 65, 185–187 (1988).
[CrossRef]

S. B. Altner, S. Bernet, A. Renn, E. S. Maniloff, F. R. Graf, U. P. Wild, “Spectral holeburning and holography VI: photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal,” Opt. Commun. 120, 103–111 (1995).
[CrossRef]

M. A. Neifeld, L. Zhang, “Limits on the bitwise information density of spectral storage,” Opt. Commun. 177, 171–179 (2000).
[CrossRef]

Opt. Lett.

Other

W. E. Moerner, Persistent Hole Burning: Science and Application (Springer, Berlin, 1998).

S. Benedetto, D. Divsalar, G. Montorsi, F. J. Pollara, “Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes,” in 1995 IEEE International Conference on Communications (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 112–117.

W. R. Babbitt, Y. S. Bai, T. W. Mossberg, “Convolution, correlation, and storage of optical data in inhomogeneously broadened absorbing materials,” in Optical Information Processing II, D. R. Pape, ed., Proc. SPIE639, 240–247 (1988).
[CrossRef]

J. Y. Choi, J. F. Walkup, T. F. Krile, D. J. Mehrl, “Bit error rates for a photon echo memory,” in Advanced Optical Memories and Interfaces to Computer Storage, P. A. Mitkas, Z. U. Hasan, eds., Proc. SPIE3468, 248–257 (1998).
[CrossRef]

C. Berrou, A. Glavieux, P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: turbo-codes (1),” in IEEE International Conference on Communications Proceedings, (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 1064–1070.

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Figures (9)

Fig. 1
Fig. 1

TSHB storage system. (a) A reference pulse interferes with a data pulse train to record a spectral hologram in the SHB material. (b) A data echo is obtained when the spectral hologram is illuminated with a readout pulse.

Fig. 2
Fig. 2

Ground-state population of a TSHB material (left side) and the corresponding data echoes (right side) in the case of various noise sources. (a) No noise (M = 9). (b) ISI (i.e., cross-talk noise) associated with small M (M = 9). (c) ISI associated with large M (M = 16). (d) Combination of ISI and dephasing (M = 16). (e) ISI, dephasing, and saturation distortion (M = 16). (f) ISI, dephasing, saturation, and detector shot noise (M = 16).

Fig. 3
Fig. 3

Simplified discretized TSHB memory model used for algorithm development purposes.

Fig. 4
Fig. 4

Schematic depiction of γ, ΓT, and Γ. The shaded bins represent the stored data bit di, and γ is defined as the data sequence excluding di. ΓT is the entire set including all possible (M - 1) neighbor patterns, and Γ denotes the subset of truncated six-neighbor patterns.

Fig. 5
Fig. 5

Calculation of the LLR for a binary Poisson channel with equal priors.

Fig. 6
Fig. 6

Flow chart for the ILL algorithm with the iteration index n. The channel knowledge is included within the soft-decision and update rule functional elements.

Fig. 7
Fig. 7

Convergence properties of the ILL algorithm for various values of β. The two groups of curves correspond to different data amplitudes: Ed = 60 and 110 V/m.

Fig. 8
Fig. 8

Output BER results for the new ILL algorithm compared with five other detection techniques: STH, ATH, SWF, AWF, PRE. (a) BER results for M = 400. (b) BER results for M = 800.

Fig. 9
Fig. 9

Comparison of the minimum data amplitude required to achieve a BER of 10-4 as a function of the number of stored data bits M. The different values of Mmax can be translated into storage capacity.

Tables (3)

Tables Icon

Table 1 Physical TSHB Channel Parameters Used In our Simulation

Tables Icon

Table 2 Storage Capacity of Various Detection Schemes

Tables Icon

Table 3 Computational Complexity of Various Detection Schemes

Equations (30)

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

est  -R*νGνRνD*ν+R*νDν4|RνDν|Lνexpj2πνtdν,
est-R*νRνD*νLνGνexpj2πνtdν.
htpthchant=Ed Rectt/τGt; σt2,
Ni=η0hνl=- di-lhl2exp-iτT2,
hl=tl-tl+ htdt,
Pri=k=exp-NiNikk!.
hl= 0.0005 0.024 0.23 0.49 0.23 0.024 0.0005 .
Edi=MEdi=1MexpiMexpiM,
θ=N¯1-N¯0ln N¯1-ln N¯0,
Nidi=1, γ=000000=η0hνh02 exp-iτT2, Nidi=1, γ=000001=η0hνh0+h-32 exp-iτT2, Nidi=1, γ=000011=η0hνh0+h-2+h-32×exp-iτT2,
N¯i,1=164γΓ Nidi=1, γ, N¯i,0=164γΓ Nidi=0, γ,
θ=arg minθi PeN¯i,0, N¯i,1=arg minθiexp-N¯i,1n=0θN¯i,1nn!-exp-N¯i,0n=0θN¯i,0nn!,
dˆi=md+l=-QQ r0,i-jfj,
m fmEri-jri-m=Ediri-j,
mr=i,j=-LLσd2δi-j+md2Rhi; j,
Ediri-j=2mdσd2i=-LL Rhi; j,
Eri-jri-m=j,m=-LLj,m=-LL Edi-jdi-md-jd-m×Rhj; mRhj; m,
Pdi=1|ri 01 Pdi=0|ri,
Pdi|ri=γΓT Pdi|ri, γPγ,
Pdi|riγΓ Pdi|ri, γPγ.
LLRdi|rilogPdi=1|riPdi=0|ri=logPri|di=1Pri|di=0+logPdi=1Pdi=0.
LLRdi|ri=N¯i,0-N¯i,1+riln N¯i,1-ln N¯i,0,
Ni=dih0+l=-L,l0L di-lhl2=dih0+NISIi2.
log Pdi|ri=logγΓ Pdi|ri, γPγmaxΓlog Pdi|ri, γ+log Pγ.
LRdi=1|ri=maxΓlogexp-Ni,1Ni,1riri!+dγ,d=1LLRd,
LRdi=0|ri=maxΓlogexp-Ni,0Ni,0riri!+dγ,d=1LLRd,
LLRun=LRdi=1|ri-LRdi=0|ri.
LLRn+1=1-βLLRn+βLLRun.
dˆi=1 when LLR>00 when LLR<0.
ΔCi=MmaxILL-MmaxiMmaxi,

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