Abstract

Data reliability at the output of the error-correction code decoder in a compact-disc system is influenced by the decoding strategy employed by the decoder, as well as by the statistical distribution of errors that contaminate the recorded data. Recovered-data reliability estimates have been computed by use of error statistics obtained from the measurement of errors that contaminate the actual data stored on clean write-once and read-only-memory compact discs. These estimates consist of probabilities that specify the occurrence of residual errors in the data that appear at the output of a compact-disc player’s cross-interleaved Reed–Solomon code (CIRC) decoder. Data reliability estimates that apply to five specific CIRC decoding strategies are reported.

© 1998 Optical Society of America

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References

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  1. European Computer Manufacturers Association (ECMA), “Standard ECMA-130: data interchange on READ-ONLY 120 mm optical data disks (CD-ROM),” ECMA rep. (ECMA, Geneva, Switzerland, July1988).
  2. K. C. Pohlmann, The Compact Disc Handbook (A-R Editions, Madison, Wisc., 1992).
  3. L. M. E. Driessen, L. B. Vries, “Performance calculation of the compact disc error correcting code on a memoryless channel,” in Proceedings of the Fourth International Conference on Video and Data Recording, University of Southampton,Southampton, UK, 20–23 April 1982.
  4. B. Tehranchi, D. G. Howe, “Error characteristics of read-only-memory versus write-once-read-many compact discs: CD-ROM versus CD-WORM,” Appl. Opt. 35, 5831–5838 (1996).
    [CrossRef] [PubMed]
  5. Z. Yang, “Statistical reliability analysis of data recovered from compact discs,” M.S. thesis (Department of Electrical and Computer Engineering, University of Arizona, Tucson, Ariz., 1995).
  6. B. Tehranchi, D. G. Howe, “Real-time, high-resolution, PC-based system for measurement of errors on compact discs,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2338, 156–159 (1994).
  7. D. G. Howe, B. Tehranchi, “Compact disc error studies,” Optical Data Storage Center Quarterly Report (Optical Sciences Center, University of Arizona, Tucson, Ariz., 15September1996).
  8. B. Tehranchi, D. G. Howe, “A channel model for characterization of error data recovered from compact discs,” IEEE Trans. Commun. (to be published).
  9. W. W. Peterson, E. J. Weldon, Error-Correcting Codes (MIT Press, Cambridge, Mass., 1981).
  10. S. Lin, J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).
  11. The recovered bytes were actually measured for error contamination at the input of the CIRC decoder. We subsequently obtained C1 code words by mathematically performing the deinterleaving step that rearranges the sequential byte stream at the CIRC input to form the corresponding sequence of C1 code words.
  12. B. R. Frieden, Probability, Statistical Optics and Data Processing, 2nd ed. (Springer-Verlag, Berlin, 1991).
    [CrossRef]

1996 (1)

Costello, J.

S. Lin, J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Driessen, L. M. E.

L. M. E. Driessen, L. B. Vries, “Performance calculation of the compact disc error correcting code on a memoryless channel,” in Proceedings of the Fourth International Conference on Video and Data Recording, University of Southampton,Southampton, UK, 20–23 April 1982.

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics and Data Processing, 2nd ed. (Springer-Verlag, Berlin, 1991).
[CrossRef]

Howe, D. G.

B. Tehranchi, D. G. Howe, “Error characteristics of read-only-memory versus write-once-read-many compact discs: CD-ROM versus CD-WORM,” Appl. Opt. 35, 5831–5838 (1996).
[CrossRef] [PubMed]

B. Tehranchi, D. G. Howe, “A channel model for characterization of error data recovered from compact discs,” IEEE Trans. Commun. (to be published).

B. Tehranchi, D. G. Howe, “Real-time, high-resolution, PC-based system for measurement of errors on compact discs,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2338, 156–159 (1994).

D. G. Howe, B. Tehranchi, “Compact disc error studies,” Optical Data Storage Center Quarterly Report (Optical Sciences Center, University of Arizona, Tucson, Ariz., 15September1996).

Lin, S.

S. Lin, J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Peterson, W. W.

W. W. Peterson, E. J. Weldon, Error-Correcting Codes (MIT Press, Cambridge, Mass., 1981).

Pohlmann, K. C.

K. C. Pohlmann, The Compact Disc Handbook (A-R Editions, Madison, Wisc., 1992).

Tehranchi, B.

B. Tehranchi, D. G. Howe, “Error characteristics of read-only-memory versus write-once-read-many compact discs: CD-ROM versus CD-WORM,” Appl. Opt. 35, 5831–5838 (1996).
[CrossRef] [PubMed]

D. G. Howe, B. Tehranchi, “Compact disc error studies,” Optical Data Storage Center Quarterly Report (Optical Sciences Center, University of Arizona, Tucson, Ariz., 15September1996).

B. Tehranchi, D. G. Howe, “A channel model for characterization of error data recovered from compact discs,” IEEE Trans. Commun. (to be published).

B. Tehranchi, D. G. Howe, “Real-time, high-resolution, PC-based system for measurement of errors on compact discs,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2338, 156–159 (1994).

Vries, L. B.

L. M. E. Driessen, L. B. Vries, “Performance calculation of the compact disc error correcting code on a memoryless channel,” in Proceedings of the Fourth International Conference on Video and Data Recording, University of Southampton,Southampton, UK, 20–23 April 1982.

Weldon, E. J.

W. W. Peterson, E. J. Weldon, Error-Correcting Codes (MIT Press, Cambridge, Mass., 1981).

Yang, Z.

Z. Yang, “Statistical reliability analysis of data recovered from compact discs,” M.S. thesis (Department of Electrical and Computer Engineering, University of Arizona, Tucson, Ariz., 1995).

Appl. Opt. (1)

Other (11)

Z. Yang, “Statistical reliability analysis of data recovered from compact discs,” M.S. thesis (Department of Electrical and Computer Engineering, University of Arizona, Tucson, Ariz., 1995).

B. Tehranchi, D. G. Howe, “Real-time, high-resolution, PC-based system for measurement of errors on compact discs,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds., Proc. SPIE2338, 156–159 (1994).

D. G. Howe, B. Tehranchi, “Compact disc error studies,” Optical Data Storage Center Quarterly Report (Optical Sciences Center, University of Arizona, Tucson, Ariz., 15September1996).

B. Tehranchi, D. G. Howe, “A channel model for characterization of error data recovered from compact discs,” IEEE Trans. Commun. (to be published).

W. W. Peterson, E. J. Weldon, Error-Correcting Codes (MIT Press, Cambridge, Mass., 1981).

S. Lin, J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

The recovered bytes were actually measured for error contamination at the input of the CIRC decoder. We subsequently obtained C1 code words by mathematically performing the deinterleaving step that rearranges the sequential byte stream at the CIRC input to form the corresponding sequence of C1 code words.

B. R. Frieden, Probability, Statistical Optics and Data Processing, 2nd ed. (Springer-Verlag, Berlin, 1991).
[CrossRef]

European Computer Manufacturers Association (ECMA), “Standard ECMA-130: data interchange on READ-ONLY 120 mm optical data disks (CD-ROM),” ECMA rep. (ECMA, Geneva, Switzerland, July1988).

K. C. Pohlmann, The Compact Disc Handbook (A-R Editions, Madison, Wisc., 1992).

L. M. E. Driessen, L. B. Vries, “Performance calculation of the compact disc error correcting code on a memoryless channel,” in Proceedings of the Fourth International Conference on Video and Data Recording, University of Southampton,Southampton, UK, 20–23 April 1982.

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Figures (5)

Fig. 1
Fig. 1

Compact-disc communication channel.

Fig. 2
Fig. 2

CIRC decoding–deinterleaving block diagram.

Fig. 3
Fig. 3

Error burst and gap statistics for ROM compact discs at the input of the C1 decoder.

Fig. 4
Fig. 4

Error burst and gap statistics for WO compact discs at the input of the C1 decoder.

Fig. 5
Fig. 5

P(32, r) plotted versus r at the input of the C1 decoder.

Tables (7)

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Table 1 Symbol-State Probabilities at the Output of the C2 Decoder for ROM Compact Discs

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Table 2 Symbol-State Probabilities at the Output of the C2 Decoder for WO Compact Discs

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Table 3 Decoding Strategy 1: A Simple Correction Strategya

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Table 4 Decoding Strategy 2: A Midlevel Correction Strategya

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Table 5 Decoding Strategy 3a

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Table 6 Decoding Strategy 4a

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Table 7 Decoding Strategy 5: Superstrategya

Equations (34)

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2 t + e d - 1 ,
R = T + E ,
P 00 = 1 - P 11 - P 10 - P 01 .
NP n ,   r ,   f ,   j P l / r n ,   d ,   q ,   t ,   r P w / l n ,   d ,   q ,   t ,   r ,
P C 1 11 a = 1 n r = 3 n f = 0 n j = j _ min j _ max w = d n   wP n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t ,   r × P w / 2 n ,   d ,   q ,   t ,   r ,
P C 1 11 b = 1 n r = 3 n f = 0 n j = j _ min j _ max   rP n ,   r ,   f ,   j 1 - γ n , d , q , t r .
P C 1 11 = P C 1 11 a + P C 1 11 b .
P n ,   r ,   f ,   j = P n ,   r P f | n ,   r P j | n ,   r ,   f ,
P j | n ,   r ,   f = 1 ,     j = f , = 0 ,     j f .
P f | n ,   r = N F f ,   r N R r , n = 32 ,     1 r 32 ,     0 f r ,
P n ,   r ,   f ,   j = n r r j n - r f - j × P C 1 11 j P C 1 10 r - j P C 1 01 f - j P C 1 00 n - r - f + j ,
a b = a ! / b ! a - b ! .
Number   of   interpolated   samples   per   hour = 7350 × 24   user   bytes / s 3600   s / h × P 11 + P 01 flagged   byte / byte .
P C 1 11 a = 1 n r = 3 n f = 0 n j = j _ min j _ max w = d n   wP n ,   r ,   f ,   j × P 2 / r n ,   d ,   q ,   t ,   r P w / 2 n ,   d ,   q ,   t ,   r ,
P C 1 11 b = 1 n r = 3 n f = 0 n j = j _ min j _ max   rP n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 1 01 a = 1 n r = 3 n f = 0 n j = j _ min j _ max w = d n n - w P n ,   r ,   f ,   j × P 2 / r n ,   d ,   q ,   t ,   r P w / 2 n ,   d ,   q ,   t ,   r ,
P C 1 01 b = 1 n f = 0 n j = j _ min j _ max   nP n ,   r ,   f ,   j ,     r = 2 ,
P C 1 01 c = 1 n r = 3 n f = 0 n j = j _ min j _ max n - r P n ,   r ,   f ,   j × 1 - γ n , d , q , t r ,
P C 1 10 = 1 n r = d - t n f = 0 n j = j _ min j _ max w = d n   wP n ,   r ,   f ,   j θ n , d , q , t r ,   w , t = 1 .
P C 2 11 a = 1 n r = 3 n f = 0 2 j = j _ min j _ max   rP n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 2 11 b = 1 n r = 3 n f = 3 n j = j _ min j _ max   jP n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 2 11 c = 1 n r = 0 n f = 5 n j = j _ min j _ max   jP n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t ,
P C 2 11 d = 1 n r = 0 n f = 0 n j = j _ min j _ max   rP n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t , if f 3   and   j = 1 or f 2   and   j = 0 ,
P C 2 11 e = 1 n r = 0 n f = 0 n j = j _ min j _ max   jP n ,   f ,   r ,   j P 2 / r n ,   d ,   q ,   t , if f 4 and f > 3   or   j 1 and f > 2   or   j 0 and j 2 ,
P C 2 01 a = 1 n r = 3 n f = 0 2 j = j _ min j _ max n - r P n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 2 01 b = 1 n r = 3 n f = 3 n j = j _ min j _ max f - j P n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 2 01 c = 1 n r = 0 n f = 5 n j = j _ min j _ max f - j P n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t ,
P C 2 01 d = 1 n r = 0 n f = 0 n j = j _ min j _ max n - r P n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t , if f 3   and   j = 1 or f 2   and   j = 0 ,
P C 2 01 e = 1 n r = 0 n f = 0 n j = j _ min j _ max f - j P n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t , if f 4 and f > 3   or   j 1 and f > 2   or   j 0 and j 2 ,
P C 2 10 a = 1 n r = d - t n f = 0 n j = j _ min j _ max w = d n   wP n ,   r ,   f ,   j θ n , d , q , t r ,   w , t = 1 ,
P C 2 10 b = 1 n r = 3 n f = 3 n j = j _ min j _ max r - j P n ,   r ,   f ,   j 1 - γ n , d , q , t r ,
P C 2 10 c = 1 n r = 0 n f = 5 n j = j _ min j _ max r - j P n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t ,
P C 2 10 d = 1 n r = d - t n f = 0 4 w = d n   wP n ,   r ,   f ,   j θ n , d , q , t r ,   w , j = 2 ,     t = 2 ,
P C 2 10 e = 1 n r = 0 n f = 0 n j = j _ min j _ max r - j P n ,   r ,   f ,   j P 2 / r n ,   d ,   q ,   t , if f 4 and f > 3   or   j 1 and f > 2   or   j 0 and j 2 ,

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