Abstract

We present an optical low-density parity-check (LDPC) decoder suitable for implementation above 100 Gbits/s, which provides large coding gains when based on large-girth LDPC codes. We show that a basic building block, the probabilities multiplier circuit, can be implemented using a Mach–Zehnder interferometer, and we propose corresponding probabilistic-domain sum-product algorithm (SPA). We perform simulations of a fully parallel implementation employing girth-10 LDPC codes and proposed SPA. The girth-10 LDPC(24015,19212) code of the rate of 0.8 outperforms the BCH(128,113)×BCH(256,239) turbo-product code of the rate of 0.82 by 0.91 dB (for binary phase-shift keying at 100 Gbits/s and a bit error rate of 109), and provides a net effective coding gain of 10.09 dB.

© 2009 Optical Society of America

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References

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  1. Y. Miyata, W. Matsumoto, and T. Mizuochi, in Proceedings of the OFC/NFOEC (2008), paper OTuE4.
  2. J. Hagenauer, M. Moerz, and A. Schaefer, in Proceedings of the 2002 International Zurich Seminar on Broadband Communications (2002), pp. 3-1-3-6.
  3. W. E. Ryan, in CRC Handbook for Coding and Signal Processing for Recording Systems (CRC Press, 2004).
  4. M. P. C. Fossorier, IEEE Trans. Inf. Theory 50, 1788 (2004).
    [CrossRef]

2004 (1)

M. P. C. Fossorier, IEEE Trans. Inf. Theory 50, 1788 (2004).
[CrossRef]

Fossorier, M. P. C.

M. P. C. Fossorier, IEEE Trans. Inf. Theory 50, 1788 (2004).
[CrossRef]

Hagenauer, J.

J. Hagenauer, M. Moerz, and A. Schaefer, in Proceedings of the 2002 International Zurich Seminar on Broadband Communications (2002), pp. 3-1-3-6.

Matsumoto, W.

Y. Miyata, W. Matsumoto, and T. Mizuochi, in Proceedings of the OFC/NFOEC (2008), paper OTuE4.

Miyata, Y.

Y. Miyata, W. Matsumoto, and T. Mizuochi, in Proceedings of the OFC/NFOEC (2008), paper OTuE4.

Mizuochi, T.

Y. Miyata, W. Matsumoto, and T. Mizuochi, in Proceedings of the OFC/NFOEC (2008), paper OTuE4.

Moerz, M.

J. Hagenauer, M. Moerz, and A. Schaefer, in Proceedings of the 2002 International Zurich Seminar on Broadband Communications (2002), pp. 3-1-3-6.

Ryan, W. E.

W. E. Ryan, in CRC Handbook for Coding and Signal Processing for Recording Systems (CRC Press, 2004).

Schaefer, A.

J. Hagenauer, M. Moerz, and A. Schaefer, in Proceedings of the 2002 International Zurich Seminar on Broadband Communications (2002), pp. 3-1-3-6.

IEEE Trans. Inf. Theory (1)

M. P. C. Fossorier, IEEE Trans. Inf. Theory 50, 1788 (2004).
[CrossRef]

Other (3)

Y. Miyata, W. Matsumoto, and T. Mizuochi, in Proceedings of the OFC/NFOEC (2008), paper OTuE4.

J. Hagenauer, M. Moerz, and A. Schaefer, in Proceedings of the 2002 International Zurich Seminar on Broadband Communications (2002), pp. 3-1-3-6.

W. E. Ryan, in CRC Handbook for Coding and Signal Processing for Recording Systems (CRC Press, 2004).

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Figures (2)

Fig. 1
Fig. 1

SPA implementation building blocks: (a) MZI probability multiplier, (b) parity-check node probability update circuit, (c) variable-node probability update circuit, and (d) circuit to calculate the normalization factor required in steps (2) and (3).

Fig. 2
Fig. 2

BER performance of large-girth LDPC codes employing the optical LDPC decoder operating at 100 Gbits/s for binary phase-shift keying (BPSK) modulation format.

Equations (6)

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r j > i = q l > j ( 1 q m > j ) + ( 1 q l > j ) q m > j .
q i > j = r s > i r t > i / [ r s > i r t > i + ( 1 r s > i ) ( 1 r t > i ) ] .
P i r s i r t i r s i r t i + ( 1 r s i ) ( 1 r t i ) , P i P i r j i P i r j i + ( 1 P i ) ( 1 r j i ) .
v ̂ i = 1   for   log [ ( 1 P i ) / P i ] < 0     ( 0   otherwise ) .
P out , 1 / P in = sin 2 ( Δ φ / 2 ) = p ,     P out , 2 / P in = 1 p .
H = [ I I I I I P S [ 1 ] P S [ 2 ] P S [ c 1 ] I P 2 S [ 1 ] P 2 S [ 2 ] P 2 S [ c 1 ] I P ( r 1 ) S [ 1 ] P ( r 1 ) S [ 2 ] P ( r 1 ) S [ c 1 ] ] ,

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