Abstract

We propose two reduced-complexity (RC) LDPC decoders, which can be used in combination with large-girth LDPC codes to enable ultra-high-speed serial optical transmission. We show that optimally attenuated RC min-sum sum algorithm performs only 0.46 dB (at BER of 10−9) worse than conventional sum-product algorithm, while having lower storage memory requirements and much lower latency. We further study the use of RC LDPC decoding algorithms in multilevel coded modulation with coherent detection and show that with RC decoding algorithms we can achieve the net coding gain larger than 11 dB at BERs below 10−9.

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References

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  1. R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100Gb/s transport,” in Proc. OFC/NFOEC 2010, Paper No. NMB2, San Diego, CA, March 21–25, 2010.
  2. I. B. Djordjevic, W. Ryan, and B. Vasic, Coding for Optical Channels (Springer, 2010).
  3. I. B. Djordjevic, and H. G. Batshon, Lei Xu and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. OFC/NFOEC 2010, Paper No. OMK2, San Diego, CA, March 21–25, 2010.
  4. J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
    [CrossRef]
  5. M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
    [CrossRef]

2005 (1)

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

1999 (1)

M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
[CrossRef]

Chen, J.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Dholakia, A.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Eleftheriou, E.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Fossorier, M.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Fossorier, M. P. C.

M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
[CrossRef]

Hu, X.-Y.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Imai, H.

M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
[CrossRef]

Mihaljevic, M.

M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
[CrossRef]

IEEE Trans. Commun. (2)

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

M. P. C. Fossorier, M. Mihaljevic, and H. Imai, “Reduced-complexity iterative decoding of low-density parity-check codes based on belief propagation,” IEEE Trans. Commun. 47(5), 673–680 (1999).
[CrossRef]

Other (3)

R. Saunders, M. Traverso, T. Schmidt, and C. Malouin, “Economics of 100Gb/s transport,” in Proc. OFC/NFOEC 2010, Paper No. NMB2, San Diego, CA, March 21–25, 2010.

I. B. Djordjevic, W. Ryan, and B. Vasic, Coding for Optical Channels (Springer, 2010).

I. B. Djordjevic, and H. G. Batshon, Lei Xu and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. OFC/NFOEC 2010, Paper No. OMK2, San Diego, CA, March 21–25, 2010.

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Figures (6)

Fig. 1
Fig. 1

Assignment of v-nodes and c-nodes to BPEs and CPEs, respectively. I denotes the identity matrix of size pxp (p is a prime), P is the permutation matrix given by P = (pij ) p x p , pi , i +1 = pp ,1 = 1 (zero otherwise), and r and c represent the number of block-rows and block-columns in parity-check matrix. The set of integers S are carefully chosen from the set {0,1,…,p-1} so that the cycles of short length (4 and 6) are avoided.

Fig. 2
Fig. 2

BER performance of RC LDPC decoding algorithms in comparison with SPA. Min-sum-CT: min-sum-plus-correction-term algorithm. (The constant in front of algorithm refers to optimum attenuation factor. The attenuation factor in SPA is introduced in box plus operator only.)

Fig. 3
Fig. 3

Quantization effect influence on BER performance.

Fig. 4
Fig. 4

PolMUX PEG-LDPC-coded IPQ modulation scheme: (a) transmitter and (b) receiver configurations. MAP: maximum a posteriori probability.

Fig. 5
Fig. 5

32-IPQ constellation.

Fig. 6
Fig. 6

BER performance of PolMUX LDPC-coded IPQ scheme. CT: correction term.

Tables (2)

Tables Icon

Table 1 Memory allocation requirements of LDPC(16935, 13550) code of column-weight 3 (for p = 1129 and |S| = 15)

Tables Icon

Table 2 Specifications for 32-IPQ-based modulation

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