Abstract

A new generation of combined ADC-DSP scheme is proposed. It is based on a novel non-uniform quantization method, optimized for MLSE based receivers. This inclusive optimization enables the use of extremely low-resolution analog-to-digital-converters devices, which form a major bottleneck in high speed optical communications receivers’ architecture. Through Monte-simulation it is demonstrated that the proposed method leads to a significant SNR gain over conventional designs, and may provide low cost and low power consumption digital implementation solution for datacenter interconnects.

© 2016 Optical Society of America

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References

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  1. statista, The Statistics Portal (2014), “Global data center IP traffic from 2012 to 2017, by data center type,” http://www.statista.com/statistics/227268/global-data-center-ip-traffic-growth-by-data-center-type .
  2. C. Kachris and I. Tomkos, “A survey on optical interconnects for data centers,” IEEE Comm. Surv. and Tutor. 14(4), 1021–1036 (2012).
    [Crossref]
  3. A. Gorshtein, O. Levy, G. Katz, and D. Sadot, “Blind channel estimation for MLSE receiver in high speed optical communications: theory and ASIC implementation,” Opt. Express 21(19), 21766–21789 (2013).
    [Crossref] [PubMed]
  4. D. Sadot, G. Dorman, A. Gorshtein, E. Sonkin, and O. Vidal, “Single channel 112Gbit/sec PAM4 at 56Gbaud with digital signal processing for data centers applications,” Opt. Express 23(2), 991–997 (2015).
    [Crossref] [PubMed]
  5. O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-likelihood sequence estimation in dispersive optical channels,” J. Lightwave Technol. 23(2), 749–763 (2005).
    [Crossref]
  6. J. Singh, P. Sandeep, and U. Madhow, “Multi-gigabit communication: The ADC bottleneck,” in IEEE International Conference on Ultra-WideBand (2009), pp. 22–27.
  7. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
    [Crossref]
  8. B. Widrow and I. Kollár, Quantization noise (Cambridge University Press, 2008).
  9. B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
    [Crossref]
  10. N. F. Kiyani, P. Harpe, and G. Dolmans, “Performance analysis of OOK modulated signals in the presence of ADC quantization noise,” in Vehicular Technology Conference (2012), pp. 1–5.
    [Crossref]
  11. U. Rizvi, G. Janssen, and J. Weber, “BER analysis of BPSK and QPSK constellations in the presence of ADC quantization noise,” in Proceeding 14th Asia-Pacific Conf. Communication (2008), pp. 1–5.
  12. Y. Yoffe and D. Sadot, “DSP-Enhanced Analog-to-Digital Conversion for High-Speed Data Centers’ Optical Connectivities,” IEEE Photon. J. 7(4), 1–13 (2015).
    [Crossref]
  13. S. P. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28(2), 129–137 (1982).
    [Crossref]
  14. J. Max, “Quantization for minimum distortion,” IRE Trans. Inf. Theory 6(1), 7–12 (1960).
    [Crossref]
  15. J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
    [Crossref]
  16. R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
    [Crossref]
  17. J. G. Proakis, Digital Communications, (McGraw-Hill Science/Engineering/Math, 4th edition, 2000).
  18. A. Charles and J. E. Dennis., “Analysis of Generalized Pattern Searches,” SIAM J. Optim. 13(3), 889–903 (2003).
  19. IEEE 802.3bj specification, 400GbE Task Force, Berlin Germany, March 2015.

2015 (2)

D. Sadot, G. Dorman, A. Gorshtein, E. Sonkin, and O. Vidal, “Single channel 112Gbit/sec PAM4 at 56Gbaud with digital signal processing for data centers applications,” Opt. Express 23(2), 991–997 (2015).
[Crossref] [PubMed]

Y. Yoffe and D. Sadot, “DSP-Enhanced Analog-to-Digital Conversion for High-Speed Data Centers’ Optical Connectivities,” IEEE Photon. J. 7(4), 1–13 (2015).
[Crossref]

2013 (1)

2012 (2)

C. Kachris and I. Tomkos, “A survey on optical interconnects for data centers,” IEEE Comm. Surv. and Tutor. 14(4), 1021–1036 (2012).
[Crossref]

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

2009 (1)

J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
[Crossref]

2005 (1)

2003 (1)

A. Charles and J. E. Dennis., “Analysis of Generalized Pattern Searches,” SIAM J. Optim. 13(3), 889–903 (2003).

1999 (1)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[Crossref]

1996 (1)

B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
[Crossref]

1982 (1)

S. P. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28(2), 129–137 (1982).
[Crossref]

1960 (1)

J. Max, “Quantization for minimum distortion,” IRE Trans. Inf. Theory 6(1), 7–12 (1960).
[Crossref]

Agazzi, O. E.

Carrer, H. S.

Charles, A.

A. Charles and J. E. Dennis., “Analysis of Generalized Pattern Searches,” SIAM J. Optim. 13(3), 889–903 (2003).

Crivelli, D. E.

Dabeer, O.

J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
[Crossref]

Dennis, J. E.

A. Charles and J. E. Dennis., “Analysis of Generalized Pattern Searches,” SIAM J. Optim. 13(3), 889–903 (2003).

Dolmans, G.

N. F. Kiyani, P. Harpe, and G. Dolmans, “Performance analysis of OOK modulated signals in the presence of ADC quantization noise,” in Vehicular Technology Conference (2012), pp. 1–5.
[Crossref]

Dorman, G.

Gorshtein, A.

Harpe, P.

N. F. Kiyani, P. Harpe, and G. Dolmans, “Performance analysis of OOK modulated signals in the presence of ADC quantization noise,” in Vehicular Technology Conference (2012), pp. 1–5.
[Crossref]

Hueda, M. R.

Janssen, G.

U. Rizvi, G. Janssen, and J. Weber, “BER analysis of BPSK and QPSK constellations in the presence of ADC quantization noise,” in Proceeding 14th Asia-Pacific Conf. Communication (2008), pp. 1–5.

Kachris, C.

C. Kachris and I. Tomkos, “A survey on optical interconnects for data centers,” IEEE Comm. Surv. and Tutor. 14(4), 1021–1036 (2012).
[Crossref]

Katz, G.

Kiyani, N. F.

N. F. Kiyani, P. Harpe, and G. Dolmans, “Performance analysis of OOK modulated signals in the presence of ADC quantization noise,” in Vehicular Technology Conference (2012), pp. 1–5.
[Crossref]

Kollar, I.

B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
[Crossref]

Levy, O.

Liu, M.-C.

B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
[Crossref]

Lloyd, S. P.

S. P. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28(2), 129–137 (1982).
[Crossref]

Lu, M.

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

Madhow, U.

J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
[Crossref]

J. Singh, P. Sandeep, and U. Madhow, “Multi-gigabit communication: The ADC bottleneck,” in IEEE International Conference on Ultra-WideBand (2009), pp. 22–27.

Max, J.

J. Max, “Quantization for minimum distortion,” IRE Trans. Inf. Theory 6(1), 7–12 (1960).
[Crossref]

Narasimha, R.

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

Rizvi, U.

U. Rizvi, G. Janssen, and J. Weber, “BER analysis of BPSK and QPSK constellations in the presence of ADC quantization noise,” in Proceeding 14th Asia-Pacific Conf. Communication (2008), pp. 1–5.

Sadot, D.

Sandeep, P.

J. Singh, P. Sandeep, and U. Madhow, “Multi-gigabit communication: The ADC bottleneck,” in IEEE International Conference on Ultra-WideBand (2009), pp. 22–27.

Shanbhag, N. R.

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

Singer, A. C.

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

Singh, J.

J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
[Crossref]

J. Singh, P. Sandeep, and U. Madhow, “Multi-gigabit communication: The ADC bottleneck,” in IEEE International Conference on Ultra-WideBand (2009), pp. 22–27.

Sonkin, E.

Tomkos, I.

C. Kachris and I. Tomkos, “A survey on optical interconnects for data centers,” IEEE Comm. Surv. and Tutor. 14(4), 1021–1036 (2012).
[Crossref]

Vidal, O.

Walden, R. H.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[Crossref]

Weber, J.

U. Rizvi, G. Janssen, and J. Weber, “BER analysis of BPSK and QPSK constellations in the presence of ADC quantization noise,” in Proceeding 14th Asia-Pacific Conf. Communication (2008), pp. 1–5.

Widrow, B.

B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
[Crossref]

Yoffe, Y.

Y. Yoffe and D. Sadot, “DSP-Enhanced Analog-to-Digital Conversion for High-Speed Data Centers’ Optical Connectivities,” IEEE Photon. J. 7(4), 1–13 (2015).
[Crossref]

IEEE Comm. Surv. and Tutor. (1)

C. Kachris and I. Tomkos, “A survey on optical interconnects for data centers,” IEEE Comm. Surv. and Tutor. 14(4), 1021–1036 (2012).
[Crossref]

IEEE J. Sel. Areas Comm. (1)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[Crossref]

IEEE Photon. J. (1)

Y. Yoffe and D. Sadot, “DSP-Enhanced Analog-to-Digital Conversion for High-Speed Data Centers’ Optical Connectivities,” IEEE Photon. J. 7(4), 1–13 (2015).
[Crossref]

IEEE Trans. Commun. (1)

J. Singh, O. Dabeer, and U. Madhow, “On the limits of communication with low-precision analog-to-digital conversion at the receiver,” IEEE Trans. Commun. 57(12), 3629–3639 (2009).
[Crossref]

IEEE Trans. Inf. Theory (1)

S. P. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. Theory 28(2), 129–137 (1982).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

B. Widrow, I. Kollar, and M.-C. Liu, “Statistical theory of quantization,” IEEE Trans. Instrum. Meas. 45(2), 353–361 (1996).
[Crossref]

IEEE Trans. Signal Process. (1)

R. Narasimha, M. Lu, N. R. Shanbhag, and A. C. Singer, “BER-Optimal Analog-to-Digital Converters for Communication Links,” IEEE Trans. Signal Process. 60(7), 3683–3691 (2012).
[Crossref]

IRE Trans. Inf. Theory (1)

J. Max, “Quantization for minimum distortion,” IRE Trans. Inf. Theory 6(1), 7–12 (1960).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

SIAM J. Optim. (1)

A. Charles and J. E. Dennis., “Analysis of Generalized Pattern Searches,” SIAM J. Optim. 13(3), 889–903 (2003).

Other (7)

IEEE 802.3bj specification, 400GbE Task Force, Berlin Germany, March 2015.

statista, The Statistics Portal (2014), “Global data center IP traffic from 2012 to 2017, by data center type,” http://www.statista.com/statistics/227268/global-data-center-ip-traffic-growth-by-data-center-type .

J. G. Proakis, Digital Communications, (McGraw-Hill Science/Engineering/Math, 4th edition, 2000).

J. Singh, P. Sandeep, and U. Madhow, “Multi-gigabit communication: The ADC bottleneck,” in IEEE International Conference on Ultra-WideBand (2009), pp. 22–27.

N. F. Kiyani, P. Harpe, and G. Dolmans, “Performance analysis of OOK modulated signals in the presence of ADC quantization noise,” in Vehicular Technology Conference (2012), pp. 1–5.
[Crossref]

U. Rizvi, G. Janssen, and J. Weber, “BER analysis of BPSK and QPSK constellations in the presence of ADC quantization noise,” in Proceeding 14th Asia-Pacific Conf. Communication (2008), pp. 1–5.

B. Widrow and I. Kollár, Quantization noise (Cambridge University Press, 2008).

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Figures (5)

Fig. 1
Fig. 1 Combined ADC-DSP system model. The QN D{ x(n)+z(n) } model is operating on the channel deterministic analog branches x(n) . The ADC outputs r(n) , which represent analog regions, are post-processed by the MLSE for data detection. The ADC-DSP block computes (a) the MLSE metrics and (b) the transition probabilities from x i to r i , for each of the channel branches.
Fig. 2
Fig. 2 (a) Each of the channel branches x n can be assigned to one of the four digital output values (assuming 2 bits quantization). The probability to receive each value depends on the channel noises and the analog value of the branch compared to the thresholds (reference levels { t i } i=1 4 ). (b) Quantization of a sequence of 2 consecutive ADC samples: x=( x n , x n+1 ) .
Fig. 3
Fig. 3 Channel impulse response.
Fig. 4
Fig. 4 BER vs. SNR curve for an infinite precision ADC, 2 bits uniform ADC, 3 bits uniform ADC and 4 bits uniform ADC respectively.
Fig. 5
Fig. 5 BER vs. SNR curve for an infinite precision ADC, 3 bits uniform ADC, 2 bits uniform ADC, 2 bits Loyd-Max (LM) ADC and a 2 bits MLSE optimal ADC respectively.

Equations (12)

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q(n)=y(n)D{ y(n) }
Φ x (u)=0for| u |> 2π Δ
SQNR=6.02B+4.820 log 10 R 2 σ y
P er ε W H ( ε)P(ε)= ε W H ( s i s j )P( s i | s j )P( s j )
y(n)=x(n)+z(n)
P( s i | s j )=Q( x i x j 2 σ z )
P{ D{ y }= r i |x }=P{ D{ x+z }= r i |x }= p r (x+z r i )= p r ( t i <x+z t i+1 ) D{ y }=D{ x+z }={ r 1 r 2 r K p r ( t 1 <x+z t 2 ) p r ( t 2 <x+z t 3 ) p r ( t K <x+z t K+1 ) }
p r (y r i |x)= 1 2π σ z 2 t i t i+1 exp( ( yx ) 2 2 σ z 2 ) dy=Q( x t i σ z )Q( x t i+1 σ z )
P( s i | s j )= R (i) P( D{ y (j) } R (i) ) = R (i) P( D{ y 1 (j) }= r 1 (i) D{ y 2 (j) }= r 2 (i) ...D{ y N (j) }= r N (i) )
P( s i | s j )= R (i) P( D{ y 1 (j) }= r 1 (i) ) P( D{ y 2 (j) }= r 2 (i) )...P( D{ y N (j) }= r N (i) )
P er ε W H ( ε)P(ε) = ε W H ( s i s j ){ R (i) P( D{ y 1 (j) }= r 1 (i) ) P( D{ y 2 (j) }= r 2 (i) )...P( D{ y N (j) }= r N (i) ) }P( s j )
P er ε W H ( ε)P(ε) W H ( ε max j>i )P( ε max j>i ) W H ( s i s j ){ R (i) P( D{ y 1 (j) }= r 1 (i) ) P( D{ y 2 (j) }= r 2 (i) )...P( D{ y N (j) }= r N (i) ) }P( s j )

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