Abstract

This paper focuses on the capacity-approaching, nonuniform signaling for the pulse amplitude modulated (PAM) visible light communications under the non-negativity, peak power, and dimmable average power constraints. The input distribution is characterized by three parameters, i.e., the intensities, the probabilities, and the number of mass points in the PAM constellation. In the open literature, no analytical expression can be used to obtain the capacity-achieving input distribution. In this paper, a computationally simple but capacity-approaching input distribution is alternatively derived by determining the three aforementioned parameters. The resulting input distribution can serve as a useful tool not to approach the channel capacity but to guide the practical system design. Numerical results substantiate that the derived input distribution is a capacity-approaching distribution and can offer a better performance gain in comparison with the commonly employed uniform input distribution.

© 2014 Optical Society of America

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References

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  1. IEEE, “IEEE standard for local and metropolitan area networks—part 15.7: short-range wireless optical communication using visible light,” (2011).
  2. S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
    [CrossRef]
  3. F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
    [CrossRef]
  4. J. A. Anguita, I. B. Djordjevic, M. Neifeld, and B. V. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. 4, 586–601 (2005).
    [CrossRef]
  5. S. M. Hass and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun. 21, 1346–1357 (2003).
    [CrossRef]
  6. K. Chakraborty and P. Narayan, “The Poisson fading channel,” IEEE Trans. Inf. Theory 53, 2349–2364 (2007).
    [CrossRef]
  7. K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
    [CrossRef]
  8. L. Jing and M. Uysal, “Optical wireless communication: system model, capacity and coding,” in Proceedings of IEEE 58th Vehicular Technology Conference (IEEE, 2003), pp. 168–172.
  9. A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25, 1702–1710 (2007).
    [CrossRef]
  10. J. Jiang and K. R. Narayanan, “Multilevel coding for channels with nonuniform inputs and rateless transmission over the BSC,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2006), pp. 518–522.
  11. S. Hranilovic and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50, 784–795 (2004).
    [CrossRef]
  12. A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
    [CrossRef]
  13. A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inf. Theory 49, 2426–2467 (2003).
    [CrossRef]
  14. S. M. Moser, “Duality-based bounds on channel capacity,” Ph.D. dissertation (Swiss Federal Institute of Technology Zurich, 2005).
  15. R. You and J. M. Kahn, “Upper-bounding the capacity of optical IM/DD channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,” IEEE Trans. Inf. Theory 48, 514–523 (2002).
    [CrossRef]
  16. X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).
  17. A. A. Farid and S. Hranilovic, “Upper and lower bounds on the capacity of wireless optical intensity channels,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2007), pp. 2416–2420.
  18. A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory 56, 6066–6077 (2010).
    [CrossRef]
  19. A. A. Farid and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Commun. 27, 1553–1563 (2009).
    [CrossRef]
  20. J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications,” J. Lightwave Technol. 31, 3771–3779 (2013).
    [CrossRef]
  21. J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22, 1455–1457 (2010).
    [CrossRef]
  22. K. Ahn and J. K. Kwon, “Capacity analysis of M-PAM inverse source coding in visible light communications,” J. Lightwave Technol. 30, 1399–1404 (2012).
    [CrossRef]
  23. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
    [CrossRef]
  24. J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
    [CrossRef]
  25. J. G. Smith, “The information capacity of amplitude and variance constrained scalar Gaussian channels,” Inf. Control 18, 203–219 (1971).
    [CrossRef]
  26. T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
    [CrossRef]
  27. R. E. Blahut, “Computation of channel capacity and rate-distortion functions,” IEEE Trans. Inf. Theory 18, 460–473 (1972).
    [CrossRef]
  28. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

2013

2012

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

K. Ahn and J. K. Kwon, “Capacity analysis of M-PAM inverse source coding in visible light communications,” J. Lightwave Technol. 30, 1399–1404 (2012).
[CrossRef]

S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[CrossRef]

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

2010

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory 56, 6066–6077 (2010).
[CrossRef]

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22, 1455–1457 (2010).
[CrossRef]

2009

A. A. Farid and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Commun. 27, 1553–1563 (2009).
[CrossRef]

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
[CrossRef]

2008

K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
[CrossRef]

2007

2005

T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
[CrossRef]

J. A. Anguita, I. B. Djordjevic, M. Neifeld, and B. V. Vasic, “Shannon capacities and error-correction codes for optical atmospheric turbulent channels,” J. Opt. Netw. 4, 586–601 (2005).
[CrossRef]

2004

S. Hranilovic and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50, 784–795 (2004).
[CrossRef]

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[CrossRef]

2003

A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inf. Theory 49, 2426–2467 (2003).
[CrossRef]

S. M. Hass and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun. 21, 1346–1357 (2003).
[CrossRef]

2002

R. You and J. M. Kahn, “Upper-bounding the capacity of optical IM/DD channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,” IEEE Trans. Inf. Theory 48, 514–523 (2002).
[CrossRef]

1997

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

1972

R. E. Blahut, “Computation of channel capacity and rate-distortion functions,” IEEE Trans. Inf. Theory 18, 460–473 (1972).
[CrossRef]

1971

J. G. Smith, “The information capacity of amplitude and variance constrained scalar Gaussian channels,” Inf. Control 18, 203–219 (1971).
[CrossRef]

Ahn, K.

Anguita, J. A.

Armstrong, J.

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Blahut, R. E.

R. E. Blahut, “Computation of channel capacity and rate-distortion functions,” IEEE Trans. Inf. Theory 18, 460–473 (1972).
[CrossRef]

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Chakraborty, K.

K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
[CrossRef]

K. Chakraborty and P. Narayan, “The Poisson fading channel,” IEEE Trans. Inf. Theory 53, 2349–2364 (2007).
[CrossRef]

Chan, T. H.

T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
[CrossRef]

Chen, C.-W.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

Chen, M.

Dey, S.

K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
[CrossRef]

Djordjevic, I. B.

Farid, A. A.

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory 56, 6066–6077 (2010).
[CrossRef]

A. A. Farid and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Commun. 27, 1553–1563 (2009).
[CrossRef]

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25, 1702–1710 (2007).
[CrossRef]

A. A. Farid and S. Hranilovic, “Upper and lower bounds on the capacity of wireless optical intensity channels,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2007), pp. 2416–2420.

Franceschetti, M.

K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
[CrossRef]

Hass, S. M.

S. M. Hass and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun. 21, 1346–1357 (2003).
[CrossRef]

Ho, C.-H.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

Hranilovic, S.

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory 56, 6066–6077 (2010).
[CrossRef]

A. A. Farid and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Commun. 27, 1553–1563 (2009).
[CrossRef]

A. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightwave Technol. 25, 1702–1710 (2007).
[CrossRef]

T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
[CrossRef]

S. Hranilovic and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50, 784–795 (2004).
[CrossRef]

A. A. Farid and S. Hranilovic, “Upper and lower bounds on the capacity of wireless optical intensity channels,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2007), pp. 2416–2420.

Hu, Q.-S.

Huang, H.-T.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

Jiang, J.

J. Jiang and K. R. Narayanan, “Multilevel coding for channels with nonuniform inputs and rateless transmission over the BSC,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2006), pp. 518–522.

Jing, L.

L. Jing and M. Uysal, “Optical wireless communication: system model, capacity and coding,” in Proceedings of IEEE 58th Vehicular Technology Conference (IEEE, 2003), pp. 168–172.

Jungnickel, V.

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

Kahn, J. M.

R. You and J. M. Kahn, “Upper-bounding the capacity of optical IM/DD channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,” IEEE Trans. Inf. Theory 48, 514–523 (2002).
[CrossRef]

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[CrossRef]

Kschischang, F. R.

T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
[CrossRef]

S. Hranilovic and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50, 784–795 (2004).
[CrossRef]

Kwon, J. K.

K. Ahn and J. K. Kwon, “Capacity analysis of M-PAM inverse source coding in visible light communications,” J. Lightwave Technol. 30, 1399–1404 (2012).
[CrossRef]

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22, 1455–1457 (2010).
[CrossRef]

Lapidoth, A.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
[CrossRef]

A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inf. Theory 49, 2426–2467 (2003).
[CrossRef]

Li, X.

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

Lim, S.-K.

S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[CrossRef]

Lin, C.-T.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

Moser, S. M.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
[CrossRef]

A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inf. Theory 49, 2426–2467 (2003).
[CrossRef]

S. M. Moser, “Duality-based bounds on channel capacity,” Ph.D. dissertation (Swiss Federal Institute of Technology Zurich, 2005).

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[CrossRef]

Narayan, P.

K. Chakraborty and P. Narayan, “The Poisson fading channel,” IEEE Trans. Inf. Theory 53, 2349–2364 (2007).
[CrossRef]

Narayanan, K. R.

J. Jiang and K. R. Narayanan, “Multilevel coding for channels with nonuniform inputs and rateless transmission over the BSC,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2006), pp. 518–522.

Neifeld, M.

Rajagopal, S.

S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[CrossRef]

Roberts, R. D.

S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[CrossRef]

Shapiro, J. H.

S. M. Hass and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun. 21, 1346–1357 (2003).
[CrossRef]

Smith, J. G.

J. G. Smith, “The information capacity of amplitude and variance constrained scalar Gaussian channels,” Inf. Control 18, 203–219 (1971).
[CrossRef]

Uysal, M.

L. Jing and M. Uysal, “Optical wireless communication: system model, capacity and coding,” in Proceedings of IEEE 58th Vehicular Technology Conference (IEEE, 2003), pp. 168–172.

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Vasic, B. V.

Vucic, J.

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

Wang, J.

Wang, J.-B.

Wang, J.-Y.

Wei, C.-C.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

Wigger, M. A.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
[CrossRef]

Wu, F.-M.

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

You, R.

R. You and J. M. Kahn, “Upper-bounding the capacity of optical IM/DD channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,” IEEE Trans. Inf. Theory 48, 514–523 (2002).
[CrossRef]

IEEE Commun. Mag.

S. Rajagopal, R. D. Roberts, and S.-K. Lim, “IEEE 802.15.7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[CrossRef]

IEEE J. Sel. Areas Commun.

S. M. Hass and J. H. Shapiro, “Capacity of wireless optical communications,” IEEE J. Sel. Areas Commun. 21, 1346–1357 (2003).
[CrossRef]

A. A. Farid and S. Hranilovic, “Channel capacity and non-uniform signalling for free-space optical intensity channels,” IEEE J. Sel. Areas Commun. 27, 1553–1563 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22, 1455–1457 (2010).
[CrossRef]

F.-M. Wu, C.-T. Lin, C.-C. Wei, C.-W. Chen, H.-T. Huang, and C.-H. Ho, “1.1  Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photon. Technol. Lett. 24, 1730–1732 (2012).
[CrossRef]

IEEE Trans. Commun.

X. Li, J. Vucic, V. Jungnickel, and J. Armstrong, “On the channel capacity of intensity-modulated direct-detection systems and the information rate of ACO-OFDM for indoor optical wireless applications,” IEEE Trans. Commun. 60, 700–809 (2012).

IEEE Trans. Consum. Electron.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[CrossRef]

IEEE Trans. Inf. Theory

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory 56, 6066–6077 (2010).
[CrossRef]

T. H. Chan, S. Hranilovic, and F. R. Kschischang, “Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs,” IEEE Trans. Inf. Theory 51, 2073–2088 (2005).
[CrossRef]

R. E. Blahut, “Computation of channel capacity and rate-distortion functions,” IEEE Trans. Inf. Theory 18, 460–473 (1972).
[CrossRef]

R. You and J. M. Kahn, “Upper-bounding the capacity of optical IM/DD channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method,” IEEE Trans. Inf. Theory 48, 514–523 (2002).
[CrossRef]

S. Hranilovic and F. R. Kschischang, “Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise,” IEEE Trans. Inf. Theory 50, 784–795 (2004).
[CrossRef]

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55, 4449–4461 (2009).
[CrossRef]

A. Lapidoth and S. M. Moser, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inf. Theory 49, 2426–2467 (2003).
[CrossRef]

K. Chakraborty and P. Narayan, “The Poisson fading channel,” IEEE Trans. Inf. Theory 53, 2349–2364 (2007).
[CrossRef]

K. Chakraborty, S. Dey, and M. Franceschetti, “Outage capacity of MIMO Poisson fading channels,” IEEE Trans. Inf. Theory 54, 4887–4907 (2008).
[CrossRef]

Inf. Control

J. G. Smith, “The information capacity of amplitude and variance constrained scalar Gaussian channels,” Inf. Control 18, 203–219 (1971).
[CrossRef]

J. Lightwave Technol.

J. Opt. Netw.

Proc. IEEE

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[CrossRef]

Other

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

J. Jiang and K. R. Narayanan, “Multilevel coding for channels with nonuniform inputs and rateless transmission over the BSC,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2006), pp. 518–522.

L. Jing and M. Uysal, “Optical wireless communication: system model, capacity and coding,” in Proceedings of IEEE 58th Vehicular Technology Conference (IEEE, 2003), pp. 168–172.

S. M. Moser, “Duality-based bounds on channel capacity,” Ph.D. dissertation (Swiss Federal Institute of Technology Zurich, 2005).

IEEE, “IEEE standard for local and metropolitan area networks—part 15.7: short-range wireless optical communication using visible light,” (2011).

A. A. Farid and S. Hranilovic, “Upper and lower bounds on the capacity of wireless optical intensity channels,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2007), pp. 2416–2420.

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Figures (10)

Fig. 1.
Fig. 1.

Previous dimming control schemes under different dimming targets.

Fig. 2.
Fig. 2.

Proposed joint dimming scheme under different dimming targets.

Fig. 3.
Fig. 3.

Two equivalent channels for Case 1. Here, Z˜ is a Gaussian variable with zero mean and variance σ˜2=σ2/[r2G2χ2(η1)]σ2/[r2G2χ2(η2)]>0.

Fig. 4.
Fig. 4.

Two equivalent channels for Case 2. Here, Z˜ is also a Gaussian variable with zero mean and variance σ˜2=σ2/[r2G2χ2(η1)]σ2/[r2G2χ2(η2)]>0.

Fig. 5.
Fig. 5.

Normalized mass point spacing versus dimming target at transition OPSNR.

Fig. 6.
Fig. 6.

Mutual information versus A/σ with different η when ξ=0.4 and K=1.

Fig. 7.
Fig. 7.

Mutual information versus A/σ with different ξ when η=0 and K=2.

Fig. 8.
Fig. 8.

Mutual information of the input distribution (27) with K¯ and K^ and the uniform input distribution and capacity bounds from [20] with ξ=0.4.

Fig. 9.
Fig. 9.

Optimal number of mass points in the input distribution (27) with K¯ and K^ and the uniform source distribution when ξ=0.4.

Fig. 10.
Fig. 10.

Resulting input distribution with K^ and uniform source distribution for different A/σ when ξ=0.4.

Equations (27)

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Y=rGX+Z,
G={(m+1)AR2πd2cosm(φ)TS(ψ)g(ψ)cos(ψ),if0ψΨC0,ifψ>ΨC,
X0.
XA,
E(X)=ξA,
0ξ1.
T={fX(x):0xA,E(x)=ξA}.
C=maxfX(x)TI(X;Y),
D={pX(x):pX(x)=k=0Kakδ(xxk),xk[0,A],ak0,k=0Kak=1,KZ+,k=0Kakxk=ξA},
C=maxfX(x)DI(X;Y).
fX*(x)=argmaxfX(x)DI(X;Y).
ak=1K+1
xk={kADshiftK,if0ξ0.5kADshiftK+Dshift,if0.5<ξ1,
Dshift=A|12ξ|,ξ[0,1].
xk=kAK.
k=0Kakk=ξK.
xk={kAηDshiftK,if0ξ0.5kAηDshiftK+ηDshift,if0.5<ξ1={AηDshiftAxk,if0ξ0.5AηDshiftAxk+ηDshift,if0.5<ξ1,
xk={[1η(12ξ)]xk,if0ξ0.5[1η(2ξ1)]xk+ηA(2ξ1),if0.5<ξ1.
k=0Kakχ(η)xk=ξA.
I(X;Y2)I(X;W2)=I(X;W1)=I(X;Y1),
k=0Kakχ(η)xk+A[1χ(η)]=ξA.
I(X;Y2)I(X;W2)=I(X;W1)=I(X;Y1).
xk=xk=kAK,k{0,1,,K}.
maxakQH(X),
lσ=AσK¯(γ0)=γ0·1K¯(γ0).
K^=max{1,A2.2σ},
pX(x)=k=0K^akδ(xkAK^).

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