Analytical results on channel capacity in uncompensated optical links with coherent detection: erratum

G. Bosco; P. Poggiolini; A. Carena; V. Curri; F. Forghieri

doi:10.1364/OE.20.019610

Abstract

We recently realized that there was an error in the expression of the non-linear interference power in case of distributed amplification reported in [G. Bosco Opt. Express 19 B438 (2011)] Eq. (4). In this erratum we correct the error in Eq. (4) and in all related equations and plots.

The correct expression of the non-linear interference (NLI) power for distributed amplification (DA) reported in Eq. (4) in [1] is:

P_{NLI}^{DA} \approx \frac{16}{27} γ^{2} L_{tot} P_{Tx, ch}^{3} \frac{ln (π^{2} | β_{2} | L_{tot} N_{ch}^{2} R_{s}^{2})}{π | β_{2} | R_{s}^{3}} B_{n}

where the constant

{(\frac{2}{3})}^{3} = \frac{8}{27}

in [1] has been substituted by

\frac{16}{27}

.

The expression of the constant d in Eq. (11) has to be modified accordingly:

d = \frac{16}{27} γ^{2} \frac{ln (π^{2} | β_{2} | L_{tot} B_{WDM}^{2})}{π | β_{2} |}

Inserting the same correction factor in Eqs. (13) and (18), which directly depend on the expression of $P_{N L I}^{D A}$ , the following expressions are obtained for the peak capacity and the value of the optimum signal PSD which maximizes the channel capacity, respectively:

C_{max}^{DA} = 2 {log}_{2} (1 + \frac{1}{L_{tot} {[4 α h ν K_{T}]}^{\frac{2}{3}} {[γ^{2} ln (π^{2} | β_{2} | L_{tot} B_{W D M}^{2})]}^{\frac{1}{3}}})

G_{T x, opt}^{D A} = {(\frac{c}{2 d})}^{\frac{1}{3}} = \frac{3}{2^{4 / 3}} {(\frac{2 α h ν K_{T} π | β_{2} |}{γ^{2} ln (π^{2} | β_{2} | L_{tot} B_{WDM}^{2})})}^{\frac{1}{3}}

Using the corrected formulas, Fig. 1(a), reporting the capacity as a function of the launch power per channel at different system lengths with ideal distributed-amplification, is modified as:

Fig. 1 Capacity limit vs. launch power per channel at different system lengths with ideal distributed-amplification with F=5 dB, L_s=100 km. Assumptions: UT and PM-Gaussian constellation, 125 channels at 32 GBaud, channel spacing equal to symbol-rate, resulting in a total optical bandwidth of 4 THz. Dashed lines: Shannon limit - Eq. (7). Solid lines: non-linear capacity limit - Eq. (9),(10).

Download Full Size | PDF

All other equations and figures, as well as comments and conclusions reported in [1], remain unchanged.

References and links

1. G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Opt. Express 19, B438–B449 (2011). [CrossRef]

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Figures (1)

Fig. 1

Fig. 1 Capacity limit vs. launch power per channel at different system lengths with ideal distributed-amplification with F=5 dB, L_s =100 km. Assumptions: UT and PM-Gaussian constellation, 125 channels at 32 GBaud, channel spacing equal to symbol-rate, resulting in a total optical bandwidth of 4 THz. Dashed lines: Shannon limit - Eq. (7). Solid lines: non-linear capacity limit - Eq. (9),(10).

View in Article | Download Full Size | PDF

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

P_{NLI}^{DA} \approx \frac{16}{27} γ^{2} L_{tot} P_{Tx, ch}^{3} \frac{ln (π^{2} | β_{2} | L_{tot} N_{ch}^{2} R_{s}^{2})}{π | β_{2} | R_{s}^{3}} B_{n}

d = \frac{16}{27} γ^{2} \frac{ln (π^{2} | β_{2} | L_{tot} B_{WDM}^{2})}{π | β_{2} |}

C_{max}^{DA} = 2 {log}_{2} (1 + \frac{1}{L_{tot} {[4 α h ν K_{T}]}^{\frac{2}{3}} {[γ^{2} ln (π^{2} | β_{2} | L_{tot} B_{W D M}^{2})]}^{\frac{1}{3}}})

G_{T x, opt}^{D A} = {(\frac{c}{2 d})}^{\frac{1}{3}} = \frac{3}{2^{4 / 3}} {(\frac{2 α h ν K_{T} π | β_{2} |}{γ^{2} ln (π^{2} | β_{2} | L_{tot} B_{WDM}^{2})})}^{\frac{1}{3}}

Analytical results on channel capacity in uncompensated optical links with coherent detection: erratum

Abstract

References and links

Cited By

Figures (1)

Equations (4)

Optics Express