P Pth in .NET Receive Data Matrix ECC200 in .NET P Pth

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P Pth generate, create data matrix ecc200 none for .net projects Visual Studio Development Language 1 exp (14.33) ..

P N 2 P Pth + exp Pth N P Pth 1 . The result in Eq. (14 .33) shows that in the high-power limit P/Pth , the channel capacity reduces to C = log(1 + ) with 0, or C 0.

Nonlinearity, thus, asymptotically obliterates channel capacity. Since in the linear regime channel, capacity increases with signal power, we then expect that a maximum can be reached at some power value. It can be shown that such a maximum capacity is reached for the optimal signal power Popt as analytically de ned: Popt =.

2 N Pth 2 (14.34). Gaussian channel and Shannon Hartley theorem Replacing this de nit ion of Popt into Eq. (14.33) yields the maximum achievable channel capacity Cmax : Cmax = 2 2 Pth log 3 3 3 N .

(14.35). A different model tha .net vs 2010 Data Matrix barcode t I developed,18 which takes into account the quantum nature of ampli er noise leads to an alternative de nition C of the channel capacity: C = log 1 + P(1 s) 1 + 2N + s 1 + 1 1 s P . P N (14.

36). P = log 1 + N 1 s 2+ 1 1 +s 1+ N 1 s The new de nition of capacity in Eq. (14.36) yields different expressions for the optimal power and maximum capacity, namely Popt and Cmax , as de ned by: Popt Cmax.

2 (1/2 + N )Pth 3 = , Visual Studio .NET gs1 datamatrix barcode 2 2 2 2Pth = log . 3 3 3(1 + 2N ).

(14.37) (14.38).

We note from Eqs. (14 datamatrix 2d barcode for .NET .

34) (14.35) and Eqs. (14.

37) (14.38) that the optimal powers Popt , Popt and maximal capacities Cmax , Cmax actually have very similar values. With respect to the classical model, the quantum model of the nonlinear channel provides a small correction to the maximum SNR of the order of 2 1/3 0.

8, which, in base-2 logarithms, represents about 30%. Figure 14.6 shows plots of thee nonlinear-channel capacities C, C (according to the two above models), as plotted vs.

the linear SNR, i.e., SNR = P/N , as expressed in decibels,19 with different parameter choices for N and Pth .

The SHT capacity corresponding to the linear-channel case is also shown. Figure 14.6(a) corresponds to the worst case of a channel with a nonlinear threshold relatively close to the linear noise (N = 5 and Pth = 15).

In contrast, Figure 14.6(b) corresponds to the case of a comparatively low linear-noise channel having a relatively high nonlinear threshold (N = 1 and Pth = 100). It is seen from the gure that in both cases, and regardless of the nonlinear model (classical or quantum), the channel capacity is bounded to a power-dependent maximum, unlike in the linear information theory where from SHT the capacity increases as log(SNR).

. 18 19. E. Desurvire, Erbium- datamatrix 2d barcode for .NET Doped Fiber Ampli ers, Devices and System Developments (New York: J.

Wiley & Sons, 2002), Ch. 3. With SNR(dB) = 10 log10 (SNR).

. 14.2 Nonlinear channel Channel capacity C,C VS .NET ECC200 ((bit/s)/Hz). c ar (S el 0 10 5 0. SNR (dB). Channel capacity C,C ((bit/s)/Hz). 7 6 5 4 3 2 1 0 10 5 0 5 10. r ea Lin ) HT l (S ne an ch C C 15 20. SNR (dB). Figure 14.6 Nonlinear .NET gs1 datamatrix barcode channel capacities C, C , as functions of linear signal-to-linear-noise ratio P/N according to classical and quantum models with SHT linear-channel capacity shown for reference (thick line), with dimensionless parameters (a) N = 5 and Pth = 15, and (b) N = 1 and Pth = 100.

. The consequences of t hese developments concerning nonlinear channels remain to be fully explored. It is important to note that the assumption of channel nonlinearity does not affect the key conclusions of Shannon s (linear) information theory, namely the channel coding theorem and the SHT. Indeed, error-correction codes are used in realistic (nonlinear) optical communication systems to enhance SNR and BER performance.

The fact that in these nonlinear optical channels the noise is power-dependent does not affect the effectiveness of such codes. The key conclusion is that the capacity limits imposed by Shannon s information theory still apply, despite the new complexities introduced by channel nonlinearity, which introduces yet another upper bound. It should not be interpreted, however, that nonlinearity de nes an ultimate capacity limit for optical communication channels, present or future.

Indeed, optical ber design makes it possible effectively to reduce ber nonlinearity by increasing the ber core size (referred to as the effective area ), so as to decrease the nonlinearity threshold, Pth , and, hence, effectively achieve the operating conditions P Pth (s 0). Furthermore, there exist several types of countermeasures and power SNR tradeoffs to alleviate optical nonlinearities, which it is beyond the purpose of this chapter to describe. Overall, the key conclusion.

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