# Two-Code Keying and Code Conversion for Optical Buffer Design in Optical Packet Switching Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optical Buffering with Two-Code Keying (TCK) and Code Conversion

_{1}, P

_{2},…,P

_{N}are encoded with optical codes C

_{1}, C

_{2},…,C

_{N}, respectively. In this scheme, one packet may partially overlap with another. By employing appropriate detection methods and the orthogonal property among OCDMA codes, the desired packet can be decoded from the packet stack without interference. As packets are stored in the code dimension, they are not delayed or slowed, and the only waiting time comes from the encoding processes. Therefore, the OCDMA buffer has better efficiency in terms of time utilization than FDL.

_{k}, where 1 ≦ k ≦ N.

_{k}or ${\stackrel{-}{\mathrm{C}}}_{k}$, the receiver generates an exactly identical local code and performs the correlation function of (1) or (2), respectively.

## 3. System Configuration

_{i}

^{(1)}and d

_{i}

^{(0)}denote the coded signals for encoding payload bit “1” and “0” from decoder i, respectively, where 1 ≦ I ≦ K.

_{n}has the elements of {1,−1} and the order of 1, 2, and 4n, where n is a positive integer. Two Hadamard matrices with the same order n have the property of H

_{n}H

_{n}

^{T}= nI

_{n}, where I

_{n}is the identity matrix of order n. As the optical power is unipolar, the entries of H

_{n}are modified into 1s and 0s to fit for optical coding. Given that n = 4, the relationships between Hadamard matrices and the code vectors used for TCK are given as:

_{n}’s elements. For a Hadamard matrix with order m = 4n, at most (m − 1) codes are available, as the receiver cannot reject the MAI resulting from the codes of all zeros and all ones.

_{1}= (1,0,1,0) and ${\stackrel{-}{\mathrm{C}}}_{1}$ = (0,1,0,1). As the code chip is encoded on the spectrum, the signal wavelengths corresponding to C

_{1}are (λ

_{1},0,λ

_{3},0). These two wavelengths are thrown back by the two FBGs with reflection wavelengths λ

_{1}and λ

_{3}, respectively. The passed wavelengths, λ

_{2}and λ

_{4}, form the wavelength assignment of (0,λ

_{2},0,λ

_{4}), which exactly matches the chip distribution of ${\stackrel{-}{\mathrm{C}}}_{1}$.

_{k}with length N is composed of N / 2 wavelengths filtered from a BLS spectrum by an FBG array. The remaining wavelengths not filtered by FBGs are used to modulate the packet assigned with complimentary code ${\stackrel{-}{\mathrm{C}}}_{k}$. Figure 5a,b shows the coded signals of Hadamard codes of C

_{1}= (1,0,1,0) and ${\stackrel{-}{\mathrm{C}}}_{1}$ = (0,1,0,1) in the wavelength domain, respectively. Figure 6a–c shows the time waveforms of electrical payload sequence, the optically coded packet of TCK, and the demodulated payload sequence. Note that as payload bits “1” and “0” were both encoded with SAC codes with equal power, so they had similar amplitudes, and the payload values could not be identified in Figure 6b. Furthermore, comparing Figure 6a with Figure 6c, one can find that the payload sequences had become bi-polar as the decoded results of bit “1s” and “0s” from the correlation algorithms of (1) and (2) were inverse numbers. The simulations were conducted using the Optisystem 7.0 software. The power, bandwidth, and center wavelength of the BLS are −10 dBm, 3.75 THz, and 193.1 THz, respectively. The packets were assumed to have a bit rate of 10 Gb/s. The FBGs had a bandwidth of 0.9375 THz, reflection wavelengths of 191.71 THz and 193.57 THz, and reflectivity of 0.9998.

## 4. Buffering Performance Analysis

_{TH}is the PSD of thermal noise, R is the responsiveness of the photodiode, and B is the electrical-equivalent noise bandwidth. G(v) is the PSD of the stacked packets in the buffer, which can be written as

_{sr}is the effective power of light source at the receiver, K is the packet number in the buffer, Δv is the optical source bandwidth, and c(i) is the i-th element of Hadamard code C

_{i}. $\prod (v)$ denotes a unit-width rectangular function centered at 0. As the correlation properties for Hadamard codes and their complements are similar, to simplify the analysis, we assumed that the payload sequences for K packets in the buffer were all bits “1”. Based on the assumptions on the light source in [19], the mathematical expression for the integral in (5) can be expressed as

_{sr}. The parameters used for analysis were S

_{TH}= 1.6 × 10

^{-22}W/Hz, R = 0.95 A/W, B = 1 GHz, and Δv = 0.6 THz and others were the same as the ones used in Figure 5 and Figure 6. When P

_{sr}was relatively small, the BERs for OOK and TCK were close. When P

_{sr}increased, the proposed scheme had a lower BER, due to the larger power of photo-current achieved by encoding SAC codes on both bits “1” and “0”. The BER improvement for the OOK buffer was less efficient, as the increment of photo-current was not enough to get a significantly high signal-to-noise ratio (SNR). Furthermore, the comparison between the numerical analysis and simulations were shown in this figure. Instead of using the mathematical deductions, we used electrical power meters to measure the signal powers at photo-detectors to obtain the photo-current and the PIIN power for simulation. It can be observed that the BER values from these two methods had close results, which indicated the rigidity of the used scheme for performance analysis.

_{sr}= −22 dBm for a single packet of TCK and OOK. It revealed that the eye height in Figure 8a was higher than that in Figure 8b, and the patterns were clearer. This indicated that the proposed buffer scheme had enhanced performances, despite the presence of noise sources.

^{−9}. A system with a larger bandwidth is capable of supporting higher packet rates. However, the noise power is proportional to the receiver bandwidth, so there is a tradeoff between packet rates and BER. This limitation could be partially relieved by employing the TCK buffer, which can store more packets than the OOK one, for a designated BER.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Optical buffering scheme based on (

**a**) fiber delay line (FDL) and (

**b**) optical code-division multiple access (OCDMA).

**Figure 2.**Optical coding scheme for buffered packets: (

**a**) on–off keying (OOK) and (

**b**) two-code keying (TCK).

**Figure 3.**OCDMA buffer architecture with code conversion and TCK. BLS: broadband light source; Enc: encoder; Dec: decoder; EOM: electrical-to-optical modulator; SCU: switch control unit.

**Figure 5.**The coded packet signals in the wavelength domain (

**a**) Hadamard code (1,0,1,0); and (

**b**) complementary Hadamard code (0,1,0,1).

**Figure 6.**Time waveforms of (

**a**) electrical payload sequence before optical modulation; (

**b**) optical coded packets with TCK; and (

**c**) demodulated payload sequence.

**Figure 7.**Bit-error rate (BER) versus the effective power of light source P

_{sr}for an OOK and TCK packet. Num.: numerical analysis; Sim.: simulation.

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**MDPI and ACS Style**

Chen, K.-S.; Chen, C.-S.; Wu, X.-L.
Two-Code Keying and Code Conversion for Optical Buffer Design in Optical Packet Switching Networks. *Electronics* **2019**, *8*, 1117.
https://doi.org/10.3390/electronics8101117

**AMA Style**

Chen K-S, Chen C-S, Wu X-L.
Two-Code Keying and Code Conversion for Optical Buffer Design in Optical Packet Switching Networks. *Electronics*. 2019; 8(10):1117.
https://doi.org/10.3390/electronics8101117

**Chicago/Turabian Style**

Chen, Kai-Sheng, Chien-Sheng Chen, and Xiao-Lu Wu.
2019. "Two-Code Keying and Code Conversion for Optical Buffer Design in Optical Packet Switching Networks" *Electronics* 8, no. 10: 1117.
https://doi.org/10.3390/electronics8101117