6 January 2014 Universal optical line terminal encoding and decoding architecture in two-code keying for noncoherent spectral amplitude coding optical code division multiple access systems
Author Affiliations +
Abstract
We propose a new code family, called extended shifted prime codes, and the universal encoding architecture for spectral amplitude coding optical code division multiple access systems using a two-code keying scheme. The proposed system can eliminate multiuser interference and suppress phase-induced intensity noise. In addition, we design the ESP codes to be an encoding/decoding architecture based on the array waveguide grating architecture and reduce the power loss and the complexity of the optical line terminal. The numerical results demonstrate that the proposed system with ESP codes outperforms the existing one-dimensional shifted prime codes system.
Yeh, Lin, and Yang: Universal optical line terminal encoding and decoding architecture in two-code keying for noncoherent spectral amplitude coding optical code division multiple access systems

1.

Introduction

Optical code division multiple access (OCDMA) can provide high-speed connections with bandwidth sharing and secure communications in next-generation optical access networks.1 Spectral amplitude coding (SAC) in OCDMA systems has been exploited in the optical networking units of passive optical networks (PONs).2,3 However, in the on–off keying, the codewords are unidimensional and require the codewords power of bit “1” and the zero codewords power of bit “0” to control the unequal power to accommodate more simultaneous users in PONs.4 The codewords in two-code keying (TCK) are a better event because the codewords power of bit “1” and the codewords power of bit “0” control the equal power. In addition, the performance of OCDMA systems is limited by the multiuser interference (MUI).5 To address this issue, shifted prime (SP) codes with TCK are proposed to remove MUI.6 In this letter, we propose extended shifted prime (ESP) codes with TCK to further reduce the phase-induced intensity noise (PIIN) and support more simultaneous users. The variance of PIIN current is effectively reduced by employing the proposed ESP codes. We also propose a novel array waveguide grating (AWG) architecture to decrease the power loss and complexity of the optical line terminal (OLT).

In the following sections, we first review the SP codes.6 The SP codes are designed to eliminate MUI without chip stuffing of the codes. A code sequence of the SP code is denoted as Cm,n=[cm,n(0),cm,n(1),,cm,n(p1)], where m=0, 1,,p1,n=0,1,,p1, and Cm,npp. The pp represents the set of all p-tuples over GF(p). The corresponding codeword is denoted as Xm,n=[xm,n(0),xm,n(1),,xm,n(p21)]. Therein, we set xm,n(i)=1 as i=cm,n(b)+bp and b=0,1,,p1, where cm,n(b)=mbn. Otherwise, xm,n(i)=0. The • and are the modulo-p multiplication and addition, respectively. The codewords Xm,n with the same value m belong to the same code group. The cross-correlations between the two SP codewords Xm,n and Xq,r are Xm,nXq,r=p as m=q, n=r, Xm,nXq,r=0 as m=q, nr, or Xm,nXq,r=1 as mq, where is the dot-product of two vectors.

2.

1-D ESP Codes with TCK

In the letter, we design ESP codes to reduce PIIN and increase the number of simultaneous users. Specifically, we describe the ESP codes as follows: xe,m,n(j)=1, for j=(e1)p+cm,n(b)+bNp, b=0,1,,p1; otherwise, xe,m,n(j)=0, where e{1,2,,N}. The code weight is p, the code length is Np2, the number of codewords is M=Np2, and the code size is Ms=N(p2p)/2. Table 1 uses an example with N=2, p=3, M=18, and Ms=6.

Table 1

Extended shifted prime (ESP) codes for N=2, code weight p=3, and code size Ms=6.

emnXe,m,n
100100 000 100 000 100 000
101010 000 010 000 010 000
102001 000 001 000 001 000
110100 000 010 000 001 000
111010 000 001 000 100 000
112001 000 100 000 010 000
120100 000 001 000 010 000
121010 000 100 000 001 000
122001 000 010 000 100 000
200000 100 000 100 000 100
201000 010 000 010 000 010
202000 001 000 001 000 001
210000 100 000 010 000 001
211000 010 000 001 000 100
212000 001 000 100 000 010
220000 100 000 001 000 010
221000 010 000 100 000 001
222000 001 000 010 000 100

The cross-correlations of the ESP codes are specified as follows: Xe,m,nXf,q,r=p as e=f, m=q, n=r, Xe,m,nXf,q,r=0 as e=f, m=q, nr, Xe,m,nXf,q,r=0 as ef, or Xe,m,nXf,q,r=1 as e=f, mq. Moreover, we let any two codewords (Xe,m,n and Xe,m,n), which belong to the same code group, assigned to the same user for TCK. It is set as Xe,m,n=Xe,m,n+1 in this letter. Table 1 uses a codeword Xe,m,n or Xe,m,n as the encoding of information bit “0” or “1”. The modified cross correlations in ESP codes for TCK are derived as follows:

(1)

Xe,m,nXf,q,rXe,m,nXf,q,r={p,e=f,m=q,n=r,pe=f,m=q,n'=r,0otherwise.

The above subtraction method for TCK can eliminate MUI according to the difference between the two correlations. For ESP scheme, we propose a new OLT as shown in Fig. 1, which includes a 1×Ms splitter at the remote node, and Ms optical network units (ONUs). The AWG architecture can effectively combine all codes into one and concentrate the power. The ONU(τ), where τ{0,1,,Ms1}, is able to decode the ESP codes to produce the information bits “0” or “1” for user(τ). As shown in Fig. 1, the OLT transmitter includes a broadband light source (BLS), an AWG architecture, and a matrix operation circuit.

Fig. 1

Schematic block diagram of extended shifted prime (ESP) codes for two-code keying (TCK) including transmitter and receiver.

OE_53_1_016104_f001.png

The AWG architecture includes one 1×Np2 AWG demultiplexer, Np2 electro-optic modulators (EOMs), and one Np2×1 AWG multiplexer. The light outputted from BLS designs wavelength bandwidth to be first divided into Np2 wavelength chips by the 1×Np2 AWG demultiplexer. The wavelengths of Np2 wavelength chips are esignated as λ0,λ1,,λNp21. These wavelength chips are then modulated by the Np2 EOMs, respectively. At last, these modulated wavelength chips are combined by the Np2×1 AWG multiplexer and outputted into an external fiber for data transmission. The EOM modulates the incoming wavelength chips according to the variables h0,h1,,hNp21, which are calculated based on the information bits and adopted ESP codewords of each user via the matrix operation circuit. The calculation of this matrix operation circuit is performed according to H=1/p×S×BIT, where H=[h0,h1,,hM1]T, S=[X1,0,0T,X1,0,1T,,XN,p1,p1T,XN,p1,p2T], and BIT=[bit0,bit0¯,bitMs1,bitMs1¯]T. Therein, X1,0,0T and X1,0,1T are the transpose of codeword vectors for user #0, ⋯, and XN,p1,p1T and XN,p1,p2T are for user #(Ms1). In fact, a universal OLT encoding architecture can be operated with other code families, e.g., SP codes and M3 sequence codes.6,7 Only the codeword matrix S needs to be updated.

The proposed transmitter encodes ESP codes in the electrical domain, the same as the literature,89.10.11 and it has been shown that the EOM can transfer the electrical domain into the optical domain.12

In Fig. 2, the modulation voltage Vm is the input of EOM, and the optical transmitted intensity In is the output of the EOM, where the optical transmitted intensity In=In0+ψVm. If Vm=0, the optical transmitted intensity is In0. The EOM transfers the modulation voltage Vm into optical transmitted intensity In. Therefore, the ratio of transmission factor is ψ=In/Vm. Figure 2 presents the transformation from the electrical domain to optical domain with the environment described in Table 1, where N=2 in ESP codes with the code weight p=3 and the code size Ms=6.

Fig. 2

The modulation voltage versus the optical transmitted intensity of the electro-optic modulator (EOM).

OE_53_1_016104_f002.png

We first describe the matrix operation circuit in the electrical domain with H=1/p×S×BIT, where H=[h0,h1,,hM1]T, S=[X1,0,0T,X1,0,1T,,XN,p1,p1T,XN,p1,p2T], and BIT=[bit0,bit0¯,bitMs1,bitMs1¯]T. The codes are then transformed to the waveform as follows. Let h0 denote the element of H. If code X1,0,0 is transmitted and bit0 is 1, h0 is 1/3. In contrast, if the codes X1,0,0 and X1,1,0 are transmitted and bit0 is 1, h0 will be 2/3. If the codes X1,0,0, X1,1,0, and X1,2,0 are transmitted and bit0 is 1, h0 becomes 1. If the codes without X1,0,0, X1,1,0, and X1,2,0 are transmitted and bit0 is 1, h0 is 0. Let Vm,max denote the maximum value of modulation voltage Vm. Afterward, hi is included in the voltage setting in the transformation to the waveform, i.e., Vm=Vm,max+2Vm,maxhi.

Figure 3 shows the receiver structure of the proposed ONU(τ) with ESP codes for TCK in an OCDMA system. The ONU(τ) comprises two sets of fiber Bragg gratings (FBGs), one balanced detector, and an integrator. The two FBG sets are constructed based on the codewords Xe,m,n and Xe,m,n. The upper output part is connected to the input part of the photodetector (PD) as PD0, and the lower output part is connected to the input part of PD1.13 The balanced detector is connected to an integrator. The two cross-correlation results Xe,m,nXf,q,r and Xe,m,nXf,q,r lead to the output of PDs 0 to 1 in the balanced detector.

Fig. 3

The receiver structures of the ESP codes for TCK in an optical network unit (ONU, τ).

OE_53_1_016104_f003.png

The principles of the FBG-based decoder are based on the cross-correlation described as in Eq. (1). The code sequences Xf,q,r are first received by the FBG-based decoder. Then, the signature code Xe,m,n achieves the modified cross correlation as shown in Fig. 3. The input of the correlator_τ1 represents the spectral components. The first output of the correlator_τ1 is connected to the FBG for the code sequence Xe,m,n. The second output of the correlator_τ1 is connected to the PD1. The spectral components with the FBG for the code sequence Xe,m,n are reflected back toward the PD1 to obtain the photocurrent I1,bit=x. The other spectral components are passed through the FBG for the code sequence Xe,m,n.

The other spectral components are connected to the correlator_τ0. The first output of the correlator_τ0 is connected to the FBG for the code sequence Xe,m,n. The second output of the correlator_τ0 is connected to the PD0. The spectral components with the FBG for the code sequence Xe,m,n are reflected back toward the PD0 to acquire the photocurrent I0,bit=x. The other spectral components are passed through the FBG for the code sequence Xe,m,n. The average photocurrent is Ir,bit=0=I0,bit=0I1,bit=0andIr,bit=1=I0,bit=1I1,bit=1 corresponding to Eq. (1). Therefore, the principles of the FBG-based decoder are based on the cross-correlation.

Moreover, we eliminate the MUI with Eq. (1) according to the difference between the two correlations. Now, Table 2 compares the optical power budget for the conventional OLT using SP codes and the proposed OLT.6 Since the proposed OLT does not include splitter and combiner, which generally have high insertion loss, the power loss of the proposed OLT is much smaller than that of the conventional ones. This replaceable word is the insertion loss of A. The insertion loss of AWG is 3 dB according to the existing work.14 By contrast, the insertion losses in this paper are improved to 5 dB for the 1×49 AWG multiplexer and 5 dB for the 49×1 AWG demultiplexer, respectively. The total insertion loss is 10 dB. This replaceable word is the insertion loss of B and insertion loss of C. The insertion loss of AWG is 3 dB according to the literature.14 The insertion loss of 7×7 AWG is 2.4 dB according to the literature.15 By contrast, the insertion losses in this paper are improved to 4 dB for the 1×7 coarse AWG multiplexer and 4 dB for the 7×7 fine AWG, respectively. This replaceable word is the insertion loss of D. The insertion loss of the optical switch is 0.7 dB according to the existing work.16 By contrast, the insertion loss in this paper is improved to 0.9 dB for the optical switch. This replaceable word is the insertion loss of E and insertion loss of F. The insertion loss of the optical splitter (and optical combiner) is 11 dB according to the Ref. 17. Therefore, the insertion loss is 11 dB for the optical splitter (and optical combiner). This replaceable word is the insertion loss of EOM. The insertion loss of the EOM is 1.2 dB according to the existing work.18 By contrast, the insertion loss in this paper is improved to 2 dB for the EOM. The power budget difference will be increased with the value of p. Therefore, as p=7, the optical power budget (dB) decreases from 30.9 dB in the SP codes in Ref. 6 to 12 dB in the proposed OLT.

Table 2

Comparison of optical power budgets for conventional OLT with SP codes and proposed OLT with ESP codes.

Itemsn*Optical PB (Ref. 6)nOptical PB
Code Wp=7p=7
Ins. A00 dB110 dB
Ins. EOM00 dB12 dB
Ins. B14 dB00 dB
Ins. C14 dB00 dB
Ins. D10.9 dB00 dB
Ins. E111 dB00 dB
Ins. F111 dB00 dB
Total30.9 dB12 dB

Note: Optical PB: Optical Power Budget; Code W: Code Weight; Insertion loss of: Ins.; A: 1×49 and 49×1 AWG (DE)MUX; B: 1×7 Coarse AWG; C: 7×7 Fine AWG; D: 2×1 Optical Switch; E: 1×7 Splitter; F: 7×1 Combiner.

3.

System Performance

We first describe the signal-to-noise ratio (SNR) and bit error rate (BER) of the proposed scheme. The photocurrent noise variances are derived according to independent noise variances, i.e., <inoise,bit=02>=<iPIIN,bit=02>+<ishot,bit=02>+<ithermal,bit=02> and <inoise,bit=12>=<iPIIN,bit=12>+<ishot,bit=12>+<ithermal,bit=12>, where the average photocurrents in the received signals are I0,bit=0,I1,bit=0,I0,bit=1, and I1,bit=1.

Note that the cross-correlation between X1,0,0 and Xf,q,r corresponds to the cross-correlation of the PD current I0,bit=x and I1,bit=x with information bit=x Therefore, if the information bit is “0,” the two cross-correlations are I0,bit=0 and I1,bit=0. If the information bit is “1,” the two cross-correlations are I0,bit=1 and I1,bit=1. Before obtaining SNRbit=0, SNRbit=1, and BER, below we first derive the number of type-I simultaneous users, probability density function of the cross-correlation value, total cross-correlation, auto correlation, and photocurrent noise variances.

First, we derive the number of type-I simultaneous users. Let W denote the number of simultaneous users, and we randomly choose one of them as the major simultaneous user, which selects X1,0,0 code, whereas other (W1) simultaneous users will select other codes. The number of type-I simultaneous users is (W1)/N because (W1)(W1)/N simultaneous users have the cross correlation as “0.”

Second, we derive the probability density function of the cross-correlation value with “1” and “0.” The code weight is p, and p is odd. (p1) is the even because we adopt (p1) divided by 2 from the TCK, and the remainder is zero. The code size is Ms=N(p2p)/2 in TCK. The probability density function of the cross-correlation value with “0” is [(p1)/21]/[(p2p)/21]. The probability density function of the cross-correlation value with “1” is 1[(p1)/21]/[(p2p)/21].

Third, we derive the total cross-correlation. Before the derivation of the PD current, the total cross-correlation is Λ=(W1)/N(W1)/N(p3)/(p2p2), where the cross-correlation value is “0” and “1,” the number of type-I simultaneous users is (W1)/N, and the probability density function of the cross-correlation value is set with “0” and “1.”

Fourth, we derive the auto-cross correlation. (p+Λ) is the auto-cross correlation adding to the total cross-correlation. The code length (Np2) is incorporated in (p+Λ)/(Np2). The average photocurrents I0,bit=0,I1,bit=0,I0,bit=1, and I1,bit=1 are originated as follows. For information bit=0 we develop I0,bit=0 and I1,bit=0 as I0,bit=0=RPsr(p+Λ)/(Np2) and I1,bit=0=RPsrΛ/(Np2). For information bit=1 we develop I0,bit=1 and I1,bit=1 as I0,bit=1=RPsrΛ/(Np2) and I1,bit=1=RPsr(p+Λ)/(Np2). As the information bit=0 and “1,” the average photocurrent is as follows:

(2)

Ir,bit=0=I0,bit=0I1,bit=0=RPsr/(Np)andIr,bit=1=I0,bit=1I1,bit=1=RPsr/(Np),
where R is the responsivity of the photodiode.

Fifth, we derive the variance of the PIIN, shot noise, and thermal noise. According to the statistically independent noise characteristics, the variance of the PIIN current at each ONU receiver is as follows:

(3)

<iPIIN,bit=02>=BrR2Psr2p[(1+Λ/p)2+(Λ/p)2]/(ΔfNp2)=BrR2Psr2{1+2Λ/p+2Λ2/p2}/(ΔfNp),
where <iPIIN,bit=12>=<iPIIN,bit=02>. The above equations show that the ESP codes can increase the number of simultaneous users because the variance of PIIN current is reduced by N. Thus, the power of PIIN is also suppressed. Since shot noise is obtained from the mutually independent PDs 0 and 1, the variance in the shot noise current is expressed as

(4)

<ishot,bit=12>=2eBr(I0,bit=0+I1,bit=0)and<ishot,bit=12>=2eBr(I0,bit=1+I1,bit=1).

Moreover, the variance of the thermal noise current is as

(5)

<ithermal,bit=02>=<ithermal,bit=12>=4KbTnBr/RL.

Finally, we derive the SNRbit=0, SNRbit=1, and BER. We utilize the Gaussian approximation to find the BER, while the SNRs are SNRbit=0=Ir,bit=02/<inoise,bit=02> and SNRbit=1=Ir,bit=12/<inoise,bit=12>. Therefore, the BER is obtained as BER=erfc((SNRbit=0orSNRbit=1)/2)/26.

Figure 4 shows the numerical results with Δf=12.5TGz, λ0=1.55μm, the data transmission rate=2.5Gbps, Tn=300K, and RL=1030Ω. The Br of the receiver is half of the data transmission rate. Figure 4 compares the proposed ESP codes and SP codes with similar code lengths. We use the effective source power and data transmission rate to present 5dBm and 2.5 Gbps, respectively. The code weight is set as p=5, N=14, p=5, and N=8 in the ESP codes for TCK. The results indicate that the maximum number of simultaneous users for p=5 and N=14 in our proposed system can reach 60 as BER=109.

Fig. 4

Comparison of bit error rate (BER) in the proposed ESP and other codes with different numbers of simultaneous users.

OE_53_1_016104_f004.png

4.

Conclusion

We propose ESP codes and demonstrate that the effects of PIIN are effectively suppressed. Compared with the existing SP codes, our numerical results show that ESP codes can effectively increase the number of simultaneous users under 2.5-Gbps data transmission. Moreover, a universal OLT encoding architecture can be operated with other code families. Then, we also devise a AWG architecture for ESP codes to reduce the power loss and the complexity for OLT in PONs.

Acknowledgments

The authors wish to thank the High Speed Intelligent Communication (HSIC) Research Center at the Chang Gung University, Taiwan, for providing facilities and financial support which were crucial to our study.

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Biography

Bih-Chyun Yeh received his BS, MS, and PhD degrees in communication engineering from National Taiwan University, Taipei, Taiwan, in 1996, 1998, and 2009, respectively. He is now an assistant professor in the Faculty of Chang Gung University. His research interests include the lightwave and wireless communication systems.

Cheing-Hong Lin received his BS degree in communication engineering from National Chiao Tung University, in 1997, and his MS and PhD degrees in communication engineering from National Taiwan University, Taipei, Taiwan, in 1999 and 2005, respectively. His current research interests include lightwave and wireless communication systems and computer networks.

De-Nian Yang received his BS and PhD degrees from the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, in 1999 and 2004, respectively. He is now an associate research fellow in the Institute of Information Science, Academia Sinica. His research interests include multimedia and mobile networking, social networks, theoretical rigor, and practical feasibility.

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
Bih-Chyun Yeh, Cheing-Hong Lin, De-Nian Yang, "Universal optical line terminal encoding and decoding architecture in two-code keying for noncoherent spectral amplitude coding optical code division multiple access systems," Optical Engineering 53(1), 016104 (6 January 2014). https://doi.org/10.1117/1.OE.53.1.016104
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