Three-level Code Division Multiplex for Local Area Networks

Three-level Code Division Multiplex for Local Area Networks Mokhtar M. 1,2, Quinlan T. 1 and Walker S.D. 1 1. University of Essex, U.K. 2. Universiti Pertanian Malaysia, Malaysia Abstract: This paper reports potential spectral efficiency enhancements in Local Area Networks (LANs) introduced by three-level code division multiplexing. Two different data schemes: non-return-to-zero (NRZ) and return-to-zero (RZ) are multiplexed in the electronic domain to generate a three-level coding sequence, on condition that in NRZ signal, the logic state 1 is represented by a high level (+E volts) and the logic state 0 by a zero level; while in RZ signal, the logic state 1 is represented by a low voltage (-E volts) and the logic state 0 by a zero level. Preliminary laboratory experiments show errorfree transmission with a 195Mbps, 2 15-1 pseudo-random binary sequence (PRBS). The encrypted optical sequence, generated from two input signals, is conveniently produced by a standard Mach-Zehnder modulator and 1552.52nm wavelength DFB laser diode. The experimental set-up is discussed in this paper and a proposal for a sequential digital decoding technique offered. Key words: Three-level code division multiplexing, non-return-to-zero and return-to-zero code. INTRODUCTION It is well known that early fiber optic links were point-to-point and just used a single wavelength. As bandwidth requirements increased, so did the need for full networking capability. This resulted in a move to wavelengthdivision multiplexing (WDM) and routing capabilities. More recently, security issues have arisen as well as need to straightforwardly accommodate more users. It is against this background that Optical Code Division Multiplexing (OCDM) is introduced; providing a means of

2 transmitting signals in the same bandwidth [1-6]. However, multiple access interference (MAI) in OCDM can create noise that degrades transmission performance. As we are concerned with bandwidth efficiency as well as code interference, the main focus here is on maximising capacity and signal-to-noise ratio at one wavelength. To achieve this, we have developed a three-level encoding-decoding process. In this paper, we use code-division multiplexing with the encryption realised by combining two data streams, theoretically doubling the WDM bandwidth efficiency. To prove this, let the capacity of a band-limited channel, C with additive white Gaussian noise (AWGN) carried by each channel in WDM network. We use the standard form of Claude Shannon s formula for the capacity (adopted from [8]) that is represented by : P C = W log 2 1 + N where C is the capacity or maximum average rate at which information can be transmitted over the channel, and has units of bits per second; W is the bandwidth of the channel in Hertz; and P/N is the ratio of the signal power divided by the noise power passed by the receiver front-end filtering (a dimensional quantity). If the network contains of N channel, and each channel carries the capacity of C bps, then the spectral efficiency of the network would be N(C/W) bits/sec/hertz. If we combine the two data streams for each channel (as proposed in the three-level binary encoding), the network capacity becomes 2C bps, resulting to 2N(W/C) bits/sec/hertz of spectral efficiency. By evaluating this performance, we found that the proposed coding would be able to maximise the signal-to-noise ratio (Eb/No) as explained in the appendix section. By multiplexing NRZ data with a set of {+E, 0} voltage and RZ data with a set of {-E, 0} voltage respectively, the data encryption should result in a three level scheme, represented by +E, 0 and E electric field. In section A, we describe the experimental set-up for the encoding, applicable at 195Mbps data rates at 1552.52nm wavelength. Noting the encouraging results in the encoding section, we describe a novel decoding technique in section B. some conclusions are offered in the last section. A. Experimental Set-up The experimental is shown in figure 1. An NRZ binary data stream is produced by the first generator and the second generator produces binary

RZ. Both NRZ and RZ data are amalgamated in a 195Mbps, 2 15 1 PRBS. Note that the NRZ data is biased +ve (producing a set of {E,0} voltages) while the RZ data is biased ve (producing a set of {0,-E} voltages). While a transition can occur for every half-bit per RZ data, the NRZ data is constant for each bit. In fact, the multiplexed data is a summation of the modulator driver output for every half-bit in the data sequence. 3 NRZ RZ PRBS:2 15-1 195Mbps coupler Amp MZM Polarization controller EDFA PIN Photodiode Laser diode 1552.52nm Oscilloscope Figure 1 : Experimental set-up for the three level binary encoding. The encoding devices can be simply realised by a 1:1 coupler that is used to multiplex both data. The data is synchronised to each other, leaving only the delay between clock generators as an issue. Amplification to a 6V signal level with 6 gain is used to drive the Mach-Zehnder (MZ) modulator. The MZ modulator produces the three-level coding signal, which implies a three-level 1552.52nm optical signal, controlled by 3-state polarization controller. The MZ modulator is biased at the null point by adjusting the bias voltage at 6.8V with the laser diode is biased at 60mA input current at 20 o C. As shown in figure 2, with a zero input, no light is transmitted, but as the +E and E electric voltages arise, the +1 and -1 inputs are transmitted. While this is a three-level signal in terms voltage, it is a two-level signal in terms of optical power. E out MZ modulator is biased at the null Vπ Vπ V Figure 2 : Biasing of the Mach-Zehnder modulator

4 To ensure sufficient optical signal power, an EDFA is provided to compensate for the loss in the MZ modulator. The transmitted and received signals are then measured on an oscilloscope. Figure 3 shows the synchronised NRZ and RZ data signal, followed by the coding signal at the transmitter. (a) (b) (0 +E) (+E +E) (-E 0) (0 0) (c) Figure 3 : (a) NRZ data (b) RZ data (c) 3-level coding sequence

As the control voltage is added for each half-bit, four pattern possibilities appear in every single bit coding sequence. All the combinations shown in figure 3 are described in table 1. These patterns hold specific information for the NRZ and the RZ data that may be used to decode both signals. Further features of the decoding process will be discussed in the next section. 5 Table 1 : 1-bit coding sequence pattern possibilities 1-bit coding sequence Data information pattern NRZ RZ 0 0 0 0 0 +E 1 1 -E 0 0 1 +E +E 1 0 As the coded sequence propagates in the optical domain, time delays occur in the receiver system, but the signal is still correctly recovered as shown from the error-free eye in figure 4. To obtain the data synchronization between the received coding sequence and the clock decoder sequence, clock recovery at 195MHz is applied. Figure 4 : Eye diagram for the coding sequence at the receiver. B. Step-by-Step Decoding As stated previously, the pattern possibilities in table 1 hold specific information for the NRZ and the RZ data. The information would be applied here in order to retrieve both original signals. At the receiver, the voltages for each pattern could be mapped into logical signal by using a simple power detector and hence the +E and E outputs of the fiber get mapped to the same power level and detected as logical 1s. As the sequence, electric field patterns in table 1 could be routed to logic patterns as depicted in table 2.

6 Table 2 : Electric fields mapping for 1-bit coding sequence pattern possibilities. 1-bit coding sequence Data information pattern (S 1 S 2 ) NRZ RZ 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 Referring to table 2, it is shown that the pattern would be (0 0) when the both NRZ and RZ bits are 0. At first glance, it might be assumed that the S 1 value of the pattern represents NRZ value and the S 2 value refer to the RZ data. However the pattern (0 1) does not bear out this assumption (i.e NRZ is not 1 even though the RZ = 1) noting the pattern (1 0) and (1 1). As a result, every value in S 1 and S 2 is put as a variable for two functions. Each value that is obtained from each function will be present as a value of NRZ and RZ bit respectively. We derive the functions as follow in order to meet all the value of NRZ and RZ. For NRZ value, the f(n) = S 1n (1) while for RZ value, the f(r) = S 1n (+) S 2n (2) Noted that n is the data sequence for either S 1 or S 2, represented as an integer 1,2 N and (+) is a symbol of EX-OR operation. From equation (1) and (2), we design a logical circuit (as depicted in figure 5) which is just a functionality diagram, ignoring any delay propagation that might occur in the real implementation. Figure 5 : Decoder logical circuit. The circuit is consisted of a basic demultiplexer [DEMUX_1TO2], 1-bit delay [2X_DELAY] for G 1n sequence, RZ-to-NRZ format converter [RZ_2_NRZ] and logic decoder for NRZ and RZ data [DEC_NRZ] and [DEC_RZ]. As the first demultiplexer does not demultiplex the coding sequence into S 1 and S 2 directly, we put the 1-bit delay for G 1n sequence and the RZ-to-NRZ converter into the design to obtain the S 1 and S 2 sequence. Let assume that the coding sequence after the power detection is a data sequence D for the demultiplexer. D sequence is represented as (D 1, D 2, D 3, D 4.), where the odd sequence is makes enable active from t 1 and the

even sequence is start enable active from t 2. The period between t 1 and t 2 is equal to a half-bit period in the S sequence. When the D sequence is transmitted at t 1, D 1 is activated in the AND gate 1; while in the AND gate 2, 0 output is carried out. Next at t 2, D 2 is activated in the AND gate 2; while in the AND gate 1, 0 output is delivered. This process occurs continuously and generates a form of G sequence for each AND gate output that can be presented as follows: AND gate 1 output = (G 1n, 0) sequence n=1,2,3, N AND gate 2 output = (0, G 2n ) sequence n=1,2,3, N The schematic and waveform diagram for the basic demultiplexer is illustrated in figure 6. 7 Gate 1 Gate 2 Pattern (1 0) (0 1) (1 1) (0 0) Figure 6 : Demultiplexer (a) schematic diagram (b) waveform result As the (G 1n, 0) sequence is concerned, it is in fact a scheme of RZ format data which can be converted into NRZ signal simply with a positive-edge trigger D-flip-flop. The reason is that, the NRZ value of each output is in fact S 1 and S 2 sequence respectively. The RZ data is applied to D and the recovered clock is applied to the C. The timing of the clock must be delayed and precisely positioned to be the center of the RZ data pulse. For the (0, G 2n ) sequence; in order to remain the G 2n sequence contents, it is also possible to convert the data into NRZ signal by using the negative-edge D-flip-flop. The NRZ-to-RZ conversion diagram is shown in figure 7.

8 Figure 7 : NRZ to RZ converter However, this conversion results on a 1-bit delay for the output (0, G 2n ) sequence. The synchronisation of S 1 and S 2 must agree to meet the function efficiency from equation (1) and (2). Otherwise, the decoding will fail. To overcome this problem, we add a 1-bit delay after the (G 1n, 0) sequence and replace the positive-edge flip-flop by the negative-edge flipflop in the RZ-to-NRZ converter. Therefore the NRZ and RZ signal at the transmitter would be retrieved after feeding the S 1 and S 2 sequence into the logic function of f(n) and f(r) respectively. The waveform simulation result is demonstrated in figure 8. Note that the obtained original data is detected after 1 ½ bit delay at the first output but still meet the decoding requirements exactly as discussed previously. Conclusion 1 ½ bit delay Data1 Data2 Data3 Data4 Figure 8 : Decoding result of 4 patterns coding sequence. The three-level code division scheme described has the potential to double bandwidth per wavelength. Code encryption is realised within the multiple level data transmitted rather than the wavelength bandwidth (i.e. two data streams are encrypted as a new data sequence but retain the information of both signals), and avoids any multiple interference issues. The 195Mbps data rate that is demonstrated in the laboratory experiment shows the suitability of the system in LAN s. Appendix : Derivation of the Spectral Efficiency Form of Shannon s Capacity Formula [8] From equation P C = W log 2 1 + N

we obtain a capacity equation involving spectral efficiency in terms of Eb/No by making the substitution N = W. N o. Thus we get C P = W 2 W 1 (1) N Dividing both sides in (1) by C gives C P W = 2 W 1 (2) N oc C To introduce Eb/No, we now reason as follows. When operating at capacity, the average energy per information bit equals the average signal power divided by the average information rate in bits per second, i.e., E b = P / C (3) Substituting in (2) using (3) gives a useful formula relating the achievable spectral efficiency C/W to the Eb/No signal-to-noise ratio : 9 C E b W = 2 W 1 (4) N o C As the capacity in the three-level binary scheme in WDM is double than the conventional WDM network capacity, we show that the achievable spectral efficiency C/W to the Eb/No signal-to-noise ratio is maximized by the following equation : E N b o W 2 C 2C = W 1 (5)

10 REFERENCES [1] Jawad A. Salehi Code-Division Multiple-Access Techniques in Optical Fiber Networks-Part I: Fundemental Principles, IEEE Transactions on Communications, Vol. 37, No. 8, Aug 1989, pp. 824-832 [2] Habib Fatallah, Leslie A. Rusch Economically Feasible Optical Code Division Multiple Access, IEEE Network Magazine, Jan 2000 [3] Cedric Fung Lam Multi-wavelength Optical Code-Division-Multiple-Access Communication Systems, University Of California, Los Angeles, 1999 [4] Fan R.K. Chung, Jawad A. Salehi, Victor K. Wei Optical Orthogonal Codes: Design, Analysis, and Applications, IEEE Transactions on Information Theory, Vol. 35, No. 3, May 1989, pp. 595 604 [5] Jian-Guo Zhang Design of a Special Family of Optical CDMA Address Codes for Fully Asynchronous Data Communications, IEEE Transactions on Communications, Vol. 47, No. 7, July 1999 [6] Paeiz Azmi, Masoumeh Nasiri, Jawad A. Salehi Low-Rate Super-Orthogonal Channel Coding for Fiber-Optic CDMA Communication Systems, Journal of Lightwave Technology, Vol. 19, No. 6, June 2001 [7] James R. Andrews, RZ vs. NRZ, Application Note AN-12, Copyright September, 2001 : http://www.picosecond.com [8] http://www.rand.org/publications/mr/mr960/mr960.appd.pdf