Elsevier

Optical Fiber Technology

Volume 16, Issue 5, October 2010, Pages 309-314
Optical Fiber Technology

Optical CDMA system using 2-D run-length limited code

https://doi.org/10.1016/j.yofte.2010.07.001Get rights and content

Abstract

In this paper, time-spreading wavelength-hopping optical CDMA system using 2-D run-length limited code is investigated. The run-length limited code we use here is predicated upon spatial coding scheme, which can improve system performance significantly. In our proposed system, we employ carrier-hopping prime code and its shifted version as signature sequences. Based on the zero auto-correlation sidelobes property of signature sequence, we propose a two-state trellis coding architecture, which utilizes 2-D parallel detection scheme. The proposed scheme is compact and simple that can be applied to more complicated trellis to further enhance system performance. Multiple access interference is the main deterioration factor in optical CDMA system that affects system performance adversely. Aside from the multiple access interference, some of the adverse impacts of system performance are also taken into consideration, which include thermal noise, shot noise, relative intensity noise, and beat noise.

Introduction

As the bandwidth requirements are rapidly growing, the fiber-optic communication is preferable over the conventional transmission technology. Since the broadband access for local area networking is the last mile toward high-speed information network, optical code division multiple access (CDMA) techniques have been widely discussed for implementing digital subscriber loop [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15].

The time-spreading/wavelength-hopping (T/W) optical CDMA systems (i.e. 2-D) can provide more benefits than 1-D systems in terms of carnality, flexible code sequences, multiple access interference (MAI), and number of simultaneous access users; thus the 2-D optical CDMA systems have been extensively discussed for applications in local access links [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15].

The physical implementation of encoders/decoders is the key for the deployment of 2-D optical CDMA systems. Due to the rapid progress of optical encoders/decoders, time-spreading/wavelength-hopping coding technologies are widely investigated in optical CDMA systems. To implement 2-D optical CDMA configurations, some of the mature technologies have been demonstrated to achieve the functionalities such as array waveguide grating (AWG), fiber delay lines (FDL), fiber Bragg grating (FBG) [3], [4], [5], [6], [7], [11]. These devices have been commercialized with varying maturity and can be viewed as off-the shelf devices.

In optical CDMA system, the correlation property of signature sequence determines multiple access interference among the accommodated users, which will influence system performance significantly. In general, out-of-phase auto-correlation and out-of-phase cross-correlation must be as small as possible. In the 2-D time-spreading/wavelength-hopping optical CDMA systems, the signature sequences can be classified into two categories: single pulse per row and multi-pulse per row [12], [15]. The 2-D time-wavelength code structure can be represented by a time-wavelength code matrix [8], [9], [10], [12], [15]. The number of columns stands for the length of the signature sequence (also, the number of time-slots), and the number of rows represents the code weight (also, the number of wavelengths). There are different kinds of approaches to construct a 2-D time/wavelength signature sequences [8], [9], [10].

If each wavelength occurs only “once” on different time slots in the code matrix, the signature sequence is referred to as symmetric, or equivalently single pulse per row [12], [15]. Carrier-hopping prime code, prime hopping code, and some multi-wavelength optical orthogonal code (MWOOC) are this case [12], [15]. The symmetric code has zero auto-correlation sidelobes and the cross-correlation function at most one. In this paper, we will employ carrier-hopping prime code [9] as signature sequence to analyze system performance.

The run-length limited codes (RLL) are often utilized in magnetic or optical data storage system [16], [17], [18], [19]. In such systems, the detection scheme is like that of OOK (on–off keying) signaling scheme, which causes the transition probabilities for bit “1” and “0” different. This asymmetric property (i.e. different transition probabilities for bit “1” and “0”) is similar to that of optical CDMA system. Run-length limited code with error correction capability is preferable for it can further reduce detection error. Some of the error correctable RLL codes employing trellis structures had been discussed [16], [17], [18], [19]. For trellis decoding, the truncation length is about five times of constraint length [17], [18], [19]. The simple trellis structure with short constraint length is efficient for Viterbi algorithm in terms of computational complexity and memory requirement [17], [18], [19].

In digital transmission systems, the important reason for employing run-length limited code is to avoid a long consecutive bits “1” or “0”.There are two main reasons for this [17], [18]. For on thing, run-length limited coding leads to the spectral null which will free from the low-frequency loss in signal’s power spectrum. Furthermore, transmission using run-length limited code is composed of adequate timing information (i.e. sufficient level transitions), hence receiver utilizing self-synchronization scheme will benefit for the clock recovering. Our proposed 2-D optical CDMA system is an asynchronous transmission system. For asynchronous transmission systems, each user transmits data asynchronously with each other; hence network synchronization is unnecessary. However, transmitter and intended receiver should be in exact synchronism; otherwise, timing error brings about impairment of system performance [17], [18]. In this paper, we employ the trellis run-length limited code for application, but extend from 1-D into 2-D. Our proposed 2-D RLL scheme not only has sufficient timing content in transmission but also has the error correction correcting capability. Also, it can be easily applied to more complicated structure to further enhance system performance.

MAI is the major deterioration factor in optical CDMA systems. It had been investigated that optical beat noise (BN) will also affect system performance significantly [12], [13], [14], [15]. The beat noise depends on the wavelengths distribution in the code sequences, and the total BN variance is the sum of variances of signal–interferer and interferer–interferer [12], [15]. As discussed in [12], [15], the signal–interferer beat parameter is the total number of interferers’s pulses that hit the active wavelengths in the desired codeword, and the interferer–interferer beat parameter is the sum of combinational values of hits that have occurred at each wavelength of the desired codeword.

Aside from MAI and beat noise, we also take account of thermal noise, shot noise, and relative intensity noise (RIN). This paper is organized as follows. System architecture is depicted in Section 2, where 2-D coding scheme is presented. System performance using trellis-coded scheme is analyzed in Section 3. The numerical results and discussions are presented in Section 4. Finally, the concluding remarks are given in Section 5.

Section snippets

2-D T/W signature sequence

In this paper, we employ carrier-hopping prime codes as signature sequences, which are constructed with 2-D algebraic approach [9]. The code weight is w and the code length is p1p2···pk (i.e. the number of columns in the code matrix), where {p1p2···pk} is a set of prime numbers. The code weight w is the number of available wavelengths (also, the number of rows in the code matrix), where pkpk-1···p2p1w. The carrier-hopping prime code is a symmetric code; thus the out-of phase

Performance analysis

In our proposed architecture, we apply carrier-hopping prime code and its shifted version as signature sequences. In the 2-D trellis, we can observe that the probabilities for transmitting bit 1 and 0 are equally probably. For symmetric code, the error probability for transmitting bit 1 and 0 under K number of simultaneous users can be represented, respectively, as [12], [13], [14], [15]P1=i=1K-1K-1i2-(K-1)×j=1iij(Hav)j(1-Hav)i-j×P(e/1)P0=i=1K-1K-1i2-(K-1)×j=1iij(Hav)j(1-Hav)i-j×P(e/0)where

Numerical results and discussion

The link parameters are the same as those in [13] (unless otherwise specified) given as follows. The data rate is 100 Mbps, RIN = −120 dB/Hz, Pd = Pc = 1 μW, normalized threshold D = 0.5.

In Fig. 4, the bit error probability with and without coding scheme is plotted against the number of simultaneous users K for code length N = 101, and code weight w = 7, 9, 11, respectively. The proposed system can drastically improve system performance especially in fewer accommodated users. The larger simultaneous users K

Concluding remarks

In this paper, we propose a 2-D coding scheme for optical CDMA system. Our proposed two-state trellis coding scheme is based on run-length limited code, which extends from 1-D into 2-D. Predicated upon the spatial coding method, our scheme can further enlarge the free distance. Appling the orthogonality of time shifting version of signature sequences, the precoded data symbols are fed into 2-D optical CDMA encoder to produce signature sequences a(t), a′(t), or 0, respectively. In the receiver,

Acknowledgement

This work was supported in part by National Science Council, under Grant NSC 99-2221-E-197-013.

Maw-Yang Liu was born in Hualien, Taiwan, ROC, in 1970. He received the Ph.D. degree in electrical engineering and computer science from National Taiwan University, Taipei, Taiwan, in 2001. From 1993 to 2006, he was with National Taiwan Police Telecommunication Agency, where he worked on digital microwave radio, ATM, digital transmission systems, and WLAN. He joined the faculty of the Department of Electrical Engineering, National Ilan University in 2007. His main research interests are optical

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Maw-Yang Liu was born in Hualien, Taiwan, ROC, in 1970. He received the Ph.D. degree in electrical engineering and computer science from National Taiwan University, Taipei, Taiwan, in 2001. From 1993 to 2006, he was with National Taiwan Police Telecommunication Agency, where he worked on digital microwave radio, ATM, digital transmission systems, and WLAN. He joined the faculty of the Department of Electrical Engineering, National Ilan University in 2007. His main research interests are optical communication systems, spread spectrum techniques, and networking.

Joe-Air Jiang was born in Tainei, Taiwan, in 1963. He received the M.S. and Ph.D. degrees in electrical engineering from National Taiwan University, Taipei, Taiwan, in 1990 and 1999, respectively. From 1990 to 2001, he was with Kuang-Wu Institute of Technology, Taipei, Taiwan. Currently, he is a Professor of bio-industrial mechatronics engineering at National Taiwan University, Taiwan. His areas of interest are in computer communications, neuro-engineering, and bio-effects of electromagnetic wave.

Part of this article was presented in Conference IEEE ICIEA, Taichung Taiwan, June, 2010.

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