ISIT2001, Washington, DC, June 24–29, 2001
A New Modulation Scheme Using Asymmetric Error Correcting Code Embedded in Optical Orthogonal Code for Optical CDMA Katsuhiro Kamakura and Iwao Sasase Department of Information and Computer Science Keio University 3-14-1 Hiyoshi, Kohoku Yokohama, 223-8522, Japan e-mail:
[email protected]
I. I NTRODUCTION Conventionally, optical CDMA systems with on-off keying (OOK) require a time duration equaling a signature sequence length to transmit only one bit. Since the crosscorrelation between the signature sequences results in multiaccess interference (MAI), the signature sequences are designed so that their weight distribution is sparse for their long length, and then the MAIs rarely occur. With this view, optical orthogonal codes (OOCs) are investigated [1], which are characterized by a quadruple (L, W, λa , λc ), where L and W are length and weight of sequences, respectively, and λa and λc are maximum off-peak autocorrelation and maximum crosscorrelation, respectively. Thus, the use of OOCs makes the effect of MAI small, but has to spend a long duration for one bit. In this paper, we propose an embedded modulation scheme, where an asymmetric error correcting (AEC) code is embedded in an OOC used for identification in optical CDMA. We show that the proposed scheme achieves the same bit error rate (BER) as the conventional systems, with less average number of photons.
encounters fewer than t + 1 asymmetric errors, then it correct them successfully. Fig. 2 shows the BER versus the average number of photons per bit µ for the proposed scheme using different AEC codes and OOCs. For reference, the BERs of the conventional optical CDMA systems using the correlation and the chip-level receivers with OOK [2]. We see that the proposed scheme achieves better BER than the correlation and chip-level receivers in the area of smaller µ. Both the conventional optical CDMA systems depend only on the low interference probability of OOC for reduction in MAI, while the proposed scheme increases the tolerance for MAI by using the AEC code, as well as the low crosscorrelation of OOC. It follows that the proposed scheme using the AEC code with large t achieves better BER at a small value of µ. : Electrical : Optical : Optical Delay line
(i)
where an ∈{1, 0} and the (W, k, t) AEC code can correct up to t asymmetric errors within block length W with k information bits. (i ) an modulates a pulse, which is delayed with the optical delay line, in the nth weighted position of the th signature sequence, where 1 (i) and 0 of an correspond to a mark and a space, respectively. The resultant output of the th transmitter is given by W (i) (i) () (1) an c () λ pTc t − jn Tc , s (t) = n=1
, jn
where λ is the intensity in the delay lines of the th user, Tc is the chip duration, and pTc (t) is a unit pulse waveform of duration Tc . When we consider an N-user optical CDMA system, the received optical intensity is a superposition of N users’ signals. The received intensity in the ith frame duration is detected with a photodetector. The photodetected signal is integrated over each chip position and then sampled at the corresponding weighted position ends of the desired user’s signature sequence. The obtained photocounts are independently compared to the threshold θ. If each photocount is equal to θ or more, a mark (a bit 1) is decided to be transmitted in the corresponding weighted position; otherwise, a space (a bit 0) is decided to be transmitted. Thus, a codeword composed of these W bits is received in the frame duration. If the decoder of the AEC code
( )
(i)
j2 Tc
( )
jW Tc
MSM
a (i) 2
k bits
( )
j1 Tc
a (i) 1
MSM
(W, k, t ) AEC Coder
aW(i)
MSM (i)
sn ( t )
1×W Combiner ( L ,W,1,1) OOC Encoder
Fig. 1: The block diagram of the th transmitter using the proposed modulation scheme. 10
10
Bit error rate
() denotes jn , where n∈{1, . . . , W }. Fig. 1 shows a block diagram of the optical CDMA system using the embedded scheme. Let denote k to k (i) , the (W, k, t) bits in the ith frame duration by k (i ) . According (i) (i ) (i) AEC coder generates a codeword a(i) = a1 , . . . , an , . . . , aW ,
1×W Splitter
MSM: Mark/Space Modulator
II. E MBEDDED M ODULATION S CHEME We assume that the set of the signature sequences is the (L, W, 1, 1) OOC, and that the th user is assigned the th signature sequence c = c,1 , . . . , c, j , . . . , c,L , c, j ∈{1, 0}. We call the chip position with c, j = 1 the weighted position, whose index j
Laser
10
0
a. b. c. d.
-2
AEC (8, 5, 1) (10, 4, 2) (11, 3, 3) (14, 3, 4)
OOC (6000, 8)
(4800, 10) (3600, 11) (3600, 14)
-4
a 10
10
10
-6
b c
-8
N = 10 Correlation Chip-level Embedded
-10
0
10
20
30
d
40
50
60
70
Average number of photons µ (photons/bit)
80
90
Fig. 2: BER versus the average photons per bit µ for four AEC codes, provided that N = 10, where the bit rate and the chip rate are identical. R EFERENCES [1] F. R. K. Chung, J. A. Salehi, and V. K. Wei, “Optical orthogonal codes: design, analysis, and applications,” IEEE Trans. Inform. Theory, vol. IT35, pp. 595–604, May 1989. [2] H. M. H. Shalaby, “Chip-level detection in optical code division multiple access,” J. Lightwave Technol., vol. 16, no. 6, pp. 1077–1087, June 1998.
