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IEEE Transactions on Communications

Limits to the encoding and bounds on the performance of coherent ultrashort light pulse code-division multiple-access

D. J. Hajela, Jawad A. Salehi

Published Jan 1, 1992• 21 citations
Publisher

Abstract

The authors obtain lower and upper bounds on the peak intensity of a spectrally phase encoded ultrashort light pulse as a function of the length of spectral phase encoding. It is shown that using random phase codes for spectral encoding of ultrashort light pulses in a coherent ultrashort light pulse code-division multiple-access (CDMA) system is almost optimal. Furthermore, simple upper bounds and an asymptotic approximation on the bit error rate (BER) for a wide class of ultrashort light pulse CDMA systems are obtained. It is shown that, in spite of being simple, these upper bounds can be used to evaluate the performance of a coherent ultrashort light pulse CDMA system.>

DOI
10.1109/26.129194

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Optical CDMA is being proposed as a suitable multiaccess technique to take advantage of the large bandwidth available in single-mode fiber-optic communications. In a CDMA system the communication link is shared by a number of users, each of which has a unique address code called signature. Recently an all-optical CDMA system based upon encoding and decoding coherent ultrashort light pulses was introduced. An important factor in the performance of the CDMA system is the peak intensity of the encoded signals. We consider using random signatures for the phase encoding of the light pulses in this system and prove that they result in a fairly low peak intensity of the signals. In particular, we obtain an upper bound on the probability that the peak intensity of the encoded signal is greater than some value. This bound is strictly better than previously reported bounds and decreases exponentially with the length of the signatures. We also find a lower bound on the maximum number of minimally interfering signatures (or, to be more accurate, A-separated signatures, which will be defined) of length No that can be designed. Assuming that the communication is reliable if and only if any pair of signatures in the system is A-separated, a notion of capacity is defined and a lower bound on it is found.

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The authors obtain lower and upper bounds on the peak intensity of a spectrally phase encoded ultrashort light pulse as a function of the length of spectral phase encoding. It is shown that using random phase codes for spectral encoding of ultrashort light pulses in a coherent ultrashort light pulse code-division multiple-access (CDMA) system is almost optimal. Furthermore, simple upper bounds and an asymptotic approximation on the bit error rate (BER) for a wide class of ultrashort light pulse CDMA systems are obtained. It is shown that, in spite of being simple, these upper bounds can be used to evaluate the performance of a coherent ultrashort light pulse CDMA system.>
Optical CDMA is being proposed as a suitable multiaccess technique to take advantage of the large bandwidth available in single-mode fiber-optic communications. In a CDMA system the communication link is shared by a number of users, each of which has a unique address code called signature. Recently an all-optical CDMA system based upon encoding and decoding coherent ultrashort light pulses was introduced. An important factor in the performance of the CDMA system is the peak intensity of the encoded signals. We consider using random signatures for the phase encoding of the light pulses in this system and prove that they result in a fairly low peak intensity of the signals. In particular, we obtain an upper bound on the probability that the peak intensity of the encoded signal is greater than some value. This bound is strictly better than previously reported bounds and decreases exponentially with the length of the signatures. We also find a lower bound on the maximum number of minimally interfering signatures (or, to be more accurate, A-separated signatures, which will be defined) of length No that can be designed. Assuming that the communication is reliable if and only if any pair of signatures in the system is A-separated, a notion of capacity is defined and a lower bound on it is found.
Optical CDMA is being proposed as a suitable multiaccess technique to take advantage of the large bandwidth available in single-mode fiber-optic communications. In a CDMA system the communication link is shared by a number of users each of which has a unique address code, called signature. Recently an all-optical CDMA system based upon encoding and decoding coherent ultrashort pulses was introduced [l]. In the proposed optical CDMA system the transmitter consists of a bandhiited signal source, that generates a train of ultrashort light pulses. The output of the bandlimited source is multiplied by a data source that takes values 0 or 1 (ON-OFF Keying). If the data is 0, then no energy is transmitted. If the data is 1, then the ultrashort pulse is sent to the spectral-phase encoder which adds a determinate phase shift to each spectral component of the ultrashort pulse. When a pseudorandom set of spectral phase shifts is selected, spectral phase coding spreads the incident ultrashort pulse into a longer, lower intensity pseudonoise burst 111. The receiver is assumed to be a correlation receiver which is matched to the desired signal. The correlation process (optical decoder) is similar to that of the optical encoder, except that the decoder's spectral-phase code is the complex conjugate of the encoder's spectral-phase code. Thus a pulse is properly decoded when the encoding and decoding masks are a complex conjugate pair, in which case the spectral phase shifts are removed and the original pulse is recovered. On the other hand, when the encoding and decoding masks do not match, the spectral phase shifts are rearranged but not removed, and the output remains a low intensity pseudonoise burst. A threshold device is set to detect data corresponding to intense, properly decoded pulses and to reject low intensity, improperly decoded, pseudonoise bursts. An important factor in the performance of the proposed CDMA systrm is the peak intensity of the encoded signals. We consider using random signatures for the phase encoding of the phase pulses in the system and prove that they result in a fairly low peak intensity of the signals. We assume that the ultra-short light pulses are characterized by an ideal rectangular spectrum with bandwidth W. The ultrashort light pulse has peak intensity Po and duration t, $. Pulses of this form had been used in the experiments reported in [l]. The encodfng is taking place in the frequency domain. The signal
The performance of coherent time-spreading (TS) and asynchronous TS phase coding optical code division multiple access (OCDMA) systems is investigated and analyzed. Particular consideration is given however to both beat noise (BN) and multiple-access interference (MAI) effects, and the impact of decision threshold on the bit-error-rate (BER) performance is evaluated. Improvement of the BER performance can be obtained by use of optimum threshold detection, and the improvement is more apparent in the asynchronous TS OCDMA scheme for a low number of simultaneous users with long code length.
Enhanced security has often been cited as an important benefit of optical code-division multiple-access (O-CDMA) signaling but has seldom been analyzed in detail. This paper presents a theoretical analysis of the degree of confidentiality that can be provided by spectral-phase-encoded O-CDMA. Two eavesdropping detector structures are presented that can theoretically break the confidentiality of spectral-phase-encoded signals by detecting the code words in use by a specific user. One of them, an optical beat detector, is quantitatively analyzed to determine the probability of correctly detecting user code words. The confidentiality of user signals is shown to be vulnerable to such a detector if an eavesdropper can isolate a single user signal with a sufficiently high signal-to-noise ratio (SNR). At lower SNRs, combining multiple bits is shown to dramatically increase the probability of an eavesdropper correctly detecting user code words; even for codes long enough to strain implementation capabilities (e.g., 2048 code elements), the probability of correct detection is shown to rise from negligibly low values to virtually 100% by the combining of less than 100 transmitted bits at the eavesdropper's receiver.
The performance of optical code-division multiple-access (CDMA) communication systems utilizing number-state light field is evaluated. Lossy direct-detection optical channels are assumed. Both on-off keying (OOK) and pulse-position modulation (PPM) schemes are investigated. For OOK, the exact bit error rate is evaluated taking into account the effect of both multiple-user interference and transmission loss. Upper and lower bounds on the bit error probability for PPM-CDMA systems are derived under the above considerations. The effect of both background and thermal noise is neglected in our analysis. Performance comparison between the number-state and coherent-state OOK/PPM-CDMA networks is also presented. Our results demonstrate that the number-state system requires less than half the energy consumed by the coherent-state one in order to attain the same performance. Lower bounds on the maximum number of simultaneous users are derived for both number- and coherent-state PPM-CDMA systems with asymptotically zero error rate.>
The performance of optical code-division multiple-access (CDMA) communication systems utilizing number-state light field is evaluated. Lossy direct detection optical channels are assumed. Both on-off keying (OOK) and pulse-position modulation (PPM) schemes are investigated. For OOK, the exact bit error rate is evaluated taking into account the effect of both multiple-user interference and transmission loss. Upper and lower bounds on the bit error probability for PPM-CDMA systems are derived under the above considerations. The effect of both background and thermal noise is neglected in the analysis. A comparison between the performance of the number- and coherent-state OOK/PPM-CDMA networks is also presented. The results demonstrate that the number-state system requires less than half the energy consumed by the coherent-state one in order to attain the same performance.>