Dicode pulse-position modulation: a novel coding scheme for optical-fibre communications

M.J.N. Sibley

Abstract: Pulse position modulation (PPM) schemes have been proposed as a method of utilising the bandwidth available in optical fibres, with a 5-1 I dB improvement in sensitivity being achieved compared to an equivalent pulse code modulation (PCM) system. However, this improvement comes at a cost. If digital PPM is used, the final data rate can be almost 23 times that of the original PCM, and this makes implementation difficult. The author describes a novel coding technique that combines dicode, a tertiary code sometimes used in magnetic recording, and digital PPM to form dicode PPM. It is shown that dicode PPM gives a receiver sensitivity greater than digital PPM while operating at only four times the original data rate. Original results presented predict that a high fibre bandwidth dicode PPM system can give sensitivities of -50.44dBm and -44.27dBin when operating with 155.52 Mbit/s and 1 Gbit/s PCM data, respectively. This should be compared to typical PCM sensitivities of -38 dBm and -28 dBm. It is also shown that dicode PPM outperforms digital PPM at low fibre bandwidths by 3.02 dB.

1 Introduction

Various pulse position modulation (PPM) schemes have been proposed for usc in optical communications links [I-IS]. Although these schemes operate with higher data rates than their pulse code modulation (PCM) counterparts, they do offer a better sensitivity, with digital PPM giving a 5-1 1 dB improvement [ I -1 I] at the cost of increased band- width. The optimum receive filter for digital PPM consists of a noise-whitcncd matched filter and a proportional- derivative-delay (PDD) network [ 1 4 1 . Implementation is complicated because the PDD network has to be adjusted for individual links.

The dicode technique is usually used in magnetic recording channels [ 19-21] wherc bandwidth is limitcd, although there is some interest in using it in optical fibre links [22-251. In this signalling format, only data transi- tions are sent and no signal is transmitted when the data is constant.

This paper describes an original coding scheme that combines dicode and digital PPM to form dicode PPM. Like digital PPM, this new scheme offers a better sensi- tivity than PCM. However, unlike digital PPM, the system described in this paper achieves this with only a fourfold increase in speed. Original thcorctical results show that a simple. leading-edge, threshold-detection, dicode PPM system gives sensitivities slightly better than that of digital PPM at high fibre bandwidths, whereas for low fibre bandwidths, the sensitivity is significantly greater. Although results are presented for 155.52 Mbit/s and I Ghit/s PCM fihrc transmission, the technique could be

(Q IEE. 2003 IEE ~ ' ~ ~ ~ ~ ~ ~ i i ~ ~ ~ . ~ no. 200303x6 DO/: 10.I049/ip-opt:20030386 Paper first reccived 161h April and in revised form 23rd September 2002 Thc author i s with thc Deparlincnt of Flcctrical Engineering, Uniwrsity of Huddersfield, Queensgate, Huddersfield, West Yorkshire, HDI 3DH, UK

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used at higher hit-rates (technology permitting). I t can also be applied to free-space links and other detection schemes [ 16-1 81.

Before examining the performance of dicode PPM, it will be useful to discuss digital and dicode PPM in general.

1 .7 Digital PPM In digital PPM, the position of a pulse in a frame is controlled by the original PCM wor4 Fig. I . There are ta'o main variables in digital PPM signalling [l-31: the coding level (the number of PCM bits coded) and the modulation index (a measure of how much of the frame is used for data pulses).

The final data rate, /&f,,w, can be quite high, and is given by

2" fDPPM

where M is the coding level, B is the PCM bit-rate and m is the modulation index given by

\-I 2" + g

with g being the number of guard bits in the frame. If a coding level of 7 is used with a modulation index of 0.8, the line rate is 22.8 times the original PCM rate and this places great demands on system design [12]. To maintain frame synchronisation, a scheme has been developed to generate phase bearing events. It relies on the presence of a pulse in the last slot of one frame followed by a pulse in the first slot of the next frame [26-291.

Three sources of error affect digital PPM pulses: false alarms, erasures and wrong slots. To combat these errors, a noise-whitened matched filter and a PDD network can be used [2, 31.

125

Fig. 1 (hottom rrace)

Convemion of 4 hifs of PCM (top truceJ 10 digicol PPM

1.2 Dicode PPM In dicode signalling [19, 201, data transitions from logic zero to logic one are coded as +V and transitions from logic one to logic zero are coded as -V As shown in Fig. 2, a zero signal is transmitted if there is no change in the PCM signal. The positive pulse can be regarded as setting the data to logic one (pulse SET), whereas the negative pulse resets the data to logic zero (pulse RESET).

In dicode PPM, these SET and RESET signals are converted into two pulse positions in a data frame. Thus a PCM transition from zero to one produces a pulse in slot S and a one to zero transition generates a pulse in slot R, Fig. 2 . If the PCM data is constant, no signal is transmitted. (Although two guard slots have been used in this system, to reduce the effects of inter-symbol interference (ISI), this depends on the channel characteristics. If there is minimal ISI, zero guard slots could be used.)

In this particular system, four slots are used to transmit one bit of PCM, and so thc line rate is four times that of the original PCM: a considerable reduction in speed compared to digital PPM. As thc bandwidth requirement is much smaller than digital PPM, dicode PPM could be used in dense wavelength division multiplexing (DWDM) systems.

Dicode PPM uses a 4 symbol alphabet as shown in Table I , and a typical sequence would he R, x N , S with symbol probabilities of a, (f)~', f . The S signal has a probability o f f because there are only two possible PCM sequences (00 or 01) after an R pulse has been transmitted. If the original PCM is line coded so that the run of like symbols is limited to n, the maximum dicode PPM run would he R, nN, S. With this condition, the S symbol has a

photodiode I

Fig. 2 rmceJ ond dicude PPM (bottom trace)

Convcwion qf PCM dura (top traceJ into dicode (middle

Table 1: Dicode PPM symbol alphabet

PCM Dicode PPM Symbol

00 no pulse N 01 10

SET RESET

S R

11 no pulse N

probability of one because its presence is guaranteed at the end of a run of n lots of N symbols.

In common with digital PPM, the optimum filter for a dicode PPM receiver consists of a noise-whitened matched filter and a PDD network, as shown in Fig. 3. A voltage comparator then slices the data and the pulses are applied to a flip-flop, which is programmed according to the decoding rules given in Fig. 3. In operation, the decoder only examines the active data slots, and the decoding pro- cess stops as soon as a valid data pulse has been received in the frame.

To maintain fmme synchronisation, a slot clock can be extracted from the data and used to generate different phases of a DATA VALID signal, Fig. 4. The coding rule

S E l = S.~hfD,ppMUATAVALIU

RESET = Sl/zfDipppMDATA VALID voltage

~.... , " L a m parator m ~ ~ ~ ~ ~ ~ ~ ~ . . .

decoding logic

I .......... : I .......... : noise-whitening matched filter propoliional~

delay network

DiPPM receiver

filter derivative^

timing extraction (Fig. 4) I

Fig. 3 The dashed boxes are optional, see Section 3

I26

Schematic o j a dicode PPM receiver

1 - $1

Slot-Clock four-phase - $2 phase-

I "'DipPM

e extractlo" - 'DipPM

PPM

dicode PPM

generator Selecting b DATA VALID

--c $3 logic

--* $4

fDiPPM

DATA VALID

... -.

for dicode PPM is such that pulscs can only appear whcn this signal is true. Thus its phase caii be automatically adjusted to maintain synchronisation.

2 Error sources and probabilities

Three types of detection error occur in PPM systems: wrong-slot, erasure and false alarm [2, 31. The following Sections develop the equivalent PCM error probabilities for thcsc errors as applied to digital and dicode PPM.

in which (n;) is thc mcnn square noise of the receiver, and slope(t,,) is the slope of the received pulse at the threshold crossing instant, td.

For a digital PPM system, noise can cause a pulse to appear either before or after the original slot. Thus the probability of a wrong-slot error for digital PPM is

which zives rise to an eauivalent PCM error probability - 2. I Wrong-slot errors of PI These errors occur when noise on the rising edge of a detected pulse causes the pulse to appear in adjacent time (6)

2" 2(2" - 1) PewSLlPPM = p>wsDPP.U

slots. To minimise this error, the pulse should be detccted

slot. In the first case, 110 detection error occurs because the preceding slot is a guard and the decoder will not recognise the false threshold crossing. In addition, as the pulse is still present in the S slot, it will he detected correctly. In the second instance, the S pulse appears in aniR slot and this leads to detection errors. The probability of this happening is P,, as defined by (3).

P,\ = 0.5erfL 2 (3) ($1 where

(4) T s/upe(t<,)

2m Q,> = L'

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This detection error causes an immediate PCM error, and all following bits will be in error until an R pulse is received. ( I t is assumed that the probability of two errors occurring in a particular sequence is small.) If the number of following N signals is I, the transmitted and received sequences would be as given in Table 2 . Thus the number of PCM errors is x + I . As prcviously mentioned, line coding results in a maximum number of consecutive N symbols of n. With this condition, the probability of an R pulse will be one. Thus the PCM error probability is given by

Wrong-slot errors can cause an R pulse to appear in the preceding S slot or the following guard slot. In the first instance, the dctcction error gives the same number of errors as the S-R error, and so the PCM error probability is given by

,1+2 " -1

-=a Pea,,RS = (f)'v+3P.(x + 1) + (;I P,(n + 1) (8)

Loss of the R pulse due to noise shifting the rising edge into the following guard slot has a similar effect and so the PCM error probability is given by

The total, equivalent PCM error probability due to wrong slots is thereforc

P~~~~DIPP,II = Pe,,sn + Pe.Ins + Pe,,lRG ( IO)

2.2 Erasure errors Erasure of a pulse occurs when the noise is large enough to reduce the peak signal voltage to below the threshold level. This error occurs with probability Pe,. given by

where

vpr is the peak signal voltage at the output of the receiver and vI{ is the threshold crossing voltage.

In a digital PPM system, erasure of a pulse gives an equivalent PCM error probability of [SI

Table 2: Transmitted and received sequences with a wrong-slot error

Transmitted S XN R Received R XN R

1 Probability a p* (1)" i

128

In a dicode PPM system, erasure of a SET or a RESET pulse generates the same number of PCM errors and so the PCM error probability for erasures is

2.3 False-alarm errors False-alarm errors are due to noise causing a threshold- crossing event in any unoccupied data slot. The probability of this happening is

where

The number of uncorrelated samples per time slot can be approximated to TJrR where T~ is the time at which the autocorrelation function of thc receive filter has become small. The probability of a false alarm error then becomes

In a digital PPM system, this error source generates an equivalent PCM error probability of [8]

To cause PCM errors in a dicode PPM system, a false- alarm error must be of the opposite type to the symbol that started a sequence. With a pulse in slot S, a false alami could occur in the following R slot but, as the decoder stops when a pulse is received, no PCM errors will he generated. Howcvcr, an crrnr will be generated if a false alarm occurs in the following string of N signals. The severity of the error depcnds on where the false alarm occurs, as Tablc 3 shows.

The false-alarm error occurs on the kth N symbol in a run of xN symbols, and so the PCM error is (.x + I ~ k ) . In this instance, x must he greater than zero because, when an S pulse is transmitted a false-alarm error in the R slot has no effect. Thus the PCM error probability for this condi- tion is

A similar situation applies to false-alarm errors with an R pulsc. However, a false alarm could occur in the S slot

Table 3: Transmitted and received sequences with a false-alarm error

Transmitted S N N N N N R Received S N N R N N R

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immediately beforc the pulse. Thus the PCM error prob- ability is

The equivalent PCM error probability due to false alarms is therefore

pefD~PP,LI p @ X R + p#XS (20)

The total equivalent PCM error probability is found by adding together (6), ( I 3) and ( I 7) for digital PPM, whereas for the dicode PPM system, (IO), (14) and (20) should be used. The pcrformance criterion is that these error proh- abilities should be the same as for the PCM.

3 Signal and noise analysis

In common with digital PPM, the optimum predetection filter for dicode PPM consists of a noise-whitened matched tilter and a PDD network. which can be dispensed with ifthe pulsc dispersion is low [SI. In addition, if the reccivcr has a whitc noise spectrum over its bandwidth, the pre- detection filter becomes a classical matched filter and this is the system used in this paper.

The input pulse shape, h,(t), is assumed to have the following property:

h,,(f)dt = I (21) , [Y -Lv

Thus the preamplifier output voltage is

l:,Jf) = /~WLz,,,(t) * h,,(f)) 0c

= ""1 Z,,,(o)H,(w)exp(jwr)dw (22)

where b is the number of photons per pulse, hl' is the photon energy, R, is thc responsivity of the detector, 11 is the quantum efficiency of,the detector, y is the electronic charge, Zl,r~,(u) is the frequency dependent transimpedance of the preampliticr and H J w ) is the Fourier transform of the input pulse. The output of the matched tilter will therefore be

2n __

The input pulse shape is assumcd to be Gaussian and so

and

The pulsc variance, a_ is linked to the fibre bandwidth by

where T,, is the PCM bit time andf;, is the fibre bandwidth normalised to the PCM data rate.

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Assuming the receiver has a single pole response with a -3 dB bandwidth ofh., and a mid-hand transimpedance of R , the output voltage and its derivative are given by

(28)

The receiver noise appearing at the output of thematched tilter is

(29) 11)

= S,> R:.exp(a'wS)e~~(aw,) 2

wherc S,, is the double-sided, equivalent input noise current spectral density of the prcamplifier, assumed white. I t i s also assumed that a PIN photodiode is used, and that its shot noise can be ncglected.

The time at which the autocorrelation function of the noise at the output of the filter hecomcs small has been taken to be a. Although this is an approximation, the results are only slightly more pessimistic than actual. Thus

iR = U (30)

4 Performance evaluation

Instead of using the threshold crossing voltage as a system variable, another variable can he defined, v, as the ratio of the decision voltage to the peak signal voltage. Thus

V _ v d (31) "pk

-30 1

normalised frequency f,

Fig. 5 Con~puri.so,t of link sensitivity at 155.52 Mbirls irnd varying the $h,u bandwidth ,fop digiral PPM, uptiniised digirul PPM and &ode PPM

I29

Table 4: Comparison of sensitivities for digital PPM. dicode PPM and PCM at 155.52 Mbitjs and 1 Gbitjs PCM data rates

PCM data rate 155.52 Mbit/s sensitivity in dBm 1 Gbit/s sensitivity in dBm

Normalised fibre bandwidth fn f,,=l f,= 100 f"=1 f,=lOO

Digital PPM M = 7 m=0.8 -32.44 optimised -37.11

r u n lengh of 10 -40.13 Dicode PPM run length of 5 -39.75

PCM

-50.25 -25.94 -44.08 -50.25 -30.61 -44.08 -50.07 -33.25 -43.90 -50.44 -33.63 -44.27 -38 -28

Provided the fibre bandwidth is known, the pulse shape and noise can be determined. Assuming a PCM error rate of 1 in IO', the equivalent error rate of both systems must equate to this. Thus it is a matter of finding the optimum value of v that produces the lowest number of photons per pulse, b. The required optical power for the digital PPM system, PDpp,M, can then be found from

For the dicode PPM system, the required optical power, PDiPplM, is given by

where n is the maximum number of consecutive like symbols.

Simulations have been performed for a system operating at a wavelength of 1.55 pm, a photodiode quantum effi- ciency of loo%, and PCM data rates of 155.52 Mbit/s and 1 Cbit/s. Data relating to two commercially available receivers was used. For the 155.52 Mbit/s simulations, the Philips TZA 3043 was used with a bandwidth of 1.2 GHz and a white, double-sided noise spectral dcnsity of 16 x 1 0 - 2 4 A 2 / H ~ when referred to the input. For operation at 1 Gbit/s, the Philips CFY2lIOCU was used with a bandwidth of 10CHz and white noise of 50 x A2/Hz. It was initially assumed that the PCM data was line coded so that n = 5.

5 Results

Fig. 5 shows the variation in receiver sensitivity with fibre bandwidth for the digital PPM and dicode PPM systems operating at 155.52 Mbit/s. The results represented by the dotted line for the digital PPM system were obtained using 7 level coding and a modulation index of 0.8. As can be seen, the dicode PPM system offers a sensitivity slightly lower than digital PPM: approximately 0.2 dB at a fibre bandwidth of 100. However, if line coding results in n= IO , the dicode PPM system offers an improvement in sensitivity of 0.2 dB.

As the fibre bandwidth reduces, the sensitivity of the digital PPM system also reduces because the slot width is quite narrow with 7-level coding. Thus wrong-slot errors become significant for fibre bandwidths below IO. It is possible to compensate for this by adjusting the coding parameters, and the crosses in Fig. 5 represent the perfor- mance of a digital PPM system with optimised parameters. As can be seen, the dicode PPM system outperforms the digital PPM system for bandwidths less than I O even if these optimum parameters are used. This because the average power is lower in dicode PPM owing to the fact that, unlike digital PPM, only data transitions are coded. Simulations havc also been performed with the two

130

systems operating with I Gbit/s PCM data, and Table 4 summarises the results.

Also shown in Table 4 is the typical sensitivity of a PCM system, using receivers specifically designed for operation at the bit-rates used. As can be seen, dicode PPM offers a considerablc improvement in sensitivity over PCM.

6 Conclusions

This paper has described an original coding technique for use in optical fibre links. Thc technique combines dicode signalling with digital PPM to form dicode PPM. The performance of the new code has been analysed and compared to that of digital PPM and PCM.

Sensitivity calculations have been carried out with varying fibre bandwidths. With a fibre bandwidth of IO0 times the PCM bit-rate, the predicted sensitivity is -50.44 dBm with 155.52 Mbit/s data and -44.27 dBm with 1 Gbit/s data. This is comparable to digital PPM, and 12 dB and 16dB better than typical, equivalent PCM links. At a fibre bandwidth of one times the bit-rate, the dicode PPM system outperforms digital PPM with predicted sensitivities of -40.13 dBm (at 155.52 Mbit/s) and -33.63 dBm (at I Gbit/s).

As well as offcring a better sensitivity, this particular dicode PPM system operates at only four times the PCM data rate. This should be compared to digital PPM that could, potentially, run at 23 times the PCM data rate. Thus this new code is a viable alternative to traditional PCM and digital PPM systems. The technique should be applicable t o free- space systems, and could run with higher PCM data rates.

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