Frame synchronization performance of SONET signals

Computer Networks and ISDN Systems 25 (1992) 183-190 North-Holland

183

Frame synchronization performance of SONET signals * Z. Luan, J.F. Hayes and M.K. Mehmet Ali Concordia University, Department of Electrical and Computer Engineering, 1455 de Maisonneuve Bh, d. West, Montreal, Que., H3G 1M8 Canada

Abstract Luan, Z., J.F. Hayes and M.K. Mehmet Ali, Frame synchronization performance of SONET signals, Computer Networks and ISDN Systems 25 (1992) 183-190. This paper investigates the frame synchronization performance of the current SONET signal. The main result is the demonstration of degradation in the frame synchronization performance of the higher level STS-Ns. Since STS-N has a framing pattern which is N times longer than STS-1, the framing is more easily corrupted by transmission errors. A long framing pattern reduces the probability of random data mismatching the frame pattern; however, beyond a certain framing length, this mismatch is quite unlikely. Increasing the framing length worsens both search and maintenance performance. Therefore, it is proposed that the framing pattern of all the higher level STS-Ns (N > 3) be 48 bits (the framing length of the current STS-3). An analysis of the proposed approach shows an improvement in frame search and maintenance performance of high level STS-Ns while holding the performance of low STS-1 and STS-3 at the same level as the current SONET signal.

Keywords." SONET; frame; synchronization.

1. Introduction to S O N E T

Synchronous Optical NETwork (SONET) has been recommended by CCITT as a synchronous optical digital hierarchy of signalling rates and formats [2]. It is designed to meet the requirements of the future transport of many different types of payload. Since the S O N E T signals are constructed in a synchronously framed structure, frame synchronization is basic to proper system operation. The entire hierarchy of S O N E T signals are defined by the definition of the first level STS-1, since the higher level signals are obtained by synchronously multiplexing lower level signals.

Correspondence to: Dr. J.F. Hayes, Concordia University, Department of Electrical and Computer Engineering, 1455 de Maisonneuve Blvd. West, Montreal, Que., H3G 1M8 Canada. Tel. (514) 848 7896, Fax (514) 848 2802. * This work was supported by the Natural Science and Engineering Research Council of Canada, grant GSA 5949.

Figure 1 shows the frame structure of the STS-1 consisting of 9 rows each consisting of 90 bytes. The first two bytes (A 1, A 2) of 90 columns and 9 rows of 8-bit bytes form the framing signal. Since the order of transmission of bytes is row by row, left to right, the framing is transmitted at the beginning of a frame. Higher level STS-N is formed by byte-interleaved multiplexing of the lower level signals with frame alignment. With the single-stage interleaving, i.e., interleaving N STS-ls to form a STS-N, the first byte of the STS-N shall be the A 1 framing byte from STS-1 #1 followed sequentially by the A1 byte from STS-1 # 2 through #N. For example, the framing signal for STS-3 is A ~ A 1 A ~ A 2 A z A 2, six bytes at the beginning of the frame. Although the longer framing pattern of STS-N reduces the possibility of random data mismatch, it becomes vulnerable to transmission errors. This may result in frame synchronization failure occurring more often than system specification. Furthermore, a long framing pattern also requires

0169-7552/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

Z. Luan et al. / Frame synchronization performance of SONET signals

184

90

Bytes

tween frame synchronization failure and frame synchronization acquisition.

7\

~

~

87

Bytes

2. Framing accepting / rejecting probabilities 9 ROWS

\

/

Transport Overhead

Fig. 1. STS-1 frame: A i A 2 two-byte flaming, C I STS-1 ID.

more complex framing circuitry in the receivers. It is the purpose of this paper to choose a framing pattern length which strikes a balance be-

Frame synchronization circuits employ two operation modes, named search mode and maintenance mode [5]. The search mode searches sequentially through all candidate framing bit positions until framing is detected. Once the framing is detected, the circuit is switched into the maintenance mode, which continuously monitors for correlation between the received framing pattern and the expected framing pattern. If the maintenance mode detects a loss of frame synchronization, the search mode is reentered.

Zaihua Luan received the S.B. and S.M. degrees in 1982 and 1984, respectively, from the Beijing Institute of Posts & Telecommunications, Beijing, China, and the Ph.D. degree in 1989 from Keio University, Tokyo, Japan, all in electrical engineering. She taught in the Department of Information and Control at Xi'an Jiaotong University, China, in 1984-1985. In 1989-1990, she was with the Department of Electrical Engineering at Concordia University, Montreal, Canada, as a post-doctoral researcher. Since April 1990, she has been at Bell Northern Research, Ottawa, Canada, where she is a member of scientific staff working on SONET network synchronization. Her research interests include network synchronization, timing distribution and recovery, and digital transmission systems.

Jeremiah F. Hayes (S'65-M'66-F'83) received the BEE from Manhattan College, NY, in 1956, the MS in mathematics from New York University in 1961 and the Ph.D. in electrical engineering from the University of California, Berkeley in 1966. He is currently a member of the faculty of Concordia University, Montreal, Que. He has also served on the faculties of McGill University, Montreal, Que. (1978-1984) and Purdue University, Laffayette, Ind. (1966-1969). From 1969 to 1978, he was at Bell Labs, Holmdel, NJ. Dr Hayes' research interests have been in the computer communications networks and communications theory. He has written a number of papers on these subjects, two of which were awarded prizes by the IEEE Communications Society and the IEEE Information Theory Group, respectively. He is the author of the book Modeling and Analysis of Computer Communications Networks (Plenum Press) 1984 and the forthcoming Data Communications Principles (with R.D. Gitlin and S.B. Weinstein) (Plenum Press). He is currently a member of the IEEE scholarship committee and has just accepted the position of Senior Editor of the IEEE Journal of Selected Areas in Communications. Mustafa K. Mehmet Ali received BSc and MSc degrees from Bogazichi University, Istanbul, Turkey, in 1979 and a Ph.D. degree from Carleton University, Ottawa, Ontario, Canada in 1983 all in electrical engineering. He was a Research Engineer at TELESAT Canada until the end of 1984. Since then he has been with the Department of Electrical and Computer Engineering at Concordia University, Montreal, Canada, where currently be is an Associate Professor.

Z. Luan et al. / Frame synchronization performance of SONET signals

It is recognized that, b e c a u s e of the framing sequence, not all of the bits in a S O N E T frame are truly random. However, because the number of such positions is very small compared with the random data positions (about 0.2 percent), we ignore this difference and treat them as the random data positions. Therefore, except the first bit position in a S O N E T frame, all bit positions are considered to be the random data position. A detection of framing means that there is a match of the received framing pattern with the expected pattern when there are • or fewer bit errors. In practice, • = 0 or 1. Correspondingly, there is a detection of frame loss during the maintenance mode if the mismatch exceeds the criterion of mismatch in • bit positions. If the candidate bit position is the true framing positions, it has a probability of PAT to be accepted as framing position and probability of PRT to be rejected. If we assume that bit errors occur independently from the position to a position with the same probability, Pe, the probabilities PAT and PRI can be calculated from the binomial distribution. If, as is usual, the probabilities of bit error are small, we obtain a simplifying approximation.

i=E+l\ l

LPe, • = 0

--

I

L( L -

PAT = 1 -- PRT

1) p~, • = 1

(la)

(lb)

where L is the framing pattern length in bits. For STS-N, L = 16N bits. In the search mode, a bit position in the midst of random data has a probability PAF of being falsely accepted as the framing, due to the random data mismatching, and a probability PRF of being rejected. PAF-- 2 L i:0~ t PRF : l -- PAF

8

0

1O" N~

STS-1 16 24

:12

185

40

STS-3 Framing length 48 56 64

'

i

I

I

I

I

1() ~.

~

10 ' ; . / ~

10 ~'

10 ~ ' j

Z III I,

l0 I'., Fig. 2. Probability of rejecting the true framing position, PRT, and probability of accepting a false framing position. PAF, with respect to the framing length L when e = 0.

in the received framing pattern not matching the expected one. On the other hand, for a longer framing pattern, PAF falls almost exponentially with L. For example, STS-3 ( L = 48) has PRT = 4.79 × 10 -3 and P~,F = 3.55 × 10 -15 when e = 0 and Pe = 10-4, while STS-12 ( L = 196) has PRT = 1.90 × 10 2 and PAF = 4.47 X 10 -44. As L increased four times, PRT increases a factor of about four; however, PAF is small enough to be ignored even for STS-3. This implies that increasing the framing length beyond a certain point is harmful to frame synchronization performance. Figures 2 and 3 illustrate PRT and PAy versus L when • = 0, 1, respectively. PRY is shown for several values of Pe. As we see, PRT becomes large as L increases, while PAF rapidly declines to an negligible value and it is not effected by transmission errors (or their effect can be ignored). With a tolerant criterion (• > 0), PRT falls quickly, but PAF will increase and its rate of decline with respect to L will slow down.

(2b)

where it is assumed that, in random data, "zeros" and "ones" are equiprobable. It is seen that PUT increases either linearly or quadratically with respect to L depending on e. It is clear that longer framing patterns are more easily corrupted by transmission errors, resulting

3. M e a n t i m e o f f r a m e s e a r c h a n d f r a m e m a i n t e nance

Mean Time of Frame Search (MTFS) and Mean Time of Frame Maintenance (MTFM) are two criteria which may be used to evaluate frame

Z Luan et aL / Frame synchronization performance of SONETsignals

186

8 10° ' ~ . l ]

STS-1 16 2.t p .

STS-8 Framing length 32 40 48 56 61 . . .

1 _pr

10-2 AF ~

/Xr(p), and variance Crr2(p), of the number of checks until the first occurrence of r successive failures can be shown to be

IXr(P)-- qp------7--

10-4

1 ,.0 0

(3a)

~r~(p)- (qpr)2

2r+l

qpr

p

q2

(3b)

10-G

10-1~ Fig. 3. Probability of rejecting the true framing position, PRT, and probability of accepting a false framing position, PAF, with respect to the framing length L when E = 1.

where p is the probability of a success on a trial and q = 1 - p . Both P~r(P), and ~r2(p) approach p - r as p approaches zero. This means when p is small, the average number of checks until the first occurrence of r successive failures is large with a large standard deviation. But as p approaches one, Ixr(p) approaches r and ~rr(p) approaches 0. In the sequel, we will see the cases of p -~ 1 and p ~ 0 are relevant to S O N E T frame synchronization. When false synchronization is considered, p = PRF, while for true synchronization, p = PRT"

Mean time of frame search synchronization performance. MTFS expresses the performance of the search mode operation as the mean time required for frame synchronization reconstruction after a frame loss has occurred. While MTFM, the mean time of holding frame synchronization describes the frame maintenance performance. In order to discuss MTFS and M T F M of S O N E T signals, the most commonly used method of r-successive failures is considered for frame maintenance operation. In the present digital hierarchy, for example, three successive failures are required to change mode. In this section, we treat r as a p a r a m e t e r to be determined. When it is in the maintenance mode, the synchronizer checks the expected framing position against the a c c e p t / reject criterion, if r successive checks all fail to meet the criterion, then the frame synchronization loss is declared and the search mode is initiated; if not, it remains in the maintenance mode and checks the expected framing position in the next frame. Assuming that each check succeeds or fails independently we have the well studied problem of success runs in Bernoulli trials [4]. The mean,

Suppose a true loss of flame synchronization has occurred. The search mode examines the candidate positions from a random starting point i with P(i)= 1/M(i = 1, 2,...,M), where M is the number of bits in each frame. For STS-N, M = 9 × 90 x 8 × N . If the check of a candidate position meets the accept criterion, it initiates the maintenance mode; if not, the search mode rejects it and shifts one bit to check the next candidate position. So, when the starting position is the true framing position (i = 1), the flame search time is one bit period if it is accepted with the probability PAT" If it is rejected, with probability PRY, ( M - 1) false positions have to be examined before reaching the true position in the next frame. Among these ( M - 1) false positions, on average there will be PAF(M- 1) false candidates accepted to be the true framing position, for each of these a mean number of checks IXr(PRv) is required to reject it in the maintenance mode, with M bits per check. When the search mode again reaches the true framing position, it repeats the same procedure as above until the true position is found. Therefore, for the starting position

Z. Luan et al. / Frame synchronization performance of SONET signals

of the true framing position, the mean search time is

Table 1 r

E

MTFS 1 = PAT + PAT[( M - 1) (PRF + PAF M/xr (PRF)) + MTFS1]

1

(4a) 2

Solving for MTFS 1, we find 1

MTFS1 - - 1 --

PRT

[PAT + PRT( / -- l) × (PRF +

3

PAFMIZr(PRF))]

[bits].

+ MTFS1,

i>1

PAFMI.tr(PRF)) [bits].

(5)

By averaging the mean time of frame search over the M starting positions, and dividing by the line transmission rate R we have the mean time to false synchronization in seconds 1

M

RM y'~ MTFSi i=1

1

2R(1

STS-48

68.797 167.561 910.656 74.879 272.656 1760.709 81.059 377.779 2612.543

62.978 62.502 62.500 62.978 62.502 62.500 62.978 62.502 62.500

62.533 62.504 62.503 62.533 62.503 62.503 62.533 62.503 62.503

62.621 62.501 62.501 62.621 62.501 62.501 62.621 62.50l 62.501

Table 1 gives the calculation results of MTFS for STS-1, STS-3, STS-12 and STS-48 when Pe = 10 5. For STS-I, PAFMr and PRT have values that are not negligible, therefore, its MTFS is quite large and increases with respect to e and r. For STS-3, both PAFMr and PRy are negligible, consequently, in this case MTFS is close to the minimum 62.5 txs. For STS-12 and STS-48, there is a small, but negligible increase due to the influence of PRY.

Mean time of frame maintenance

- PRT)

× [2PAT + ( M -

1)(1 +PRT)

×(PRF+PAFMtzr(PRF))]

[s]

(6)

For S O N E T signals, PRF and PAT are close to 1, as was shown in Figs. 2 and 3 with P R F = 1 PAF and PAT = 1 --PRT" Further, as we have observed/xr(p) --* r as p --* 1. Therefore, eq. (6) can be approximated by 1

MTFS =

0 1 2 0 1 2 (1 1 2

MTFS(p~s)(Pc = 10-5) STS-I STS-3 STS-12

(4b)

MTFSi = ( M - i + 1)(PRF +

MTFS =

187

2R(1 - PRT)

X[2+(M-1)(I+PAFMr)]

[s].

(7) Since PAF decreases almost exponentially as the length of framing pattern becomes long, a random data position will almost definitely be rejected, and PAFMr is approximately zero for the STS-N(N > 1). For example, we have PAFMr < 10 -v for all STS-Ns(N >~ 3). But PRT increases since a long framing pattern is vulnerable to transmission errors. Therefore, the requirements of making PAFMr and P R T close to zero to obtain fast frame search are contradictory ~vith respect to the framing pattern length.

Suppose that the true framing position has been found and the maintenance mode has been entered. The maintenance operation checks the expected framing position in the next frame and with the probability Pax the position is accepted. The true framing position is rejected with probability PRT because of transmission errors. If r consecutive failures occurred, the frame loss is declared and the search mode is initiated. The mean time of frame maintenance, therefore, is proportional to IXr(p), the mean number of checks before the first occurrence of r successive failures which was given in eq. (3a) with p = PRY" Since the check is made once a frame (in 125 ixs for SONET), M T F M is given as MTFM

=tZr(PRT)M/R =

125/xr(PRT )

[IXS]

(8) As we have seen IXr(p) is almost inversely proportional to pr when p is small, i.e., IXr(p) will be large if p is small. While here p = P R T , PRT increases as the framing becomes long. Consequently, /xr(PRT) becomes small as the framing length is increased, i.e. a longer framing pattern will result in a shorter frame maintenance time.

Z. Luan et al. / Frame synchronization performance of SONET signals

188 Table 2

a n d on m a i n t e n a n c e o p e r a t i o n . A s discussed above, a f t e r PAFMr< < 1 was satisfied, f u r t h e r inc r e a s e of f r a m i n g length results in d e g r a d a t i o n s in b o t h search a n d m a i n t e n a n c e p e r f o r m a n c e . W e can, t h e r e f o r e , c o n s i d e r the inequality

r P~

MTFM (E = 0) STS- 1

STS-3

STS- 12

1 10 4 10 5 10 6 10- 7 10 s 10 9 2 10 4 10 -.5

0.078 s 0.78 s 7.8 s

0.026 s 0.26 s 2.6 s

0.0066 s 0.065 s 0.65 s

1.3 min

26 s

6.5 s

13 min 2.2 hr 49 s 1.4 hr 5.7 days 1.5 years 152 years 1520 years 8.5 hr 11 months 949 years 9.49x105 years 9.49x10Syears 9.49x10Jlyears

4.3 min 43 min 5.5 s 9.0 rain 15 hr 2.0 months 17 years 1687 years 19 min 13 days 35 years 3 . 5 2 X 1 0 4 years 3.52x107 years 3.52x101°years

1.4 rain 14 min 0.35 s 34 s 56 min 3.9 days 1.1 years 105 years 19 s 4.9 hr 6.6 months 5.48x10 z years 5.48X105 years 5.48x10Syears

10 - 6

10 7 10 ~ 10 - 9

3

10 - 4

10 5 10 6 10 - 7

10 s 10 9

PAFMr << 1

W h e n E = 0, for e x a m p l e , we o b t a i n the following a p p r o x i m a t i o n o f M T F M from eqs. (1), (3), a n d (8). 125 M T F M = L Pd [ / z s ]

e = C

(9)

F o r the STS-N, t h e r e f o r e , its M T F M is N ~ times s h o r t e r t h a n t h a t of the STS-1, since its f r a m i n g p a t t e r n is N times l o n g e r t h a n S T S - I ' s . T a b l e 2 gives M T F M for STS-1, STS-3, a n d STS12. Obviously, the h i g h e r level S O N E T signal has a w o r s e M T F M t h a n the lower. T h e p u r p o s e of m a k i n g t h e f r a m i n g p a t t e r n long is to r e d u c e the possibility o f r a n d o m d a t a m a t c h i n g the f r a m e p a t t e r n . H o w e v e r , as the f r a m i n g p a t t e r n i n c r e a s e s to a c e r t a i n value, as shown above, the p r o b a b i l i t y o f r a n d o m d a t a mismatching, PAF, r e d u c e s to a negligible value, a n d results in the f r a m e search p e r f o r m a n c e ( M T F S ) r e a c h i n g its limit. F u r t h e r i n c r e a s e o f f r a m i n g p a t t e r n length will raise the p r o b a b i l i t y o f rejecting the true s h o r t e n e d f r a m i n g p a t t e r n d u r a t i o n s .

(10)

as the n e c e s s a r y c o n d i t i o n in selecting the framing length for h i g h e r level STS-Ns. F r o m Figs. 2 a n d 3 we have for L = 48, (framing l e n g t h o f STS-3) PAF < 10-11 (E ~< 2). Selecting f r a m i n g length of L = 48, t h e r e f o r e , will satisfy the above c o n d i t i o n a n d has

PAFMr
E~<2,

r~<3,

(11)

even for the highest level STS-48 ( M = 48 x 9 x 90 x 8 bits) c o n s i d e r e d in the c u r r e n t S O N E T s t a n d a r d . This suggests a possible f r a m i n g selection of L = 48 for all h i g h e r level signals. S u p p o s e the f r a m i n g of S T S - N ( N >/3) signal is f o r m e d by b y t e - i n t e r l e a v e d m u l t i p l e x i n g of the first t h r e e S T S - l s ' f r a m i n g signals a n d setting the f r a m i n g o f the rest S T S - l s to null o r r a n d o m data. F i g u r e 4 illustrates the f r a m i n g f o r m a t o f the STS-12 signal as an e x a m p l e . By p e r f o r m i n g the s a m e analyses as in Sections 2 a n d 3, we can o b t a i n M T F S a n d M T F M of the f r a m i n g p a t t e r n s h o r t e n e d S O N E T signals, which are given in T a b l e s 1 a n d 2, respectively, for STS-3. F o r M T F M , the f r a m i n g p a t t e r n is t h e s a m e for the h i g h e r STS-N; accordingly, the h i g h e r S T S - N has the i d e n t i c a l p r o b a b i l i t y o f b e i n g destroyed by r a n d o m e r r o r s a n d p r e s e n t s t h e identical m a i n t e n a n c e p e r f o r m a n c e ( M T F M ) as the

rA~,z~/~N N iN N IN N N N IN ,~ Ae/~N 'N 'N 'IN 'N N IN N 'N "C~'~C~C,.C~C~rC~'C~C~I

, ,,

. . . . . . . . LU.--L\ .... Byte

....

9

ROWS

4. S h o r t e n i n g f r a m i n g pattern S O N E T signals

o f higher

level

Framing length S e l e c t i o n o f the f r a m i n g l e n g t h should t a k e into a c c o u n t its effect b o t h on search o p e r a t i o n

N

Transport Overhead

/

Fig. 4. Shortened framing with L = 48 for STS-12 signals: A I A z framing bytes, A I A 2 = F 628 (H); C 1 STS-1 ID; N null byte.

Z. Luan et al. / Frame synchronization performance of SONET signals

removing the framing of the STS-ls being multiplexed as null, except for for the first three STSls', at the multiplexer; and restoring it for each STS-1 being demultiplexed at the demultiplexer. However, a shortened framing pattern will reduce the requirement of registers or buffers for frame pattern comparison. As was indicated in [1] and [2], before byte interleaving STS-1 signals to form STS-N signal, transport overhead of STS-1 must be frame aligned. The alignment is accomplished by adjusting the pointer value of the STS-ls to reflect the new relative position of the STS Synchronous Payload Envelopes (SPEs). Figure 5, given by the current SONET standard [2] as an example, illus-

STS-3, shown in Table 2. For STS-12, for example, its mean maintenance period with the shortened framing pattern becomes 3 times when r = 1, 16 times when r = 2, and 60 times when r = 3 longer than that of the current STS-12, respectively. These results show us that reducing the framing pattern of the higher level STS-N can improve its frame synchronization performance, particularly, its frame maintenance performance.

Requirements at multiplexer and demultiplexer Shortening the framing pattern of the higher level SONET signals require~ some extra operations at the multiplexers and demultiplexers, e.g.

I BIP-8 Tracer Signal Label

STS-t Pay l o a d I n f

+

OH i

I

I

dl B3 C2 GI

1 Note i

F2 H4 Z3-Z5

I

+ I STS-I BPE Unequipped

Path S t a t u s U s e r CH Pointer Growth

T

Add P a t h

189

Calculate path BIP channel and place next frame.

• I of

B

over

i n B3 o f NOTE i

STS-Nc

STS-1

STS-I Path AIS I

line OH Align

Add

Frame

© Calculate Dlaca in

next

frame

Line AIS

Other

Add~ion

ON

I

STS-Is

Framing S T S - I ID BIP-8

Ai. A2 Ci B1 Ei Fi Ol .....

Ordarwire U s e r Oh D a t e Com Byte

interleave

Note

end C1)

+ Calculate

STS--N e n d ~I

Note

~NNots

section BIP place next freme

8

over

in Bi of STS-I

of

i:

For

2 2

Note

2

NNNote

O3

3

Note Note Note Note

2 2 2 2

STS-Nc,

overhead for the

the STS-N signal except framing end STS-ID Bytes

(A1. AR.

Note Note

I

+ Scramble for the

D12

I I

J

H1. H2 H3 B2 K1. K2 D4 . . . . . Z i , Z2 E2

Growth Orderwire

llne SIP 8 over STS-I B2 o f

Pointer Pointer Action BIP-8 APS D a t e Com

2: 3:

Oniy

of

t h e STS P a t h Is only allocated first STS-I.

defined

OC-N l i n e

fop STS-I signal.

el

A1AR--FSRB(H) is d e f i n e d only for STS-¢ ~i, ~2. e n d e 3 o f OC-N l i n e signal. F o r STS--I ~4 . . . . . #N. AIA2--OOOO(H).

+ OC-N line eigKal Fig, 5. An example of STS-1 frame and OC-N line signal compositions.

190

Z. Luan et al. / Frame synchronization performance of SONETsignals .

.

.

.

.

.

.

.

.

.

.

.

.

I I I I I I

•I

Add

I

ST,~-~

,-'IN

Add

Framing

I I

rs-I \

/

/IN

"xl

I

I

Detection

. . . . . . . . . . . . .

Add

I

~,~-,

?

J

Fig. 6. Demultiplexing. trates the procedure of forming STS-1 signals and multiplexing them to form STS-N signal. Since the line and section overhead are added to the STS-1 frame after the frame alignment, we can implement framing shortening for the higher level STS-N very easily if we set the framing of STS-I #1, #2, and # 3 to A 1 A 2 = F 628 (Hex), and the framing of other STS-ls to A 1 A 2 = 0000 (Hex) or random data. As shown in Fig. 5, except for Note 3 which we add for shortening the framing pattern, the multiplexing procedure is as same as in the original. Figure 6 gives an example implementation for restoration of STS-ls' framing. After demultiplexing, the framing of A 1 A 2 = F 628 (Hex) is added to each STS-1 with respect to the detected framing position.

5. Conclusions The framing scheme of the current S O N E T standard has performance degradation in the higher level STS-Ns, due to the increased probability of transmission errors over a longer framing

pattern. Since it was shown through the analyses that a long framing pattern is unnecessary for acquiring frame synchronization, it is proposed that the frame pattern duration of higher level STS-N should be reduced. A framing length of 48 bits (the framing length of the current STS-3) was shown as a proper length for all higher STS-Ns ( N > 3), which improved the frame synchronization performance, particularly, the frame maintenance performance. S O N E T has been a standard since 1988. Issues relating to signalling rates and format have been settled for the time being, thereby allowing product development to proceed. However, there is a continual process of completion and refinement by ANSI and CCITT. For example, Phase II will be released by ANSI by the end of 1991 and work on Phase III addressing O A M has begun. Although the current standard has reserved a large overhead channel for OAM, it is quite possible that there will be a demand for more capacity as O A M functions are developed. The shortening of the framing word that we propose may provide this extra capacity, with improved system operation. This sort of change to acquire more overhead has been proposed for other systems [3].

References [1] American National Standard for Telecommunications, Digital hierarchy optical interface rates and formats specification, ANSI Doc. Tl.105 Draft, March 1988. [2] R. Ballart and Y.-C. Ching, SONET: now it's the standard optical network, IEEE Comm. Mag. 27 (1989) 8-15. [3] W.J. Buckley, Which standard for the ESF data link?, Telephone Engineer and Management 93(20) (1989) 80-83. [4] W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, NY, 1957) 322. [5] D.R. Smith, Digital Transmission Systems (Wadsworth, Belmont, CA, 1985) 131.