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					                                                                      T1E1.2/2000-041


                                                                    TR30.3/00-05-039
COMMITTEE T1 – TELECOMMUNICATIONS
Working Group T1E1.2
Lisle, Illinois May 1-5, 2000


TITLE:             Discussion of Robbed-Bit Signaling and Robbed-bit
                   Writeover (Bit Robbing in Tandem Digital Switches)

SOURCE:            Maynard Wright
                   TTC
                   9855 Scranton Road
                   San Diego, CA 92121
                   Phone: 916-726-1673
                          858-623-2573
                   Fax:   858-623-2208
                   wrightm@ttc.com


                            _____________________________




                                         ABSTRACT
This contribution discusses robbed-bit signaling and the associated
robbed-bit writeover that occurs when a DS0 is passed through a digital
message switch or through a DCS 1/0 cross-connect system.

The information here is intended for use by T1E1.2 in discussing several
matters involving robbed-bit signaling and robbed-bit writeover.




                                          NOTICE
This contribution has been prepared to assist Standard Committee T1 -
Telecommunications. This document is offered to the Committee as a
basis for discussion and is not a binding proposal on TTC or any other
company. The requirements are subject to change in form and numerical
value after more study. TTC specifically reserves the right to add to,
amend or withdraw the statements contained herein.



* CONTACT: Maynard Wright; email: mwright@ada.com; Tel: 916-726-1673; Fax: 619-623-2208
                                                           T1E1.2/99-041




1. INTRODUCTION
Robbed-bit signaling is described in Clause 4 of T1.403.02 [1]. Robbed-
bit writeover is described by Messerschmitt in [2], but will be de-
scribed in more detail here. The intent of this contribution is to pro-
vide information for use in discussing the V.90 modem problems that were
presented to T1E1.2 in February, 2000 by Jack Douglass of Conexant,
chairman of TR30.3 as well as for use in discussing the digital tandem
channel unit proposed by Lucent [5].
When the information carried by a DS0 channel [3] is extracted from a
DS1 signal incoming to a digital switch and is written into a DS0 time
slot in a different outgoing DS1 signal, the frame and superframe struc-
tures of the two DS1s will, in general, not be synchronous with each
other even if both DS1s are timed such that their bit rates are synchro-
nous or plesiochronous [4] with each other.
The incoming DS0 information must therefore be delayed in the digital
switch buffer until it may be written into the proper DS0 time slot in
the outgoing DS1. Since the DS0 may carry signaling data in the sixth
and twelfth frames if the DS1 is superframe (SF) formatted or in the
sixth, twelfth, eighteenth and twenty-fourth frames if the DS1 uses the
extended superframe (ESF) format, complete alignment with the outgoing
DS1 will require up to 1.5 ms of one way delay (3.0 ms round-trip) for
SF or 3.0 ms (6.0 ms round-trip) for ESF.
In order to avoid causing the DS0 to undergo delays of this magnitude, a
technique called “robbed-bit writeover” or “bit robbing” is generally
used. The information extracted from the incoming DS0 is delayed only
enough to ensure that it is written into the correct DS0 time slot in
the next outgoing frame, without regard to superframe alignment between
the incoming and outgoing DS0s. This requires a maximum one way delay
of 125 s (250 s round-trip: see Note 1).
Note that, unless the signaling bits are aligned by chance, the bits
carrying the robbed-bit signaling data will not be located within the
signaling frames of the outgoing DS1. In order to pass the signaling
data correctly, the switch determines the state of each incoming signal-
ing bit in the received DS0 and writes that state into the eighth bit of
each outgoing DS0 byte that occupies a signaling frame.
This technique writes over transmission information with signaling data
and causes bits that were formerly carrying signaling data to be misin-
terpreted by the distant DS0 demultiplexer as information bits. This
corruption of the digitally encoded analog signal can degrade the sig-
nal-to-noise ratio by between 1 and 2 dB in the initial tandem switch
[2]. Subsequent passes through additional switches may degrade the sig-
nal even more until the total drop in signal-to-noise ratio approaches 6
dB.
An alternate approach is suggested by Messerschmitt’s [2] second note on
page 1025. The DS0 might be delayed by a maximum of six frames so that
incoming signaling frames would be written only into outgoing signaling
frames. The possible misalignment of the A and B (SF) or A, B, C and D
signaling bits would be handled by passing the signaling information
around the switching matrix as is done when using robbed-bit writeover.
The maximum round-trip delay resulting from such a scheme would be 1.5
ms for both SF and ESF formats.




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2. EFFECTS OF DELAY
If exact superframe alignment of the incoming and outgoing DS0s is
achieved by delay, the maximum round-trip delay required is 6 ms for ESF
or 3 ms for SF. As pointed out in Section 1 of this contribution, the
round-trip delay might be reduced to a maximum of 1.5 ms by using only
partial superframe alignment with a maximum of six frames of delay in
each direction and by then passing the signaling states around the
switching matrix as is done when robbed-bit signaling is used.
The maximum round-trip delay within the local exchange network specified
by Section 8 of GR-499-CORE [6] is 0.32 ms for the equipment involved in
a transport system with no intermediate terminals. An additional delay
is allowed based on the route mileage.
Clause 4.7.2 of ANSI T1.506 [7] allow up to 10 ms of round-trip process-
ing delay between the NI and the POT, again providing an additional al-
location for the length of the circuit (Note 2). The allocation for the
terminal equipment is based, however, on a more complex circuit than is
specified in [6], and the amount of round-trip delay that is allocated
to a DCS, the network element that most closely approximates the func-
tionality proposed in [5], is 1.5 ms. The use of the partial superframe
alignment technique would thus consume the entire allocation of delay
allowed by [7] without leaving any margin for DS1 slip buffers or other
delays in the terminal equipment.


3. PROBABILITY OF WRITEOVER
Since 1 in 6 DS1 frames carry signaling data, the probability that
robbed-bit writeover will degrade a DS0 during its first pass through a
digital switch is 5 in 6. The probability that subsequent passes
through additional switches will eventually write over all the encoded
analog information that is carried in bit 8 of each DS0 is finite but
low.
Messerschmitt notes [2] that a closed form expression for the probabil-
ity that a particular number of additional signaling bits will have been
overwritten after the DS0 has been passed through a specified number of
switches is not available. [2] does, however, give an iterative proce-
dure for determining the required probabilities and the values in Table
1 were obtained by using that procedure.




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                                                                   T1E1.2/99-041




            1        2            3            4         5           6
      -----------------------------------------------------------------
  1     1            0            0            0         0           0
  2     0.16667      0.83333      0            0         0           0
  3     0.02778      0.41667      0.55556      0         0           0
  4     4.62963e-3   0.16204      0.55556      0.27778   0           0
  5     7.71605e-4   0.05787      0.38580      0.46296   0.09259     0
  6     1.28601e-4   0.01993      0.23148      0.50154   0.23148     0.01543
  7     2.14335e-5   6.75154e-3    0.12903     0.45010   0.36008     0.05401
  8     3.57225e-6   2.26838e-3    0.06902     0.36458   0.45010     0.11403
  9     5.95374e-7   7.59102e-4    0.03602     0.27756   0.49661     0.18904
 10     9.92290e-8   2.53530e-4    0.01852     0.20305   0.50637     0.27181


                                   Table 1


In Table 1 the horizontal legend represents the number of information
bits per six frames that have been overwritten and the vertical legend
represents the number of switches through which the DS0 has been passed.
Using Messerschmitt’s convention [2], the first “pass through a switch”
represents the initial robbed-bit writeover performed at the transmit-
ting DS1 terminal. The overwriting of exactly one bit per six frames is
thus certain (probability = 1) for that value.
An alternate presentation of the data, suggested by Steven Bench of TTC,
plots the probability that, after a particular number of switches have
been traversed by the DS0, at least a certain number of bits will have
been overwritten with the specified probability. Such a plot represents
the upper tail area of the cumulative distribution of the values in Ta-
ble 1. The alternate presentation is plotted below in Table 2. The
significance of each legend in Table 2 is the same as in Table 1.




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                                                                      T1E1.2/99-041




           1     2               3             4            5         6
       -----------------------------------------------------------------
   1       1     0               0             0            0         0
   2       1     0.83333         0             0            0         0
   3       1     0.97222         0.55556       0            0         0
   4       1     0.99537         0.83333       0.27778      0         0
   5       1     0.99923         0.94136       0.55556      0.09259   0
   6       1     0.99987         0.97994       0.74846      0.24691   0.01543
   7       1     0.99998         0.99323       0.86420      0.41409   0.05401
   8       1     1               0.99773       0.92871      0.56413   0.11403
   9       1     1               0.99924       0.96322      0.68566   0.18904
  10       1     1               0.99975       0.98123      0.77818   0.27181


                                     Table 2


Messerschmitt presents in equation 16 an expression for the mean value
of the number of overwrites as a function of switch sections traversed.
Table 3 presents values obtained from equation 16 for several numbers of
traversed switches:


                     switches                  mean number of
                     traversed                 bits overwritten
                     ---------                 ----------------
                        1                           1
                        2                           1.833
                        3                           1.528
                        4                           3.106
                        5                           3.589
                        6                           3.991
                        7                           4.326
                        8                           4.605
                        9                           4.837
                       10                           5.031


                                      Table 3


4. NOTES
1. The actual delay (one way) required here is about 125 s minus the
   period of one bit (647.7 ns). Here, and elsewhere in this
   contribution, the single bit offset in the delay requirement will be
   ignored for simplicity.


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                                                           T1E1.2/99-041




2. Both [6] and [7] specify a maximum delay based on route length of
   0.0168 * M, where M is the facility length in miles and the result is
   in milliseconds.


5. REFERENCES
[1]   ANSI T1.403.02-1999, Network and Customer Installation Interfaces
      - DS1 Robbed-Bit Signaling State Definitions
[2]   David G. Messerschmitt, Effect of Bit-Robbing in Tandem Digital
      Switches, IEEE Transactions on Communications, Vol. COM-27, No. 7,
      July, 1979
[3]   ANSI T1.107-1995, American National Standard for Telecommuni-
      cations - Digital Hierarchy - Formats Specifications
[4]   Working Group T1X1.3 contribution T1X1.3/2000-002R0, (draft)
      Technical Report on Synchronization Architecture
[5]   Working Group T1E1.2 contribution T1E1.2/2000-024, Digital Tandem
      Channel Unit with U-DSL Interface
[6]   Bellcore GR-499-CORE, Transport Systems Generic Requirements
      (TSGR): Common Requirements, Issue 1, December, 1995
[7]   ANSI T1.506-1997, American National Standard for Telecommuni-
      cations - Network Performance - Switched Exchange Access Network
      Transmission Specifications




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