
What
are Modems ?
|
Presented
by: |

Copyright 2000© |
|
|
|
|
MODEMS
Prepared by : Benny Assif, Yosy Breznitz,
Bat-Sheva Ovadia, Yoram Shnapp
BRIEF OVERVIEW
The modem is a device that converts
digital information to analog by MODulating it on the sending end , and
DEModulating the analog information into digital information at the
receiving end.
This document begins with an introduction
followed by the classification of modems according to their characteristics.
Later, standards and protocols are discussed.
Finally, the document overview today's status
and future trends.
INTRODUCTION
The need to communicate between distant
computers led to the use of the existing phone network for data
transmission. Most phone lines were designed to transmit analog
information - voices, while the computers and their devices work in
digital form - pulses. So, in order to use an analog medium, a converter
between the two systems is needed. This converter is the MODEM which
performs MODulation and DEModulation of transmitted data. It accepts
serial binary pulses from a device, modulates some property (amplitude,
frequency, or phase) of an analog signal in order to send the signal in
an analog medium, and performs the opposite process, enabling the analog
information to arrive as digital pulses at the computer or device on the
other side of connection.
Modems, in the beginning, were used
mainly to communicate between DATA TERMINALS and a HOST COMPUTER. Later,
the use of modems was extended to communicate between END COMPUTERS.
This required more speed and the data rates increased from 300 bps in
early days to 28.8bps today. Today, transmission involves data
compression techniques which increase the rates, error detection and
error correction for more reliability.
In order to enable modems of various
types and different manufacture to communicate, interface standards were
developed by some standard organizations
Today's modems are used for different
functions. They act as textual and voice mail systems, facsimiles, and
are connected or integrated into cellular phones and in notebook
computers enabling sending data from anywhere. The future might lead to
new applications. Modem speeds are not expected to be increased much
over today's 28.8 kbps. Further dramatic speed increases will require
digital phone technology such as ISDN and fiber optic lines.
New applications might be implemented
such as simultaneous voice and data. Videophones are an example of this.
CLASSIFICATION OF
MODEMS
The modems can be classified according to
their characteristics:
Classifying Modems according to :
Range
* Short Haul
Short haul modems are cheap solutions to
systems of short ranges (up to 15 km), which use private lines and are
not part of a public system. Short haul modems can also be used, even if
the end-to-end length of the direct connection is longer than 15 km,
when both ends of the line are served by the same central office in the
telephone system. These lines are called "local loops". Short
haul modems are distance-sensitive, because signal attenuation occurs as
the signal travels through the line. The transmission rate must be
lowered to ensure consistent and error-free transmission on longer
distances.
Short haul modems tend to be cheaper than
other modems for two reasons:
- (1) No circuitry is included in them
to correct for differences between the carrier frequency of the
demodulator and the frequency of the modulator.
- (2) Generally no circuitry is included
to reduce/correct for noise rejection, which is less of a problem
over short distances than over long distances.
There are two main types of short haul
modems:
- Analog modems, using a simple
modulation method, without sophisticated devices for error control
or equalizers. These modems usually operates at a maximum rate of
9600 bps, but there are some which supports higher rates (up to
64,000 bps).
- Line drivers increase the digital
signal, which transmit to the communication channel and do not
transmit the carrier signal, as conventional modems. Line drivers
are very cheap and tiny and connect to the RS232 connector of the
terminal (since they lack a power supply, they use the signal
voltage of the DTE-DCE interface for DC power supply).
* Voice Grade (VG)
Voice-grade modems are used for unlimited
destination, using a moderate to high data rate. These modems are
expensive and their maintenance and tuning are sophisticated.
Communication channels are leased lines and dial-up.
Voice-band telephone network is used for
data transmission. A user-to-user connection may be either dedicated or
dialed. The links in the connection are the same in the two cases, and
the only difference for the user is that for some impairments
(particularly attenuation and delay distortion), a dedicated (private
or leased) line is guaranteed to meet certain specifications, whereas a
dialed connection can only be described statistically.
* Wideband
Wideband modems are used in large-volume
telephone-line multiplexing, dedicated computer-to-computer links. These
modems exceed high data rates.
Classifying Modems according to :
Line Type
*
Leased, Private
Leased, private or dedicated lines
(usually 4-wire) are for the exclusive use of "leased-line"
modems - either pair (in a simple point-to-point connection) or several
(on a multidrop network for a polling or a contention system). If the
medium is the telephone network, their transmission characteristics are
usually guaranteed to meet certain specifications, but if the link
includes any radio transmission, the quality of it may be as variable as
that of a switched (i.e. nondedicated) line.
* Dial up
Dial-up modems can establish
point-to-point connections on the PSTN by any combination of manual or
automatic dialing or answering. The quality of the circuit is not
guaranteed, but all phone companies establish objectives. The links
established are almost always 2-wire because 4-wire dialing is tedious
and expensive.
* Two and Four-Wires Lines
A four-wire (4W) line is a pair of
two-wire (2W) lines, one for transmitting and one for receiving, in
which the signals in the two directions are to be kept totally separate.
Perfect separation can be maintained only if the four-wire configuration
is sustained from transmitter to receiver. The lines may be combined in
a 4W/2W network (often called a hybrid or a hybrid transformer)
at any point in the signal path. In this case impedance mismatches will
cause reflections and interference between the two signals.
Classifying Modems according to :
Operation Mode
* Half
Duplex
Half duplex means that signals can be
passed in either direction, but not in both simultaneously. A telephone
channel often includes an echo-suppressor, allowing
transmission in only one direction, this renders the channel
half-duplex. Echo suppressors are slowly being replaced by echo
cancelers, which are theoretically full-duplex devices.
When a modem is connected to a two-wire
line, its output impedance cannot be matched exactly to the input
impedance of the line, and some part of its transmitted signal (usually
badly distorted) will always be reflected back. For this reason half-
duplex receivers are disabled (received data is clamped) when their
local transmitter is operative.
Half-duplex modems can work in
full-duplex mode.
* Full
Duplex
Full duplex means that signals can be
passed in either direction, simultaneously. Full duplex operation on a
two-wire line requires the ability to separate a receive signal from the
reflection of the transmitted signal. This is accomplished by either FDM
(frequency division multiplexing) in which the signals in the two
directions occupy different frequency bands and are separated by
filtering, or by Echo Canceling (EC).
The implication of the term full-duplex
is usually that the modem can transmit and receive simultaneously at full
speed. Modems that provide a low-speed reverse channel are sometimes
called split-speed or asymmetric modems.
Full duplex modems will not work on
half-duplex channels.
* Simplex
Simplex means that signals can be passed
in one direction only. A remote modem for a telemetering system might be
simplex and a 2-wire line with a common
unidirectional amplifier is simplex.
* Echo Suppressor and
Echo Canceler
At the junction between the local loop,
which is usually a 2-wire circuit, and the trunk,
which is a 4-wire circuit, echoes can occur. The
effect of the echo is that a person speaking on the telephone hears his
own words after a short delay. Psychological studies have shown that
this is annoying to many people, often making them stutter or become
confused. To eliminate the problem of echoes, echo suppressors are
installed on lines longer than 2000 km. (On short lines the echoes come
back so fast that people cannot detect them). An echo suppressor is
a device that detects human speech coming from one end of the connection
and suppresses all signals going the other way. The device compares the
levels at its two input ports, and if it decides, for example that the
other end is talking, it inserts an attenuator in the return (echo)
path, and vice versa.
Echo suppressors have several properties
that are undesirable for data communication. First, they prevent full-
duplex data transmission, which would otherwise be possible, even over
the 2-wire local loop (by allocating part of the bandwidth to the
forward channel and part to the reserve channel). Even if half-duplex
transmission is adequate, they are a nuisance because the time required
to switch directions can be substantial. Double-talking totally confuses
them, and the attenuation may be switched in and out repeatedly.
Furthermore, they are designed to reverse upon detecting human speech,
not digital data.
To reduce these problems, when echo
suppressors detect a specific tone they shut down, and remain shut down
as long as the carrier is present (this is an example of inband
signaling, where control signals that activate and deactivate
internal control functions lie within the band accessible to the user).
This disabling is usually done during initial handshaking by one modem
transmitting an answer tone in either 2100 Hz (CCITT
standard) or 2225 Hz (modems following the old Bell
103 standard).
Echo suppressor are slowly being replaced
by ECs, which allow a certain amount of double-talking and do not
require "capture" time for any one talker to assume control of
the connection.
Classifying Modems according to :
Synchronization
*
Asynchronous Modems
Most of the modems that operate in slow
and moderate rates, up to 1800 bps, are asynchronous (using asynchronous
data). Asynchronous modems operate in FSK
modulation and use two frequencies for transmission and another two for
receiving. Asynchronous modems can be connected in different options to
the communication media:
In a 2-wire line,
full duplex operation can be achieved by splitting the channel into two
sub-channels.l
Figure Modem - 1
* Asynchronous
data
Asynchronous data is not accompanied by
any clock, and the transmitting and receiving modems know only the
nominal data rate. To prevent slipping of the data relative to the
modems' clocks, this data is always grouped in very short blocks
(characters) with framing bits (start and stop bits). The most common
code used for this is the seven-bit ASCII code with even parity.
*
Synchronous Modems
Synchronous modems operates in the audio
domain, at rates up to 28800 bps in audio lines, used in telephones
systems (using synchronous data). The usual
modulation methods are the phase modulation and integrated
phase and amplitude (at higher rates than 4800 bps).
In synchronous modems, equalizers are
used, in order to offset the misfit of the telephone lines. These
equalizers are inserted in addition to the equalizers, that sometimes
already exist in the telephone lines.
These equalizers can be classified into
three main groups:
- Fixed/statistical equalizer -
these equalizers offset the signal according to the average of the
known attenuation in each frequency. Tuning the equalizer is
sometimes done in the factory and stays fixed, usually they are used
to operate at low rates in a dial up line.
- Manually adjusted equalizer -
these equalizers can be tuned to optimal performance to a given
line. These equalizers should be re-tuned when the line is replaced
and periodically. Specially, it should be tuned frequently when the
line is of a low quality and it's parameters are changed frequently.
Tuning is done using a button inside the modem (or on the external
board).
- Automatic equalizer - these
equalizers are tuned automatically when the connection is
established. Depending on the line quality in a specific moment, in
a process of about 15ms to 25ms, after the first tuning, the
equalizer samples the line continually and adjusts itself to the
changed conditions, so the modem operates at each moment under
optimal conditions. The fitness process operates, in some modems, at
rates of 2400 times in a second.
Synchronous modems operate in the same
manner asynchronous modems. However, synchronous modems operates at
higher rates and since the requirements to transmit at these rates is
increasing, most of the innovations are implemented for synchronous
modems.
In synchronous modems the channel can be
split for several consumers at various speeds. Modems who have this
ability are called SSM - Split System Modem. These modems can use a
simple split or a split using multipoint connection.
Synchronous data
is accompanied by a clock signal. Synchronous data is almost always
grouped in blocks, and it is the responsibility of the data source to
assemble those blocks with framing codes and any extra bits needed for
error detecting and/or correcting according to one of many different
protocols (BISYNC, SDLC, HDLC, etc.). The data source and destination
expect the modem to be transparent to this type of data, conversely, the
modem can ignore the blocking of the data.
Classifying Modems according to :
MODULATION
Communication channels like telephone
lines are usually analog media. Analog media is a bandwidth limited
channel. In the case of telephone lines the usable bandwidth frequencies
is in the range of 300 Hz to 3300 Hz.
Data communication means moving digital
information from one place to another through communication channels.
These digital information signals have the shape of square waves and the
meaning of "0" and "1"
If such digital signals were transmitted
on analog media the square waves of the digital signals would be
distorted by the analog media as shown in figure Modem-2. The receiver
which receives these distorted signals will be unable to interpret
accurately the incoming signals. These digital signals must be converted
into analog signals so that the communication channels can carry the
information from one place to another. The technique which enables this
conversion is called modulation .
FIGURE Modem-2*
Modulation
Modulation is a technique of modifying
some basic analog signal in a known way in order to encode information
in that basic signal. Any measurable property of an analog signal can be
used to transmit information by changing this property in some known
manner and then detecting those changes at the receiver end. The signal
that is modulated is called the carrier signal, because it carries the
digital information from one end of the communication channel to the
other end.
The device that changes the signal at the
transmitting end of the communication channel is called the MODULATOR.
The device at the receiving end of the channel, which detects the
digital information from the modulated signal, is called the
DEMODULATOR .
A basic analog signal is a sinusoidal
wave which can be written in mathematical form as follows :
S(t) = A * SIN ( 2* PI * F * T + PHI )
were A is the peak amplitude, F is the signal frequency and PHI is the
phase of the signal . Modulation can use any of these three measurable
and changeable properties of the sine wave for encoding purposes.
There are three modulation techniques, each of them changes one of the
properties of the basic analog signal.
* AM - amplitude modulation
This technique changes the amplitude of
the sine wave. In the earliest modems, digital signals were converted to
analog by transmitting a large amplitude sine wave for a "1"
and zero amplitude for a "0", as shown in figure Modem-3. The
main advantage of this technique is that it is easy to produce such
signals and also to detect them. This technique has two major
disadvantages. The first is that the speed of the changing amplitude is
limited by the bandwidth of the line. The second is that the small
amplitude changes suffer from unreliable detection. Telephone lines
limit amplitude changes to some 3000 changes per second. The
disadvantages of amplitude modulation causes this technique to no longer
be used by modems, however, it is used in conjunction with other
techniques .
FIGURE Modem-3
* QAM - quadrature amplitude
modulation
This technique is based on the basic
amplitude modulation . This technique improves the performance of the
basic amplitude modulation. In this technique two carrier signals are
transmitted simultaneously. The two carrier signals are at the same
frequency with a 90 degrees phase shift. The mathematical form of the
transmitted signal will be as follows:
S(t) = A* SIN (Wc* t) + B* COS (Wc* t)
A, B, are the amplitude of the two carrier signals. Each of them can get
a value from a known set of values. In this way a few bits can be
transmitted in the period of one symbol time. For example consider the
set of values {1 , 2 , 3 , 4 }. In this example 4 different values can
represent 2 bits. During one symbol time 4 bits will be transmitted,
"A" will represent 2 bits and another 2 bits will be
represented by "B".
* FM - frequency modulation
In this technique the frequency of the
carrier signal is changed according to the data. The transmitter sends
different frequencies for a "1" than for a "0" as
shown in figure Modem-4.This technique is also called FSK - frequency
shift keying. The disadvantages of this technique are that again (as it
was with amplitude modulation) the rate of frequency changes is limited
by the bandwidth of the line, and that distortion caused by the lines
makes the detection even harder than amplitude modulation. Today this
technique is used in law rate asynchronous modems up to 1200 baud only.
FIGURE Modem-4
* CPM - continuous phase
modulation
A modern technique which derives from
basic frequency modulation. The only difference is that in the
transition from one symbol to another the phase is continuously changed,
there are no phase steps. Continuous phase means that the transmitted
signal bandwidth is limited and faster data rates can be achieved for
the same bandwidth.
* PM - phase modulation
In this modulation method a sine wave is
transmitted and the phase of the sine carries the digital data. For a
"0", a 0 degrees phase sine wave is transmitted ( PHI = 0 ).
For a "1", a 180 degrees sine wave is transmitted ( PHI = 180
) as shown in figure Modem-5. This technique, in order to detect the
phase of each symbol, requires phase synchronization between the
receiver's and transmitter's phase. This complicates the receiver's
design.
FIGURE Modem-5
A sub method of the phase modulation is DIFFERENTIAL
PHASE MODULATION. In this method, the modem shifts the phase of
each succeeding signal in a certain number of degrees for a
"0" (90 degrees for example) and a different certain number of
degrees for a "1" (270 degrees for example ) as illustrated in
figure Modem-6. This method is easier to detect than the previous one.
The receiver has to detect the phase shifts between symbols and not the
absolute phase. This technique is also called PSK - phase shift
keying. In the case of two possible phase shifts the modulation
will be called BPSK - binary PSK. In the case of 4 different phase
shifts possibilities for each symbol which means that each symbol
represents 2 bits the modulation will be called QPSK, and in case of 8
different phase shifts the modulation technique will be called 8PSK.
FIGURE Modem-6
* TCM - trellis
coded modulation
A modern technique which uses the
modulation techniques that was discussed previously like QAM or PSK in
conjunction with coding in order to improve data rates.
HOW MODULATION IS USED
FOR DATA TRANSFER ?
Any technique of the various modulation
methods discussed previously or even any combination of these methods
(integrated modulation method) can be used for data transfer.
For example we shall look at the
following table:
relative phase bit symbol
amplitude shift meaning value
-------------------------------------------------------------------
1 45 0 0 0 "0"
1 135 0 0 1 "1"
1 225 0 1 0 "2"
1 315 0 1 1 "3"
2 45 1 0 0 "4"
2 135 1 0 1 "5"
2 225 1 1 0 "6"
2 315 1 1 1 "7"
In this example a combination of
differential phase modulation and amplitude modulation is used. Each
symbol is represented by a certain amplitude and phase shift. The
transmitting modem is combining 3 succeeding bits in to one transmitted
symbol. The receiving modem interprets each detected symbol to 3
succeeding bits. For the data sequence 10100101011001010, the
transmitted symbol' sequence will be: 6 4 5 1 2.
* Data Rate
The number of signal changes transmitted
per unit of time is called the data rate of the modem. That rate
is usually expressed in terms of a unit known as a baud. The baud is the
number of times per second the line condition can switch from
"1" to "0". Data rate and transmission speed , which
is expressed in terms of bits per second, usually are not the same, as
several bits may be transmitted through the channel by the modem in each
signal change (a few bits can be transmitted as one symbol).
Claude Shennon showed, in 1948, that the
maximum capacity (bit rate) of a bandwidth limited transmission line
with limited signal to noise ratio is:
C = W * log (1 + S/N) / log (2)
Where C is the maximum capacity, W is the limited bandwidth and S/N
is the power of the signal to noise ratio.
A telephone line, for example, has a bandwidth of 3000 Hz and maximum
S/N of about 1000 (30db). Thus the theoretically maximum data rate that
can be achieved is about 30 K bps (bits per second). Earliest modems
that work through telephone lines had 1.2 K bps. Today's modems reach
data rates of 28.8 K bps.
STANDARDS and
PROTOCOLS
Communication between two devices might
work only when the interface is defined and agreed. For modems, the
standards define techniques used for modulation, for error correction
for data compression, and other attributes. There are some standard
organizations for the development of interface standards. The ITU -
International Telecommunications Union an agency of the United Nations
(Geneva, Switzerland), ISO - International Standards Organization, and
CCITT - International Telegraph and Telephone Consultative Committee a
group of ITU.
The modem standards were developed during
the years and published as V series of recommendations. In the United
States the primary standards body is the ANSI - American National
Standards Institute. Its committees, concerned with information
processing and data communication, are designated X3 and X3S3,
respectively. The organizations deal with De Jure standards.
There are also De Facto standards which were developed by a specific
manufacturer, using new features in his products, while they were not
defined yet by the standard committees. When the definitions were
adapted by another manufacturers for compatibility they became a De
Facto standard.
Some examples of De Facto standards follow. The Bell-100 standards
established by the Bell System with their 100 and 200 series of modems;
Bell Dataphone 103 of 300 bps, that was introduced at 1958 was the first
modem used to transfer data over telephone lines. The modem command
language, "AT" commands, invented by Hayes but used by all
modem vendors ("AT" stands for "Attention" and each
command begun with an "AT" command). This command language
enabled the control of the modem operation set from a simple one, such
as dialing a phone number and from a complicated one, such as answering
the phone only after 15 rings. Since only a few modem manufactures
existed at that time, "Hayse" became a leading company and the
"Hayse" commands became standard. New modem manufactures
imitated the "Hayse " commands. Most of the communication SW
companies today offer "Hayse" compatibility. The MNP protocols
that define error correction and data compression schemes, were
developed by Microcom Inc. but are widely accepted throughout the modem
industry.
The ITU (formerly CCITT) STANDARDS
:
=====================================
date speed PSTN/
standard (ratified) (bps) HDX/FDX private modulation
V.21 1964 200 FDX(FDM) PSTN FSK
V.22 1980 1200 FDX(FDM) PSTN PSK
V.22 bis 1984 2400 FDX(FDM) PSTN QAM
V.23 1964 1200 HDX PSTN FSK
V.26 1968 2400 HDX Private PSK
V.26 bis 1972 2400 HDX PSTN PSK
V.26 ter 1984 2400 FDX(EC) PSTN PSK
V.27 1972 4800 HDX Private PSK
V.27 bis 1976 4800 HDX Private PSK
V.27 ter 1976 4800 HDX PSTN PSK
V.29 1976 9600 HDX Private QAM
V.32 1984 9600 FDX(EC) PSTN QAM
V.32 bis 1991 14400 TCM
V.32 Ter 19200 TCM
V.34 (V.fast) 1994 28800 TCM
FDM means Frequency Division Multiplexing
EC means Echo Canceler
There are other standards that deal with
the modem's related functions. Some of these standards and protocols are
listed here.
Data compression involves different
methods such as Huffman coding and run length coding. The
first method deals with the frequent characters being transmitted in
less bits than the other characters. The second method transmits the bit
value and the chain length, instead of a chain of identical succeeding
bits. The main characteristic of data compression protocols is that they
buffer the desired data to be transferred, compress it and only then
transfer it to the second modem. The second modem must do the opposite
work. The data compressing algorithms are similar to the ARC, ZIP or ARJ
programs. They are located in the modem ROM and compress the data in
real time. The compression depends on the characteristics of the data.
For example, PC '.EXE' or '.COM' files may be compressed up to 40-50%.
Text files may be compressed up to 100%.
Protocols used by modems to transfer
files: The widespread protocols for transferring files are: Xmodem,
Ymodem, Zmodem. (Mainframe computers may also use the Kermit protocol).
The following is a brief description of the protocols. The Xmodem
protocol divides the data into blocks. Each block contains a sequence
number of the block, 128 Bytes of the data and 4 Bytes of checksum. The
checksum is computed for the 128 Data Bytes. The protocol on the other
side is synchronized by checking the sequence number of currently
transferred block and then calculating the checksum of 128 bytes of data
and comparing it to the transferred checksum. In the case of error, it
requests to send the same block again. In the Ymodem protocol, each
block contains 1024 Bytes. The checksum size is 4 Bytes. It is faster
then the Xmodem protocol. It also may transfer a batch of files and
information about each file to be transferred and its size. This helps
the user on the other side to see the time left of the transfer. Zmodem
is a public domain program written by Chuck Forsberg at Omen Technology.
There are several main advantages of this protocol. The block size
varies from 16 to 1024 Bytes. The protocol dynamically finds the optimal
block size for the file transfer on the current phone line. It starts
with a data block size of 1 KByte. It reduces it automatically in case
the phone line is noisy or enlarges the block size when the line
disturbance disappears. The transfer rate is fast with big block sizes
but remember that in case of an error the whole block is retransmitted
and time is wasted. Since this protocol adjusts the block size to the
line quality it combines the best characteristics on each side. It
resumes the transfer after line disconnection. The checksum size is 8
Bytes (CRC/32), therefore, it raises the protocol error correction
authenticity.
Establishing Connection
Establishing a connection between two modems involves a handshaking
process of sending and receiving coded signals to coordinate the
connection. The FallBack method is used to find a common way of
communication. The calling modem first tries to connect at its highest
speed (or best error-correction or data compression scheme). If the
called modem doesn't signal back that is can handle that protocol, the
calling modem falls back to a slower speed or less effective scheme and
tries to connect again. This cycle continues until a common ground is
found or they run out of options.
TODAY'S
STATUS and FUTURE TRENDS
Today in addition external modems, there
are internal modems which are included as an additional board within the
computer. There are advantages to each type.
Actual transfer rates are limited due to
type of phone lines. Using slower phone trunks, international circuits
where half the normal bandwidth is used, and the slow cellular
connections where it might run at only 14.4 kbps (without compression)
although the modem itself enable 28.8kbps.
More and more users are accessing the
Internet and on-line services such as Compuserve, so, use of modems has
increased dramatically. The more powerful processors such as Pentium and
PowerPC in workstations and PC's, enable the modem h/w to be less
complicated. Part of the functions done in the DSP or microcontroller
might be performed by the host. So, modems might drop in price.
The advent of semiconductor modems will
enable a wide range of applications to be implemented: Vending machines
will call up when they need more goods to vend, or elevators will call
when they require service, and so on.
The last approved standard of V.34 with
28.8 kbits/s speed will enable the Digital Simultaneous Voice and Data (DSDV)
applications. DSVD is a modem specification that lets voice and data to
be shared over a single dial-up connection. The data is multiplexed into
packets, much like an ATM stream.
V.34 is approaching the theoretical speed
limit of an analog line - estimated to be in the low 30kbps range. This
may be the last of the new modem protocols which doubled the previous
speeds.

|