TRANSMISSION OF INFORMATION
David Falconer and Halim Yanikomeroglu
Dept. of Systems and Computer Engineering
Carleton University
1
Topics to be Covered

Analog (continuous time, continuous amplitude) signals

Power spectral density and bandwidth

Analog to digital: PCM (pulse code modulation)

Digital transmission
2
Digital and Analog Signals
Some signals (like speech and video) are inherently analog; some
(like computer data) are inherently digital.
However, both analog and digital signals can be represented and
transmitted digitally.
Advantages of digital:
»
»
»
»
»
Reduced sensitivity to line noise, temp. drift, etc.
Low cost digital VLSI for switching and transmission.
Lower maintenance costs than analog.
Uniformity in carrying voice, SMS, email, data, video, etc. (a bit is a bit)
Better encryption.
3
Power Spectral Density
Power spectrum (power spectral density) describes how the
average power is distributed with respect to frequency.
Deterministic signals  Fourier transform
Random signals  Power spectral density
A statistical representation for all random signals in a particular
application
4
Power Spectrum of Analog Signals
Analog (continuous-time, continuous-amplitude) signals (like
speech) have a certain bandwidth. Their power spectrum (power
spectral density) describes how their average power is
distributed with respect to frequency.
Power
spectral
density
(watts/Hz)
“High-fidelity speech
Telephone speech
(limited by filtering)
Bandwidth
0
1
2
3
4
5
6
7....
5
Power Spectrum of Analog Signals
Source: Wikipedia
6
Bandwidth
For random signals, bandwidth is determined from the power
spectral density.
Bandwidth is determined only from the +ve frequencies.
There are different bandwidth definitions
Absolute bandwidth
Y% bandwidth (for instance, 99%)
X-dB bandwidth (for instance, 3-dB)
Null-to-null bandwidth
…
7
Bandwidth
3-dB Bandwidth
Source: Wikipedia
8
Bandwidth
Digital Communications, B. Sklar
9
Bandwidth
Digital Communications, B. Sklar
10
Bandwidth
Digital Communications, B. Sklar
11
Bandwidth
Digital Communications, B. Sklar
12
Sampling an Analog Signal
Sampling theorem: The original analog signal can be reconstructed if
it is sampled at a rate at least twice its bandwidth.
Reconstruction is by filtering samples with a low pass filter.
Sampling
Samples
Reconstruction
13
Pulse Code Modulation (PCM)

PCM is a method used to digitally represent sampled analog signals. It
is the standard form of digital audio in computers, Compact
Discs, digital telephony and other digital audio applications.

PCM signal is developed by three steps: sampling, quantizing and
encoding.

Quantizing noise is reduced by using variable sized steps. It is
independent of line length.
s(t)
s(n)
011010001...
Filter
Sample at t=n
Quantize
Encode
14
Pulse Code Modulation (PCM)
Sampling and
quantization of
a signal (red)
for 4-bit PCM

The PCM process is commonly implemented on a single
integrated circuit and is generally referred to as an analog-todigital converter (ADC)
15
Standard PCM in Wired Telephony
• Voice circuit bandwidth is 3400 Hz.
• Sampling rate is 8 KHz (samples are 125 s apart).
• Each sample is quantized to one of 256 levels.
• Each quantized sample is coded into a 8-bit word.
• The 8-bit words are transmitted serially (one bit at a time) over a
digital transmission channel. The bit rate is 8x8,000 = 64 Kb/s.
• The bits are regenerated at digital repeaters.
• The received words are decoded back to quantized samples,
and filtered to reconstruct the analog signal.
16
Quantization
Uniform (Linear PCM: LPCM)
Output signal
Nonuniform
Output signal
Input signal
Input signal
The more steps (levels) the less quantization noise. Nonuniform quantization
(e.g. -law) allows a larger dynamic range (important for speech).
LPMC: Uncompressed
Nonuniform quantization: Introduces compression
17
-Law Quantization and Coding
• Standardized in North America.
• Based on a logarithmic non-uniform quantizer.
• Range of amplitudes divided into 8 segments, each segment
with 16 uniformly spaced levels. Segment i is double the width
of segment i-1.
• 8 bit word: 1 bit for sign, 3 bits identify segment, 4 bits identify
level within segment.
• Can show for n-bit word, signal to quantization noise ratio is
approximately 6n-10 [dB]; e.g., 38 dB for n=8 bits.
• Most of the rest of the world uses a related logarithmic nonuniformity, called A-law.
18
Variants of PCM (Form of Compression)
Differential PCM (DPCM) encodes the PCM values as differences
between the current and the predicted value. An algorithm
predicts the next sample based on the previous samples, and
the encoder stores only the difference between this prediction
and the actual value. If the prediction is reasonable, fewer bits
can be used to represent the same information. For audio, this
type of encoding reduces the number of bits required per
sample by about 25% compared to PCM.
Adaptive DPCM (ADPCM) is a variant of DPCM that varies the
size of the quantization step, to allow further reduction of the
required bandwidth for a given signal-to-noise ratio.
Delta Modulation is a form of DPCM which uses one bit per
sample.
19
Adaptive Differential PCM (ADPCM)
Allows coding with a lower bit rate (with same fidelity) for speech,
based on predicting the next sample; e.g., 8 or 16 or 32 Kb/s.
More circuits accommodated in the same transmission bandwidth.
Coder:
+
Decoder:
Quant.
+
Predictor
Predictor
20
PCM Standards
G.711 is an ITU-T standard for audio companding. It is primarily used in
telephony. The standard was released for usage in 1972. Its formal
name is Pulse Code Modulation (PCM) of voice frequencies.
G.711 uses a sampling rate of 8,000 samples per second. Non-uniform
(logarithmic) quantization with 8 bits is used to represent each sample,
resulting in a 64 kbit/s bit rate.
G.711.1 is an extension to G.711, published as ITU-T Recommendation
G.711.1 in March 2008. Its formal name is Wideband embedded
extension for G.711 pulse code modulation.
G.711.1, allows the addition of narrowband and/or wideband (16000
samples/s) enhancements, each at 25 % of the bitrate of the (included)
base G.711 bitstream, leading to data rates of 64, 80 or 96 kbit/s.
G.711.1 is compatible with G.711 at 64 kbit/s, hence an efficient
deployment in existing G.711-based voice over IP (VoIP)
infrastructures is foreseen.
21
PCM Standards
G.726 is an ITU-T ADPCM speech codec standard covering the
transmission of voice at rates of 16, 24, 32, and 40 kbit/s (1990).
The most commonly used mode is 32 kbit/s, which doubles the
usable network capacity by using half the rate of G.711. It is
primarily used on international trunks in the phone network. The
principal application of 24 and 16 kbit/s channels is for overload
channels carrying voice in digital circuit multiplication equipment
(DCME).
It also is the standard codec used in DECT wireless phone systems
and is used on some Canon cameras.
Sampling frequency 8 kHz. 16 kbit/s, 24 kbit/s, 32 kbit/s, 40 kbit/s
bit rates available.
Testing under ideal conditions yields Mean Opinion Scores of 4.30
for G.726 (32 kbit/s), compared to 4.45 for G.711 (µ-law)
22
PCM Standards
Audio Interchange File Format (AIFF) is an audio file format
standard used for storing sound data for personal computers
and other electronic audio devices.
The audio data in a standard AIFF file is uncompressed pulse-code
modulation (PCM). There is also a compressed variant of AIFF
known as AIFF-C or AIFC, with various defined compression
codecs.
Like any non-compressed, lossless format, it uses much more disk
space than MP3—about 10MB for one minute of stereo audio at
a sample rate of 44.1 kHz and a sample size of 16 bits.
Developed by Apple Inc. Initial release 21 January 1988.
23
PCM Standards
MPEG-1 or MPEG-2 Audio Layer III, more commonly referred to as MP3, is a
patented digital audio encoding format using a form of lossy data compression.
It is a common audio format for consumer audio storage, as well as a de facto
standard of digital audio compression for the transfer and playback of music on
digital audio players. Initial release: 1993.
MP3 is an audio-specific format that was designed by the Moving Picture Experts
Group (MPEG) as part of its MPEG-1 standard and later extended in MPEG-2
standard.
The use in MP3 of a lossy compression algorithm is designed to greatly reduce the
amount of data required to represent the audio recording and still sound like a
faithful reproduction of the original uncompressed audio for most listeners. An
MP3 file that is created using the setting of 128 kbit/s will result in a file that is
about 1/11 the size of the CD file created from the original audio source. An
MP3 file can also be constructed at higher or lower bit rates, with higher or lower
resulting quality.
The compression works by reducing accuracy of certain parts of sound that are
considered to be beyond the auditory resolution ability of most people. This
method is commonly referred to as perceptual coding. It uses psychoacoustic
models to discard or reduce precision of components less audible to human
hearing, and then records the remaining information in an efficient manner.
24
PCM Standards
Several bit rates are specified in the MPEG-1 Audio Layer III standard: 32,
40, 48, 56, 64, 80, 96, 112, 128, 160, 192, 224, 256 and 320 kbit/s, and
the available sampling frequencies are 32, 44.1 and 48 kHz. Additional
extensions were defined in MPEG-2 Audio Layer III: bit rates 8, 16, 24,
32, 40, 48, 56, 64, 80, 96, 112, 128, 144, 160 kbit/s and sampling
frequencies 16, 22.05 and 24 kHz.
A sample rate of 44.1 kHz is almost always used, because this is also
used for CD audio, the main source used for creating MP3 files. A
greater variety of bit rates are used on the Internet. The rate of 128
kbit/s is commonly used, at a compression ratio of 11:1, offering
adequate audio quality in a relatively small space. As Internet
bandwidth availability and hard drive sizes have increased, higher bit
rates up to 320 kbit/s are widespread.
Uncompressed audio as stored on an audio-CD has a bit rate of
1,411.2 kbit/s, so the bitrates 128, 160 and 192 kbit/s represent
compression ratios of approximately 11:1, 9:1 and 7:1 respectively.
25
DS1 Format (-Law Countries)
193 bits in 125 s
(1.544 Mb/s)
S bit
24 PCM code words, each representing 1 sample
DS1
1
2
3
4
24
8 bits per code word
DS0
1
2
3
4
5
6
7
8
Hierarchical Multiplexing:
DS1: 24 DS0
DS3: 28 DS1
26
Regenerative Repeater
Regenerative
repeater
Regenerative
repeater
Amplifier/
equalizer
Structure of a regenerative
repeater:
Regenerator
Timing circuit
By appropriate repeater design and inter-repeater spacing, the effect of
occasional bit errors due to noise can be controlled. Received signal quality is
essentially independent of distance.
27
PCM Transmission Formats and Spectra
Time
..... 1
0
1
Frequency
Power spectra
1 .......
Unipolar NRZ
0
T
2T
3T
4T
-3/T -2/T -1/T 0
1/T
2/T 3/T
1/T
2/T
Bipolar NRZ
0
T
2T
3T
4T

0
-4/T
-2/T
-1/T 0
Unipolar RZ
T
2T
3T
-4/T -1/ -2/T -1/T 0
T
2T
3T
4T
1/T 2/T 1/
4/T
Min. bandwidth
Bandlimited
0
4/T
-1/2T
1/2T
28
Multilevel Transmission
1
0
1
1
0
0
0
1
Binary:
L=2
4-level:
L=4
0
T
2T
3T
4T
1
log2 L
Bit rate =
T
Bandwidth proportional to 1/T for NRZ signals
29
Bandwidth Required for Digital Transmission

required bandwidth is approximately
(bit rate)/(log2L) for L-level transmission.

more levels  less bandwidth, but greater sensitivity to noise.

Examples:
» 64 Kb/s PCM requires about 64 KHz for binary transmission, 32 KHz for 4level transmission.
» 14.4 Kb/s modem uses a symbol rate 1/T=2400 Hz, and the equivalent of
L=32.
30
Channel Capacity
Shannon channel capacity formula:
» Highest possible transmission bit rate R, for reliable communication in a
given bandwidth W Hz, with given signal to noise ratio, SNR, is
R=Wlog2(1+SNR) bits/s
R/W = 0.332 SNR [dB] bits/s/Hz (for high SNR)
» Assumptions and qualifications:
– Gaussian distributed noise added to the signal by the channel, highly complex
modulation, coding and decoding methods.
– In typical practical situations, the above formula may be roughly modified by
dividing SNR by a factor of about 5 to 10.
31
Fundamental Limits in Digital Data Rates
5G
4G
3G
Gbps
Mbps
Kbps
bps
?
Mobile device
for everything
2G
1G
AMPS
1980
1990
2000
2010
2020
Time
32
Information Theory and Digital Communications
Ralph V.L. Hartley
1888 – 1970
Harry Nyquist
1889 – 1976
Norbert Wiener
1894 – 1964
Emre Telatar
1964 –
Gerard J. Foschini
1940 –
Claude Shannon
1916 – 2001
33
Fundamental Limits in Digital Data Rates
RBS: Data rate (speed) of a wireless base station (access point)
•W: Bandwidth
•SNR: Signal-to-noise ratio at the receiver
•SE: Spectral efficiency = log2(1+SNR)
•n: Min (# of transmit antennas, # of receive antennas)
RBS = n x W x SE = n x W x log2(1+SNR)
None of the three variables (W, SE, n) scales well!
Ex 1: n = 2, W = 10 MHz, log(1+SNR) = 4
 RBS = 80 Mbps
Ex 2: n = 8, W = 100 MHz, log(1+SNR) = 4.5  RBS = 3.6 Gbps
(Cellular 4th generation LTE-Advanced)
34
Fundamental Limits in Digital Data Rates
Rnetwork: Network rate
•K: # of BSs in the network
Rnetwork = K x n x W x log2(1+SNR)
Fundamental dynamics:
4 basic factors that impact network rate: K, n, W, SE
Increasing base station rate: Not easy! (neither of n, W, SE scales well)
Increasing network rate: Possible! (by adding more base stations)
35
Summary


All information signals can be represented, switched, stored and
transmitted digitally.
We have discussed PCM systems and their key elements:
»
»
»
»

sampling
quantizing
coding
digital transmission
We have discussed the related concepts of:
»
»
»
»
»
the telephone set
bandwidth
the sampling theorem
signal to quantization noise ratio
channel capacity.
36
More Information
SYSC 5608 Wireless Communications Systems Engineering, lecture notes
E.B. Carne, “Telecommunications Primer”, 2nd edition, Prentice-Hall, 1999
J. Sklar, “Digital Communications”, Chapters 2 and 7
37