INFORMATION: ANALOG AND DIGITAL

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INFORMATION ANALOG AND DIGITAL

• David Falconer and Halim Yanikomeroglu
• Dept. of Systems and Computer Engineering
• Carleton University

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Topics to be Covered

• Analog (continuous time, continuous amplitude)
  signals
• Analog to digital PCM (pulse code modulation)
• Digital transmission

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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....
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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, data, video, fax,
  etc. (a bit is a bit)
• Better encryption.

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Pulse Code Modulation (PCM)

• Key points
• 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(n?)
s(t)
011010001...
Filter
Sample at tn? Quantize
Encode
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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
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Information Theory and Digital Communications
Ralph V.L. Hartley 1888 1970
Harry Nyquist 1889 1976
Norbert Wiener 1894 1964
Claude Shannon 1916 2001
Gerard J. Foschini 1940
Emre Telatar 1964
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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-to-digital converter
  (ADC)

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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.

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Quantization
Uniform Nonuniform
Output signal
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).
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?-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 n8 bits.
• Most of the rest of the world uses a related
  logarithmic non-uniformity, called A-law.

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DS1 Format (?-Law Countries)
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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
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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.
•  

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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.
•  

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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)
•  

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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 MP3about 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.
•  

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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.

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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 111, 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 111, 91 and 71 respectively.

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Regenerative Repeater
Regenerative repeater
Regenerative repeater
Amplifier/ equalizer
Regenerator
Structure of a regenerative repeater
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.
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PCM Transmission Formats and Spectra
Time
Frequency
..... 1 0 1 1 .......
Power spectra
Unipolar NRZ
0 T 2T 3T 4T
-3/T -2/T -1/T 0 1/T 2/T 3/T
Bipolar NRZ
0 T 2T 3T 4T -4/T
-2/T -1/T 0 1/T 2/T 4/T
Unipolar RZ
?
0 T 2T 3T -4/T
-1/? -2/T -1/T 0 1/T 2/T 1/? 4/T
Min. bandwidth
Bandlimited
0 T 2T 3T 4T
-1/2T 1/2T
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Multilevel Transmission
1 0 1 1 0 0 0
1
Binary L2
4-level L4
0 T 2T 3T
4T
Bit rate
Bandwidth proportional to 1/T for NRZ signals
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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 4-level transmission.
• 14.4 Kb/s modem uses a symbol rate 1/T2400 Hz,
  and the equivalent of L32.

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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
  
• RWlog2(1SNR) 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.

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Fundamental Limits in Digital Data Rates
?
Mobile device for everything
Gbps
Mbps
Kbps
AMPS
bps

• Time

2020
2010
2000
1990
1980
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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(1SNR)
• n Min ( of transmit antennas, of receive
  antennas)
• None of the three variables (W, SE, n) scales
  well!
• Ex 1 n 2, W 10 MHz, log(1SNR) 4 ?
  RBS 80 Mbps
• Ex 2 n 8, W 100 MHz, log(1SNR) 4.5 ?
  RBS 3.6 Gbps
• (Cellular 4th generation LTE-Advanced)

RBS n x W x SE n x W x log2(1SNR)
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Fundamental Limits in Digital Data Rates

• Rnetwork Network rate
• K of BSs in the network
• 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)

Rnetwork K x n x W x log2(1SNR)
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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.

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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