Outline
• Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2)
• Receivers (Chapter 5) (week 3 and 4) • Received Signal Synchronization (Chapter 6) (week 5)• Channel Capacity (Chapter 7) (week 6)• Error Correction Codes (Chapter 8) (week 7 and 8)• Equalization (Bandwidth Constrained Channels) (Chapter 10)
(week 9)• Adaptive Equalization (Chapter 11) (week 10 and 11)• Spread Spectrum (Chapter 13) (week 12)• Fading and multi path (Chapter 14) (week 12)
Digital Communication System:
Transmitter
Receiver
Information per bit increases
noise immunity increases
Bandwidth efficiency increases
Increasing Information per Bit• Information in a source
– Mathematical Models of Sources– Information Measures
• Compressing information– Huffman encoding
• Optimal Compression?– Lempel-Ziv-Welch Algorithm
• Practical Compression
• Quantization of analog data– Scalar Quantization– Vector Quantization– Model Based Coding– Practical Quantization
• -law encoding• Delta Modulation• Linear Predictor Coding (LPC)
Scalar Quantization
• Optimum quantization based on random variable assumption for signal is possible through nonuniform quantization
• Does not buy much, few dB
• Arbitrary non uniform quantization, such as -law, works well for speech (>20 dB) better)
Vector Quantization
• Sort of the equivalent of block coding
• Better rates obtained for groups of analog inputs coded as vectors
• Works great on statistically dependant analog samples like severely band limited signals or coded analog like speech
Vector Quantization•
L
k C
kk
n
k
kk
n
k
dpdCPD
xxn
d
d
Q
x
x
1
~
1
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2
~
~
1
)(),()(
)(1
),(
),(
)(
X
XXXXX
XX
XX
XX
X k
~
X kC
distortion
e.g., l2 norm
Average distortion
Vector Quantization
• K-Means Algorithm– Guess– Classify the vectors by
– Compute new
– Iterate till D does not change– Finds local minimum based on
)0(~
kX),(
~
XXd
kCk
k mM
iX
XX )(1
)(~
Centroid of
into kC
kCX
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kX
Vector Quantization
• Optimal Coding for lots of dimensions– If the number of dimensions is increased – Then D approaches optimal value
Practical Coding of Analog
• -law encoding
• Delta Modulation
• Linear Predictor Coding (LPC)
-law encoding
=255 reduces noise power in speech ~20dB
Delta Modulation• Sends quantized error between input and code
1
1
1
1
1 0 1 0 1
Delta modulation
• Need only 1-bit quantizer and adder (integrator)
Linear Predictor Coding
• Learn parameters of filter to fit input speech• Can solve for ai if we have a training sample• This is feasible and is one of the better speech
codes
