Outline

1
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)

2
Digital Communication System
Information per bit increases
Bandwidth efficiency increases
noise immunity increases
Transmitter
Receiver
3
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
• m-law encoding
• Delta Modulation
• Linear Predictor Coding (LPC)

4
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 (gt20 dB) better)

5
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

6
Vector Quantization

distortion
e.g., l2 norm
Average distortion
7
Vector Quantization

• K-Means Algorithm
• Guess
• Classify the vectors by
• Compute new
• Iterate till D does not change
• Finds local minimum based on

into
Centroid of
8
Vector Quantization

• Optimal Coding for lots of dimensions
• If the number of dimensions is increased
• Then D approaches optimal value

9
Practical Coding of Analog

• m-law encoding
• Delta Modulation
• Linear Predictor Coding (LPC)

10
m-law encoding

• ?255 reduces noise power in speech 20dB

11
Delta Modulation

• Sends quantized error between input and code

1
0
1
0
1
1
1
1
1
12
Delta modulation

• Need only 1-bit quantizer and adder (integrator)

13
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