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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)

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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:

Information per bit increases

Bandwidth efficiency increases

noise immunity increases

Transmitter

Receiver


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)


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

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

into

Centroid of


Vector Quantization

  • Optimal Coding for lots of dimensions

    • If the number of dimensions is increased

    • Then D approaches optimal value


Practical Coding of Analog

  • m-law encoding

  • Delta Modulation

  • Linear Predictor Coding (LPC)


m-law encoding

  • =255 reduces noise power in speech ~20dB


Delta Modulation

  • Sends quantized error between input and code

1

0

1

0

1

1

1

1

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


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