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Outline

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

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  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 (>20 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

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