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Lecturer

Prof. Robert Gallager

Class Meetings

Two sessions / week
1.5 hours / session

This is a twelve credit H-level subject, (3-0-9).

6.041 and 6.003.

Class notes to be passed out in lecture.

Handouts and graded problem sets not picked up during lecture can be collected later.

There will be 14 problem sets, corresponding to a weekly schedule, though the final problem set will not be collected. Problem sets will be shorter in weeks involving either quizzes or holidays. You are expected to do all the assigned problems, and we will assume that in making up the quizzes and final. We encourage you to cooperate with each other in doing the problem sets. The problem sets are vehicles for learning, and whatever maximizes learning for you is desirable. This usually includes discussion, teaching of others, and learning from others.

Problem sets must be handed in by the end of the class in which they are due. Problem set solutions will be available at the end of the due date lecture. Consequently, it is difficult and unfair to seriously evaluate late problem sets.

The grades assigned to problems sets will be elements of {0, 1, 2}. You are welcome to flag topics of confusion to you in the problem sets; this will not lower your grade.

There will be one midterm quiz and two mini-quizzes during the semester. A final exam will be given during the scheduled final exam period. The quizzes and final will be closed book, but you may bring three double sided 8.5" by 11" pages of notes to each of the quizzes. You may bring five double sided 8.5" by 11" pages of notes to the final. Most people find that the preparing of such notes helps them much more than their use.

The final grade in the course is based upon our best assessment of your understanding of the material. This assessment is based on four noisy measurements: the problem sets, the mini-quizzes, the midterm, and the final. The different measurements have different noise levels, and the final grade will be thus a weighted average, roughly according to the following rule:

10% - Each Mini-quiz
25% - Midterm
35% - Final Exam
20% - Problem Sets

Proakis, J. G., and M. Salehi. Communication Systems Engineering. Upper Saddle River, NJ: Prentice Hall, 1994. ISBN: 0131589326.

Proakis, J. G. Digital Communications. 4th ed. New York, NY: McGraw-Hill, 2000. ISBN: 0072321113.

Wilson, S. G. Digital Modulation and Coding. Upper Saddle River, NJ: Prentice Hall, 1996. ISBN: 0132100711.

Wozencraft, J. M., and I. M. Jacobs. Principles of Communication Engineering. New York, NY: Wiley, 1965. ISBN: 0471962406.

Lee, E. A., and D. G. Messerschmitt. Digital Communication. 2nd ed. Kluwer, 1993. ISBN: 0792393910.

Gallager, R. G. Information Theory and Reliable Communication . New York, NY: Wiley, 1968. ISBN: 0471290483.

Cover, T. M., and J. A. Thomas. Elements of Information Theory. New York, NY: Wiley, 1991. ISBN: 0471062596.

Stüber, G. L. Principles of Mobile Communication. Kluwer, 1996. ISBN: 0792397320.

1. Introduction and Objectives. Block diagram of a digital communication system. Separation of source coding and channel coding.
   
   
2. Fixed-length and variable-length codes for discrete sources. Data compression. Prefix-free codes. The Kraft inequality. Probability models for sources.
   
   
3. Expected code length criterion. Entropy bounds. Huffman codes.
   
   
4. Laws of large numbers. The asymptotic equipartition property. Shannon's source coding theorems.
   
   
5. Sources with memory. Lempel-Ziv universal data compression.
   
   
6. Compression for discrete-time analog sources. Scalar quantization. Lloyd-Max algorithm. Vector quantization. Entropy quantization.
   
   
7. Differential entropy. High-rate uniform and non-uniform scalar quantizers. High-rate uniform and non-uniform vector quantizers.
   
   
8. Review of Fourier transform, Fourier series, and discrete Fourier transform. L₂ functions. The sampling theorem. Data compression for analog waveform sources.
   
   
9. Aliasing. Representation of waveforms by orthonormal expansions. Data compression using orthonormal expansions. L₂ as a vector space.
   
   
10. L₂ as an inner-product vector space. Subspaces, bases, and dimension. Projection. Gram-Schmidt orthonormalization.
    
    
11. Channel encoding and modulation. Channel decoding and demodulation. Pulse amplitude modulation. Nyquist criterion.
    
    
12. Passband modulation. Quadrature amplitude modulation. Viewing passband at baseband. Implementation of QAM.
    
    
13. Carrier recovery and Phase tracking in QAM. Orthonormal expansions at baseband and passband. Noise and stochastic processes. Gaussian processes. Stationarity.
    
    
14. Linear functionals for Gaussian processes. Jointly Gaussian rv's. Covariance for linear functionals and filters. White Gaussian noise.
    
    
15. The white noise/L₂ dichotomy and its resolution. Signal to noise ratio. E_b/N₀. Channel capacity.
    
    
16. Binary detection. PAM signals in WGN. Binary vectors in WGN. Waveforms in WGN. The Neyman-Pearson test.
    
    
17. The irrelevance theorem. Orthogonal signal sets. Capacity in the broad band limit.
    
    
18. Wireless channels. Physical layer modeling. Free space and fixed antennas. Free space and moving antennas. Moving antennas and multiple paths. Shadowing.
    
    
19. Input-Output models for wireless. Time-varying system functions. The time-varying impulse response and convolution. Baseband equialent system. Discretetime baseband model. Time-coherence, Frequency-coherence, Doppler-spread, and time-spread.
    
    
20. Statistical channel models. Detection in Raleigh fading. Non-coherent detection.
    
    
21. Channel estimation. Rake receivers.
    
    
22. CDMA. Orthogonal codes. Convolutional codes. The Viterbi algorithm. Frequency hopping systems.