You may choose one of the following two projects:

1. Source Modeling: In class, we discussed the modeling of binary images using various Markov models. In this project, you are to model gray-scaled images, music audio or English text.

   For this purpose, I have prepared for you three real-world data sets:

   • lena.ras This file contains the ubiquitous image of Lena. Its size is 512x512 and each pixel is stored as one byte. You may look at my Matlab program, read_lena.m, for reading and displaying this image.
   • tracy.mat This file contains ten seconds of audio from the song `Fast Car' by the artist Tracy Chapman. The audio is sampled at 22,050 samples/sec. Each sample is stored as a two-byte signed integer. This is a Matlab data file which contains 70 bytes of header information. You may look at my Matlab program, read_tracy.m, for reading and playing this audio file. If you do not use Matlab, be careful about the byte-reversal problem in Unix. There should be no problem if you use a DOS machine to read this file.
   • Origin.txt This file contains the entire content of the book The Origin of Species by Charles Darwin. It contains approximately 1 million ASCII characters (about 160,000 words).

   You can choose one of the above data sets for modeling and analysis. Or you can find your own data set if you do not find these to be sufficiently large.

   Once you have decided on the source, find a mathematical model for this source. From the model, determine the entropy rate of the source (in bits/pixel, bits/sample, or bits/character).

   Now find a lossless compression algorithm which can compress the source. Compare the average rate of the compression algorithm with the entropy rate. What does this tell you about the model and/or the compression algorithm?

   Randomly generate data according to your model and compare it with the real data.

   I recommend that you use Matlab, but you can use any other programming language (Fortran, Pascal, C, C++, etc.) you want.

   Use your imagination and creativity.

2. You can choose any other project related to Information Theory. However, you must submit to me a one-page proposal outlining your project by the latest March 18, 1999 (7:00 pm). One week after receiving your report, I will either approve or disapprove your proposal. My judgement will be based on (i) whether the proposed project is related to Information Theory and (ii) whether the quality of the proposal is comparable to that of the above. If your proposal is disapproved, you must work on the Source Modeling project described above.

Grading: (60 pts Total) Your project grade will be based on the following:

1. Technical Content: (25 pts) How ``good" is your model? How `good" is the compression algorithm you used? How accurate and reliable are your results? Are your results repeatable? Did you say anything that is technically wrong? Did you say anything that is technically right? Did you make fair and meaningful comparisons?
2. Presentation: (25 pts) How clear is your written report? How clearly do you present your results? Does your report contain grammatical or typographical errors? Would another graduate student (who have taken ESE 535) understand and appreciate your work?
3. Originality: (10 pts) Does your project contain novel ideas? Did you take tradional approaches or unconventional ones? I encourage you to take risky and unconventional approaches. Even if these fail, you may include them in your report. But explain why you think they fail.

Early-Completion Incentive Program:

· If you turn in the project by 4/27/99 (7:00 pm), you will get 05% (03 pts) extra credit.

· If you turn in the project by 4/20/99 (7:00 pm), you will get 10% (06 pts) extra credit.

· If you turn in the project by 4/13/99 (7:00 pm), you will get 15% (09 pts) extra credit.

· If you turn in the project by 4/06/99 (7:00 pm), you will get 20% (12 pts) extra credit.

· If you turn in the project by 3/25/99 (7:00 pm), you will get 25% (15 pts) extra credit.

· If you don't turn in the project by 5/04/99 (7:00 pm), you will get no credit.