| Day | Topics | Preparation |
|---|---|---|
| Mon. 1/29 | Communication Channels, codes | Secs. 1.1-4 |
| Wed. 1/31 | Code performance, vector spaces over F_2 | Secs. 1.5-7 |
| Fri. 2/2 | Weight and distance, Maximum likelihood decoding | Secs. 1.7-12 |
| Mon. 2/5 | More on Maximum likelihood decoding, minimum distance | Secs. 1.8-12 |
| Wed. 2/7 | Linear codes and linear algebra over F_2 | Secs. 2.1-3 |
| Fri. 2/9 | Matrices for defining linear codes | Secs. 2.4-8 |
| Mon. 2/12 | Parity check matrices for a code, distance of a code | Secs. 2.4-9 |
| Wed. 2/14 | Cosets and syndrome decoding | Secs. 2.10-12 |
| Fri. 2/16 | Perfect codes and Hamming codes | Secs. 3.1-3 |
| Mon. 2/19 | Decoding erasures, miscellaneous things related to assignment |
. |
| Wed. 2/21 | Singleton bound, MDS codes | Secs. 3.1 |
| Fri. 2/23 | Gilbert-Varshimov bound | Secs. 3.1 |
| Mon. 2/26 | Sphere packing bound, perfect codes,
extended and punctured codes |
Secs. 3.1-4 |
| Wed. 2/28 | Extended Golay code, decoding | Secs. 3.5-6 |
| Fri. 3/2 | More on Golay codes | Secs. 3.5-7 |
| Mon. 3/5 | Euclidean algorithm, modular arithmetic |
Secs. 4.1, 5.1-2 |
| Wed. 3/7 | Z_p is a field the multiplicative structure of Z_p is cyclic |
Secs. 4.1, 5.1-2 |
| Fri. 3/9 | Finite fields, polynomials over F_2 Euclidean algorithm for polynomials |
Secs. 4.1, 5.1-2 |
| Mon. 3/19 | Finite fields: exponential notation | Secs. 4.1, 5.1-2 |
| Wed. 3/21 | Finite fields: the minimal polynomial of an element | Secs. 4.1, 5.1-2 |
| Fri. 3/23 | Cyclic codes | Sec. 4.2 |
| Mon. 3/26 | Cyclic codes | Sec. 4.3 |
| Wed. 3/28 | Cyclic codes | Sec. 4.4 |
| Fri. 3/30 | Cesar Chavez day: no classes | . |
| Mon. 4/2 | Exam | Ch. 1, 2, 3 |
| Wed. 4/4 | Encoding of cyclic codes, circuits for ploynomial multiplication and division | Sec. 4.3 |
| Fri. 4/6 | Systematic encoding, dual codes | Sec 4.3 |
| Mon. 4/9 | The dual of a cyclic code | Sec 4.5 |
| Wed. 4/11 | Cyclic Hamming codes | Sec. 5.3 |
| Fri. 4/13 | BCH 2-error correcting codes and decoding | Sec. 5.4 |
| Mon. 4/16 | Decoding 2-error correcting BCH code. General BCH codes | Sec. 5.5 |
| Wed. 4/18 | Reed-Solomon codes | Sec. 6.1 |
| Fri. 4/20 | Problem Set 4, Van der Monde Matrices | Sec. 6.2 |
| Mon. 4/23 | RS codes are MDS | Sec. 6.2 |
| Wed. 4/25 | Dual codes of RS codes | . |
| Fri. 4/27 | Equivalent codes, all RS codes of same dimension are equivalent | . |
| Mon. 4/30 | Decoding of RS codes | Handout |
| Wed. 5/2 | The Euclidean algorithm for decoding RS codes | Handout |
| Fri. 5/4 | Shift registers, convolutional codes | Sec. 8.1 |
| Mon. 5/7 | State diagrams, Decoding convolutional codes | Sec. 8.2 |
| Wed. 5/9 | Decoding of convolutional codes, minimum distance | Sec. 8.3 |
| Fri. 5/11 | Convolutional codes | Sec. 8.3 |
| Mon. 5/14 | Review: BCH codes as subfield subcodes, finite fields | . |
| Wed. 5/16 | Review | . |
| Assignment | Topics covered | Due date |
|---|---|---|
First Assignment |
Code performance, IMLD | Fri. 2/9 |
Second Assignment |
Linear Codes, generator and check matrices, syndrome decoding |
Fri. 2/23 |
Third Assignment |
Gilbert-Varshimov bound, perfect codes, Hamming codes, Golay codes | Fri. Mar. 9 |
Fourth Assignment |
Finite fields | Fri. Mar. 23 |
Fifth Assignment |
Cyclic Codes | Mon. Apr. 16 |
Sixth Assignment |
BCH Codes | Fri. Apr. 27 |
Seventh Assignment |
Reed-Solomon Codes | Wed. May 9 |
Eighth Assignment |
Convolutional Codes | Wed. May 16 |