| Day | Topics | Preparation |
|---|---|---|
| Mon. 8/30 | Communication Channels, codes | Secs. 1.1-4 |
| Wed. 9/1 | (F_2)^n as a vector space, and a metric space.
Maximum likelihood decoding. |
Secs. 1.5-7 |
| Fri. 9/3 | Minimum distance of a code. Detection vs. decoding. | Secs. 1.7-12 |
| Wed. 9/8 | Linear codes and linear algebra over F_2
(and other fields). |
Secs. 2.1-3 |
| Fri. 9/10 | Matrices for defining linear codes | Secs. 2.3,4 |
| Mon. 9/13 | Systematic encoding, equivalent codes. | Secs. 2.4,6,8 |
| Wed. 9/15 | Parity check matrices for a code. MDS codes. | Secs. 2.5,7,9; 3.1(on MDS only) |
| Fri. 9/17 | Cosets and syndrome decoding | Secs. 2.10-12 |
| Mon. 9/20 | Decoding erasures, miscellaneous things related to assignment |
. |
| Wed. 9/22 | The sphere packing bound, perfect codes and Hamming codes |
Secs. 3.1-3 |
| Fri. 9/24 | Gilbert-Varshimov bound | Secs. 3.1 |
| Mon. 9/27 | New codes from old, shortened, punctured and extended codes |
Secs. 3.1-4 |
| Wed. 9/29 | Extended Golay code and Golay code | Secs. 3.5-6 |
| Fri. 10/1 | Decoding Golay codes | Secs. 3.5-7 |
| Mon. 10/4 | Euclidean algorithm, modular arithmetic |
Secs. 4.1, 5.1-2 |
| Wed. 10/6 | Z_p is a field the multiplicative structure of Z_p is cyclic |
Secs. 4.1, 5.1-2 |
| Fri. 10/8 | Finite fields, polynomials over F_2 Euclidean algorithm for polynomials |
Secs. 4.1, 5.1-2 |
| Mon. 10/11 | EXAM | . |
| Wed. 10/13 | Finite fields: mF[x]/f(x) . | Secs. 4.1, 5.1-2 |
| Mon. 10/18 | Minimal polynomials for elements of a finite field. | Secs. 4.1, 5.1-2 |
| Wed. 10/20 | Cyclic codes | Sec. 4.2 |
| Fri. 10/22 | The generator polynomial: classifying cyclic codes | Sec. 4.3 |
| Mon. 10/25 | Duality for cyclic codes | Sec. 4.4 |
| Wed. 10/27 | Reciprocal polynomials and dual codes. Circuits for finite field operations and ploynomial multiplication and division. |
Sec. 4.3 |
| Fri. 10/29 | Encoding of cyclic codes. | Sec 4.5 |
| Mon. 11/1 | Cyclic Hamming codes | Sec. 5.3 |
| Wed. 11/3 | BCH 2-error correcting codes and decoding | Sec. 5.4,5 |
| Fri. 11/5 | Van der Monde matrics and Reed-Solomon codes. | Sec. 6.1,2 |
| Mon. 11/8 | Reed-Solomon codes and their duals. | Sec. 6.1,2 |
| Wed. 11/10 | Questions? Taking apart the field F_64 . | . |
| Fri. 11/12 | EXAM | Finite fields, polynomials, cyclic codes. |
| Mon. 11/15 | BCH codes. | . |
| Wed. 11/17 | More on BCH codes. Decoding of Reed-Solomon codes. |
6.3 |
| Fri. 11/19 | Decoding of Reed-Solomon codes. | 6.3 |
| Mon. 11/22 | The Forney formula. | 6.3 |
| Wed. 11/24 | Decoding RS codes: an example. | 6.3 |
| Mon. 11/29 | Convolutional codes: encoding and catastrophes. | Sec. 8.1 |
| Wed. 12/1 | State diagrams. Decoding with no errors. | Sec. 8.2 |
| Fri 12/3 | Decoding of convolutional codes, minimum distance. | Sec. 8.3 |