Math 525 -- Schedule and Assignments



Schedule

I will try to keep to this schedule but will update it as needed.
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