Sumários
Finite Fields
15 março 2019, 11:00 • Pedro Alves Martins Rodrigues
Basic definitions and arithmetic properties of Finite fields. Multiplicative order and primitive elements. The Frobenius automorphism.
Minimal polynomials.
Bounds of Codes
14 março 2019, 08:30 • Pedro Alves Martins Rodrigues
Packing radius and covering radius of a code.
Sphere-Covering and Sphere packing bounds.
The Varshamov and Singleton bounds
Shannon's Theorems and error probability
8 março 2019, 11:00 • Pedro Alves Martins Rodrigues
MLD and minimum distance decoding; equivalence for some channel probability distributions.
Statement and discussion of the significance of Shannon's theorems on Noisy Channel decoding.
Probability of error and code parameters.
Channels and Information
7 março 2019, 08:30 • Pedro Alves Martins Rodrigues
Mathematical model of a channel: input probability distribution, forward conditional probabilities. Output probability distribution, Joint probability distribution and Backward conditional probabilities.
Examples.
Conditional Entropy and its properties. Mutual information and capacity of a code.
Decision schemes for decoding: ideal observer and Maximum Likelihood Decoding schemes
Code equivalence and code construction
1 março 2019, 11:00 • Pedro Alves Martins Rodrigues
Review on syndrome decoding for linear codes.
Equivalence of codes.
Construction of codes: sub-codes; puncturing; extending; shortening; direct product and (u,u+v) construction. The binary Reed-Muller codes.
Dual codes, self-orthogonal and self-dual codes. The Binary Golay [24,12,8] code.