Sumários
Characterisation of canonical generators. Free distance.
10 janeiro 2025, 11:00 • Gustavo Granja
Properties characterising reduced and basic encoders. An encoder is canonical if and only if it is basic and reduced. Example. Definition of free distance. Example. Alternative characterisation in terms of long binary linear codes. Brief description of real world applications of error correcting codes.
The Viterbi algorithm
9 janeiro 2025, 11:30 • Gustavo Granja
Proof that the Viterbi algorithm computes the set of nearest codewords. Canonical generators for convolutional codes. External and internal degree of an encoder. Reduced and basic encoders. Properties.
Introduction to convolutional codes
20 dezembro 2024, 11:00 • Gustavo Granja
Definition of convolutional codes. Examples of encoding. State diagrams and the Trellis diagram. Examples. Brief description of the Viterbi decoding algorithm.
The euclidean algorithm for decoding alternant codes
19 dezembro 2024, 11:30 • Gustavo Granja
Statement and proof of correctness of the gcd algorithm for decoding alternant codes. Example.
Alternant codes
13 dezembro 2024, 11:00 • Gustavo Granja
Alternate characterisation of Reed-Solomon codes. Generalised Reed-Solomon. The dual of generalised Reed-Solomon is generalised Reed-Solomon. Definition of Alternant codes. BCH codes are alternant.