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.