Lectures:
Shannon's coding theorem. Compression and safety codes.
Linear codes.
Hamming codes.
Golayovy codes.
Reed - Muller codes.
Decoding of Reed - Müller codes.
Cyclic codes.
Finite fields and polynomials.
BCH - codes for double and triple error correction.
Convolutional codes, turbo codes
Reed - Solomon codes. BCH code decoding algorithm. Euclid codes.
Encryption.
Encryption using public keys.
Multidimensional data structures.
Image database and its operations.
The database of video sequences, organization and retrieval.
Database with audio data.
Multidimensional database architecture, query languages.
Excursion.
Exercise:
Shannon's coding theorem. Compression and safety codes.
Linear codes.
Golayovy codes.
Reed - Muller codes.
Decoding of Reed - Müller codes.
Finite fields and polynomials.
BCH - codes for double and triple error correction.
Convolutional codes, turbo codes
Encryption.
Projects:
Design chain drives and multimedia processing algorithms.
Computer labs:
Information code components, construction safety codes, encoders and decoders.
Introduction to VHDL simulation system. Design and simulation of basic gates OR, AND, NOR and NAND.
Binary linear codes, code distance, body, generating matrix, control matrix, detection and localization errors. Simulation of complex logic functions of the EX-OR, design and simulations of the encoder and decoder parity code.
Construction of Hamming codes, repair of simple errors, the construction of encoders and decoders of Hamming codes. Simulation models of Hamming code encoder.
Properties codes G23 and G24; triple error correction procedure. Operations using the codes G23 and G24 and their use. Design and simulation blocks Hamming decoder.
Semester work: Design and Simulation of Hamming code decoder
Boolean functions, logic operations, Boolean polynomials. Individual work on semester project. Simulation of channel noise model using VHDL.
Repetition codes, RM codes of the first order, General RM-codes. The calculation procedure to decode the R-M-codes. Design algorithm decoder R-M-codes.
Operations with polynomials, addition, multiplication and division of binary polynomials. The rest of the division. Generating polynomial. Control polynomial. LFSR simulation.
Roots of polynomials and primitive elements of procedure, characteristics of housing, minimal polynomials, finite fields.
Written mid-term exam.
Matrix decoding method, determining the syndrome, and multiplying the sum of geometric series. Determination of the locator error. Procedure for repairs.
Linearity, time invariance and causality convolutional codes. Free distance code, sequential decoding, multi-level decoding, Viterbi algorithm, Viterbi algorithm implementation using DSP and ASIC circuits.
Code with distance d. The planned BCH - code of length q-1. Creating a good binary codes. Simulation of the RS decoder block code using VHDL functional models. Determining the greatest common divisor. Assumptions BCH decoding - code. Locator and evaluator error, make repairs. External and internal codes and their
ties.
Single encryption key, use simplexového code encryption using random words. Simulation and code breaker encryptor using pseudo-random encryption words. Reed - Muller code R (1,3).
The method of large prime numbers, the implementation methods. A method based on the luggage problem. DES - algorithm and its use in banking. Midterm exam. Submitting the semester work.
Shannon's coding theorem. Compression and safety codes.
Linear codes.
Hamming codes.
Golayovy codes.
Reed - Muller codes.
Decoding of Reed - Müller codes.
Cyclic codes.
Finite fields and polynomials.
BCH - codes for double and triple error correction.
Convolutional codes, turbo codes
Reed - Solomon codes. BCH code decoding algorithm. Euclid codes.
Encryption.
Encryption using public keys.
Multidimensional data structures.
Image database and its operations.
The database of video sequences, organization and retrieval.
Database with audio data.
Multidimensional database architecture, query languages.
Excursion.
Exercise:
Shannon's coding theorem. Compression and safety codes.
Linear codes.
Golayovy codes.
Reed - Muller codes.
Decoding of Reed - Müller codes.
Finite fields and polynomials.
BCH - codes for double and triple error correction.
Convolutional codes, turbo codes
Encryption.
Projects:
Design chain drives and multimedia processing algorithms.
Computer labs:
Information code components, construction safety codes, encoders and decoders.
Introduction to VHDL simulation system. Design and simulation of basic gates OR, AND, NOR and NAND.
Binary linear codes, code distance, body, generating matrix, control matrix, detection and localization errors. Simulation of complex logic functions of the EX-OR, design and simulations of the encoder and decoder parity code.
Construction of Hamming codes, repair of simple errors, the construction of encoders and decoders of Hamming codes. Simulation models of Hamming code encoder.
Properties codes G23 and G24; triple error correction procedure. Operations using the codes G23 and G24 and their use. Design and simulation blocks Hamming decoder.
Semester work: Design and Simulation of Hamming code decoder
Boolean functions, logic operations, Boolean polynomials. Individual work on semester project. Simulation of channel noise model using VHDL.
Repetition codes, RM codes of the first order, General RM-codes. The calculation procedure to decode the R-M-codes. Design algorithm decoder R-M-codes.
Operations with polynomials, addition, multiplication and division of binary polynomials. The rest of the division. Generating polynomial. Control polynomial. LFSR simulation.
Roots of polynomials and primitive elements of procedure, characteristics of housing, minimal polynomials, finite fields.
Written mid-term exam.
Matrix decoding method, determining the syndrome, and multiplying the sum of geometric series. Determination of the locator error. Procedure for repairs.
Linearity, time invariance and causality convolutional codes. Free distance code, sequential decoding, multi-level decoding, Viterbi algorithm, Viterbi algorithm implementation using DSP and ASIC circuits.
Code with distance d. The planned BCH - code of length q-1. Creating a good binary codes. Simulation of the RS decoder block code using VHDL functional models. Determining the greatest common divisor. Assumptions BCH decoding - code. Locator and evaluator error, make repairs. External and internal codes and their
ties.
Single encryption key, use simplexového code encryption using random words. Simulation and code breaker encryptor using pseudo-random encryption words. Reed - Muller code R (1,3).
The method of large prime numbers, the implementation methods. A method based on the luggage problem. DES - algorithm and its use in banking. Midterm exam. Submitting the semester work.