Coding Technology

Error-correcting coding: binary channel model, error probability, basic coding concepts (geometric interpretation, code spacing, optimal codes, code spacing), general coding scheme and its complexity. Singleton and Hamming bounds. Binary linear code, generator matrix, parity check matrix, systematic code. Hamming code, Standard Array. Error correcting performance and relation between column vectors of parity check matrix. Prime and prime-power  size Galois fields, operations on prime-power Galois fields with shift registers. Nonbinary codes, Hamming codes, Reed-Solomon codes. Cyclic linear codes, generator and parity check polynomials. Error trapping algorithm. Minimal polynomials over Galois fields of prime power, BCH codes.
Data compression - source coding: prefix codes, average code word length and entropy. Shannon-Fano code. Binary Huffmann code. Distribution free coding: Adaptive Huffman codes, Lempel-Ziv codes. Predictive coding. Speech and voice compression algorithms. Image and video compression algorithms.
Cryptography – data security: basic concepts: sensitive information and its attack, cryptography (symmetric, asymmetric). Cryptographic techniques, key-stream and block cryptographs. Shift cryptography, polyalphabetic cryptography, affine cryptography, LFSR
based key stream cryptography, DES block cryptography, 3DES and AES ciphers, SSL protocol. OTP algorithm. Fundamentals of number theory. Public key cryptography. The RSA algorithm and its application.

Topics for the practices
Error correcting coding:
Tasks related to binary linear coding, Reed-Solomon codes, code combinations, applications in communication technologies, network coding, QoS communication

Data compression and source coding:
Examples for Huffman, Shannon-Fano, Sahnnon-Fano-Elias for codes, Adaptive Huffman coding, LZ family of algorithms for file compression, Adaptive predictive coding, Transform based compression (KLT and PCA)

Data security coding:
Examples of OTP algorithm, RSA algorithm