Blog 1 – Intro, signal transmission, source coding and channel coding, fixed length codes, prefix codes, uniquely decipherable codes, Kraft and McMillan inequalities
Blog 2 – Set theory, combinatorics, binomial coefficients
Blog 3 – Finite probability models, binomial distribution, random variables, expected value, variance
Blog 4 – Information and entropy
Blog 5 – Shannon’s source coding theorem, Huffman codes
Blog 6 – Noisy channels, parity codes, Hamming distance
Blog 7 – Mutual information, channel capacity, noisy coding theorem
Blog 8 – Existence of codes with low error rate, proof of noisy coding theorem
Blog 9 – Parity check codes, algebra mod two
Blog 10 – CRC codes, generator and parity check matrices, syndrome
Blog 11 – Hamming bound, Gilbert Varshamov bound, Hamming codes
Blog 20 – Prime factorization
Blog 21 – Modular arithmetic
Blog 22 – Groups, cyclic groups, cosets, quotient groups, conjugacy, permutation groups
Blog 23 – Polynomials and unique factorization, construction of fields from irreducible polynomials
Blog 24 – Finite fields
Blog 25 – Polynomial interpolation, vandermonde determinants, Reed-Solomon codes, discrete fourier transform
Blog 30 – Arithmetic codes
Blog 35 – Convolutional codes
Daniel Flath 