Spring 2017 Information and Coding Theory

Syllabus

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

Homework 1,  Solution

Homework 2, Solution

Homework 3, Solution

Test 1 solution

Homework 4, Solution

Homework 5, Solution

Homework 6, Solution

Test 2 solution

Homework 7, Solution

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