Information Theory and Coding
Entropy, compression and channel capacity.
Key idea
Entropy, compression and channel capacity.
In depth
Shannon showed information can be quantified as entropy and that reliable communication is possible at any rate below channel capacity. Source coding compresses (Huffman) and channel coding adds redundancy (Hamming, Reed–Solomon) to fix errors.
Worked example
A source with probabilities 1/2, 1/4, 1/4 has entropy 1.5 bits; Huffman codes of length 1, 2, 2 achieve it.
Formula
Real-world uses
- Compressing files, designing mobile networks and increasing data transfer speeds
Common mistake
Confusing compression (removes redundancy) with error correction (adds it).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Information Theory and Coding?
Entropy, compression and channel capacity. It is a topic at the expert level in Differential Equations, Abstract Algebra & Applied Math.
What is the formula for Information Theory and Coding?
The key formula is H = −Σ p log₂ p.
Where is Information Theory and Coding used in real life?
Real-world examples: Compressing files, designing mobile networks and increasing data transfer speeds.
What should I learn before Information Theory and Coding?
Make sure you are comfortable with Queueing Theory, the previous topic in Differential Equations, Abstract Algebra & Applied Math.
What is a common mistake with Information Theory and Coding?
Confusing compression (removes redundancy) with error correction (adds it).
How can I practise Information Theory and Coding?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Information Theory and Coding?
Move on to Cryptography Mathematics next.
Related expert topics in Differential Equations, Abstract Algebra & Applied Math
- Exact Equations – M dx + N dy = 0 with Mᵧ = Nₓ.
- Bernoulli Equations – Substitute v = y¹⁻ⁿ to linearise.
- Runge–Kutta Methods – Higher-accuracy numerical solvers.
- Second-Order Homogeneous Equations – Use the characteristic equation.
- Undetermined Coefficients – Guess the particular solution form.
- Variation of Parameters – General method for particular solutions.