wunder beta📡 Information Theory: Bits, Entropy, and Noisy Channels
Follow Shannon's framework from selected messages to bits, entropy, compression, and the capacity boundary that makes reliable communication possible through noise.
What you’ll learn
- Communication becomes a measurable selection problemExplain Shannon's medium-independent communication model, distinguish its five stages, and interpret bits as logarithmic units of resolved choice rather than semantic meaning.A device-specific engineering problem becomes a general architecture. Information measures which alternative was selected and how faithfully that selection can be reproduced.
- Entropy sets the compression targetCalculate the intuition behind self-information and entropy, connect predictable redundancy to coding, and state the source-coding limit accurately.Rare events carry more self-information; entropy averages that surprise. Long codes can remove predictable structure but cannot beat the modeled source's lossless limit.
- Noise has a capacity boundaryUse conditional uncertainty, mutual information, and capacity to explain reliable noisy communication and the distinct jobs of source and channel coding.Noise need not make reliable communication impossible. Below capacity, long structured codes can drive error probability down, while rates above the boundary cannot be rescued by coding.
Questions this course answers
Match each block in Shannon's system to its role
The block diagram separates message selection, signal encoding, constrained transport, and reconstruction so each problem can be modeled distinctly.
Why does a fair coin have more Shannon entropy per flip than a coin that lands heads 90% of the time?
Both sources use two symbols, but unequal probabilities make the biased source more predictable and reduce average self-information to below one bit.
Explain how a noisy channel can support arbitrarily reliable communication without becoming noiseless.
Below channel capacity, structured codes over sufficiently long blocks let a receiver infer the intended message with error probability made arbitrarily small despite persistent noise.
Grounded in trusted sources
- MIT Computer Science and Artificial Intelligence Laboratory — university-hosted copy of Shannon's corrected 1948 paper covering the system diagram, entropy, source coding, noisy channels, capacity, and coding theorems: https://people.csail.mit.edu/dmoshkov/courses/codes/shannon1948.pdf
- MIT OpenCourseWare — dedicated resource page for the original 1948 paper and course context on signals, systems, and information: https://ocw.mit.edu/courses/mas-160-signals-systems-and-information-for-media-technology-fall-2007/external-resources/original-1948-paper-by-shannon-pdf-443mb_324f81b7-b8d6-422b-ac4d-e2414ddfefc7/
- MIT Comparative Media Studies/Writing — research history of the paper's creation, its medium-independent communication architecture, and its technological influence: https://cmsw.mit.edu/claude-shannon-making-information-theory/
- Stanford University — tutorial deriving self-information and entropy from probability and logarithmic additivity: https://theory.stanford.edu/~blynn/pr/info.html
- Stanford University Information Science and Engineering — lecture on Shannon entropy and the lossless source-coding theorem's minimum average bits per source symbol: https://web.stanford.edu/class/engr76/lectures/lecture4_slides.pdf
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