The question
How much information can a communication system carry, and how can a message survive noise? Shannon's 1948 framework treats sources, channels and coding mathematically. It separates the engineering problem of conveying a selected message from the message's meaning. That distinction makes it possible to study shared limits across very different systems, rather than giving each telephone, alphabet or transmission method a wholly separate theory.
The idea
A probabilistic source has patterns and uncertainty. Coding can use those patterns when representing messages. A noisy channel has limits on the rate at which information can be conveyed reliably under a stated model. These are mathematical statements about specified sources and channels, with asymptotic and coding assumptions. A word such as information does not automatically give a metric for truth, intelligence, usefulness or scientific importance.
Why it matters
The contribution provides a common language for compression and communication limits. It helps distinguish an inefficient implementation from a fundamental constraint of a model. WRS's S grade concerns the 1948 information-theory contribution. Practical error-correcting codes have their own records and contributors; Hamming's constructive coding work is not absorbed into Shannon's authorship. The reference score is WRS's provisional historical estimate, not a measurement in bits reported by the original paper.
A teaching example
Imagine a toy sender choosing A half the time, B a quarter, and C and D one eighth each. A bit is one binary digit: 0 or 1. A fixed code needs two bits per symbol. Could common symbols use fewer? Try A = 0, B = 10, C = 110, D = 111. No complete code begins another, so the receiver can tell where each symbol ends. Over eight example messages with exactly those proportions, four A symbols use four bits; two B symbols use four; C and D use three each. The total is fourteen bits for eight symbols: 1.75 bits per symbol, instead of two. This invented classroom example shows how probability can shorten an average message. It assumes noiseless transmission; it does not protect against flipped bits or measure a message's meaning.
Scope and a useful next step
Read the source and channel descriptions in the linked institutional reprint, then inspect the hypotheses of any theorem you want to use. A bounded contribution might compare two explicit source distributions or reproduce one small coding example. State the alphabet, probabilities, noise model and quantity being measured. A demonstration on short messages does not establish an asymptotic coding theorem, and reliable transmission of a false statement does not make that statement true.
See how this classroom example answers a real WRS reading request
Scientific scope
The probability models, asymptotic conditions and channels of each coding theorem must be stated.
Read the original work
Sources and reading locations for this explanation
- Shannon: A Mathematical Theory of Communication, institutional reprint
Introduction and source/channel models; theorem assumptions distinguish coding limits from semantic meaning.
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
Claude Shannon
Listed source contributors; individual labor shares are not measured
Research locations and affiliations
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Documented countries / regions: United States
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