| phenomenon | information transmission over noisy channels— “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” |
| claim-type | existence— “It is possible to send information at the rate C through the channel with as small a frequency of errors or equivocation as desired by proper encoding.” |
| method — evidence | — “The method of proving the first part of this theorem is not by exhibiting a coding method having the desired properties, but by showing that such a code must exist in a certain group of codes.” |
| transfer | from statistical mechanics: entropy itself - the quantity H, its form, and its identification with the H of Boltzmann's theorem, carried out of statistical mechanics and made the measure of information in a communication channel— “The form of H will be recognized as that of entropy as defined in certain formulations of statistical mechanics8 where pi is the probability of a system being in cell i of its phase space. H is then, for example, the H in Boltzmann’s famous H theorem.” | transfers[0] |
| mechanism | quantify information as the logarithm of the number of possible messages (entropy); a noisy channel has a definite capacity C that bounds reliable transmission— “If the number of messages in the set is finite then this number or any monotonic function of this number can be regarded as a measure of the information produced when one message is chosen from the set” | mechanisms[0] |
| builds-on | Nyquist, "Certain Factors Affecting Telegraph Speed" / "Certain Topics in Telegraph Transmission Theory" and Hartley, "Transmission of Information"— “A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject.” | claim_relations[0] |
| extends | the communication theory of Nyquist and Hartley— “In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information.” | claim_relations[1] |
| builds-on | Hartley's logarithmic measure of information— “As was pointed out by Hartley the most natural choice is the logarithmic function.” | claim_relations[2] |
| builds-on | N. Wiener, Cybernetics and The Interpolation, Extrapolation and Smoothing of Stationary Time Series— “Communication theory is heavily indebted to Wiener for much of its basic philosophy and theory.” | claim_relations[3] |
| replicates | R. M. Fano's coding method (Technical Report No. 65, Research Laboratory of Electronics, M.I.T.)— “This method of encoding is substantially the same as one found independently by R. M. Fano.9” | claim_relations[4] |
| sense | information - the engineering sense: which message was selected from a known set, with meaning explicitly set aside— “Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem.” | senses[0] |
| sense | information - the significant aspect for design: one message drawn from a set of possible messages, any of which the system must handle— “The significant aspect is that the actual message is one selected from a set of possible messages. The system must be designed to operate for each possible selection, not just the one which will actually be chosen since this is unknown at the time of design.” | senses[1] |
| sense | information - a rate at which a source produces, rather than a quantity a message contains— “Can we define a quantity which will measure, in some sense, how much information is “produced” by such a process, or better, at what rate information is produced?” | senses[2] |
| sense | H - one quantity under three names: the amount of choice involved in a selection, and the uncertainty of the outcome— “Can we find a measure of how much “choice” is involved in the selection of the event or of how uncertain we are of the outcome?” | senses[3] |
| sense | rate of transmission - not the transmitted bits minus the errors; the naive subtraction is shown to credit a channel that carries nothing— “Our first impulse might be to say the rate is 990 bits per second, merely subtracting the expected number of errors. This is not satisfactory since it fails to take into account the recipient’s lack of knowledge of where the errors occur.” | senses[4] |
| sense | H - a single quantity serving as the measure of three things at once: information, choice and uncertainty— “play a central role in information theory as measures of information, choice and uncertainty.” | senses[5] |
| sense | redundancy - the fraction of a message fixed by the structure of the language rather than freely chosen— “This means that when we write English half of what we write is determined by the structure of the language and half is chosen freely.” | senses[6] |
| audit | entropy —same-as→ uncertainty — Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span is a question about measuring choice and uncertainty; it does not itself equate entropy with uncertainty.— “Can we find a measure of how much “choice” is involved in the selection of the event or of how uncertain we are of the outcome?” | concept_edges[1] |
| retracted | EVIDENCE CORRECTED (RE-GROUNDED) · redundancy —operationalised-as→ entropy — RE-GROUNDED. The old span named only one endpoint. This sentence names both and IS the definition - redundancy is one minus relative entropy, which is exactly what the edge records.— “One minus the relative entropy is the redundancy.”— “One is by calculation of the entropy of the approximations” | concept_edges[2] |
| weight | EVIDENCE CORRECTED (RE-GROUNDED) · redundancy —operationalised-as→ entropy — 0.8— “One minus the relative entropy is the redundancy.” | concept_edges[2] |
| for which use | limitation — everything the theory is ever used to say about content: THESE SEMANTIC ASPECTS OF COMMUNICATION ARE IRRELEVANT TO THE ENGINEERING PROBLEM - meaning is declared out of scope in the founding paper— “These semantic aspects of communication are irrelevant to the engineering problem.” | limitations[0] |
| duplicate of | limitation — limitations[0]— “These semantic aspects of communication are irrelevant to the engineering problem.” | limitations[1] |
| for which use | limitation — the same scope as limitations[0] - meaning is excluded by construction, not by oversight— “These semantic aspects of communication are irrelevant to the engineering problem.” | limitations[1] |
| for which use | limitation — the continuous-case results: WE WILL NOT ATTEMPT, IN THE CONTINUOUS CASE, TO OBTAIN OUR RESULTS WITH THE GREATEST GENERALITY, OR WITH THE EXTREME RIGOR OF PURE MATHEMATICS— “We will not attempt, in the continuous case, to obtain our results with the greatest generality, or with the extreme rigor of pure mathematics, since this would involve a great deal of abstract measure theory and would obscure the main thread of the analysis.” | limitations[2] |
| for which use | limitation — any practical reading of the noisy-channel coding theorem: AN ATTEMPT TO OBTAIN A GOOD APPROXIMATION TO IDEAL CODING BY FOLLOWING THE METHOD OF THE PROOF IS GENERALLY IMPRACTICAL - existence, not construction— “An attempt to obtain a good approximation to ideal coding by following the method of the proof is generally impractical.” | limitations[3] |
| for which use | limitation — capacity results for arbitrary noise: IT DOES NOT APPEAR THAT THE MAXIMIZING PROBLEM INVOLVED IN DETERMINING THE CHANNEL CAPACITY C CAN BE S[olved] explicitly— “In the case of an arbitrary perturbing noise (not necessarily white thermal noise) it does not appear that the maximizing problem involved in determining the channel capacity C can be solved explicitly.” | limitations[4] |
| for which use | limitation — the rate-versus-fidelity theory: THE ACTUAL CALCULATION OF RATES HAS BEEN CARRIED OUT IN ONLY A FEW VERY SIMPLE CASES— “In fact, the actual calculation of rates has been carried out in only a few very simple cases.” | limitations[5] |
| for which use | limitation — the axiomatic derivation of H as the theory's foundation: the paper says the theorem is not necessary and that the definitions are justified by their implications instead— “This theorem, and the assumptions required for its proof, are in no way necessary for the present theory. It is given chiefly to lend a certain plausibility to some of our later definitions. The real justification of these definitions, however, will reside in their implications.” | limitations[6] |
| for which use | limitation — the 50% redundancy of English as an unqualified figure: it excludes statistical structure beyond about eight letters— “The redundancy of ordinary English, not considering statistical structure over greater distances than about eight letters, is roughly 50%.” | limitations[7] |
| replication | untested |
| limitation | the theory deliberately excludes the semantic/meaning aspects of communication— “These semantic aspects of communication are irrelevant to the engineering problem.” | limitations[0] |
| limitation | Meaning is explicitly excluded from the theory's scope.— “These semantic aspects of communication are irrelevant to the engineering problem.” | limitations[1] |
| limitation | The continuous-case results are deliberately not developed with full generality or measure-theoretic rigour.— “We will not attempt, in the continuous case, to obtain our results with the greatest generality, or with the extreme rigor of pure mathematics, since this would involve a great deal of abstract measure theory and would obscure the main thread of the analysis.” | limitations[2] |
| limitation | The existence proof of the noisy-channel coding theorem does not yield a usable construction.— “An attempt to obtain a good approximation to ideal coding by following the method of the proof is generally impractical.” | limitations[3] |
| limitation | For non-white noise the capacity cannot be computed explicitly, only bounded.— “In the case of an arbitrary perturbing noise (not necessarily white thermal noise) it does not appear that the maximizing problem involved in determining the channel capacity C can be solved explicitly.” | limitations[4] |
| limitation | Source rates relative to a fidelity criterion have only been computed in a handful of simple cases.— “In fact, the actual calculation of rates has been carried out in only a few very simple cases.” | limitations[5] |
| limitation | Shannon states that the uniqueness theorem for H, and the assumptions behind it, are in no way necessary to the theory; the justification is deferred to the implications of the definitions.— “This theorem, and the assumptions required for its proof, are in no way necessary for the present theory. It is given chiefly to lend a certain plausibility to some of our later definitions. The real justification of these definitions, however, will reside in their implications.” | limitations[6] |
| limitation | The 50% redundancy figure for English is bounded to statistical structure within about eight letters.— “The redundancy of ordinary English, not considering statistical structure over greater distances than about eight letters, is roughly 50%.” | limitations[7] |