Abimael Martell
12e9a655e3
* fix(extractor): supply built-in metrics for non-embedded base-14 fonts PDFs may legally omit /Widths for non-embedded standard fonts (Times, Helvetica, Courier, Symbol, ZapfDingbats) — the spec requires the reader to supply the metrics. We returned None, so every glyph advanced 0 and each text item got width 0, silently breaking every gap-based heuristic downstream: space synthesis, sub/superscript detection, table column detection, heading merging. - src/extractor/base14.rs: Adobe Core-14 AFM width tables keyed by Unicode char, plus the standard Symbol/ZapfDingbats encoding vectors (their glyphs sit at byte positions unrelated to Latin text, so widths must resolve through the built-in encoding, not cp1252) - Width resolution order: Differences -> built-in encoding -> the same cp1252-style fallback the text decoder uses, so a code's advance always matches the character we emit for it - Type3 visual sizing: PK bitmap fonts (dvips) use FontMatrix [1 0 0 -1 0 0] with nominal sizes like 0.12pt; scale by FontBBox height x |matrix_y|. Applied in the page-stream and Form XObject paths. Indirect numeric array elements are resolved before use. Effect on Shannon's 'A Mathematical Theory of Communication' (1998 dvips/Distiller, the reported case): glued sentences 95 -> 5. Corpus impact: 12 of 184 eval documents, e.g. Data-Processing-Agreement recovers a paragraph that a phantom table had shredded into cells. Layout heuristics tuned on the same document (indent-based paragraph breaks, heading reclassification, table script filtering) are held back for a separate PR — they change ~98 further documents and need to be justified against the corpus, not against one PDF. * review: narrow Type3 rescaling to self-inconsistent fonts; dedup + test all width tables Addresses cubic review on #241, plus a follow-up from a local cubic run. - Type3 visual scaling was applied to every Type3 font whose FontBBox height x |matrix_y| deviated >5% from 1.0. FontBBox is the glyph box, not the em box, so a conventional 1/1000-matrix font with a descender..ascender bbox (~700 units) computed 0.7 and had every reported size shrunk by 30% — corrupting the drop-cap, heading-tier, sub/superscript and table heuristics this is meant to fix. First attempt gated on the matrix being unit-scale, but a local cubic run pointed out that wrongly excludes valid non-standard matrices (a 0.005 matrix with a full-em bbox legitimately needs a 5x scale). The product is the right discriminator, not the matrix: a self-consistent font lands near 1.0 because the matrix is the reciprocal of the glyph-space em, so only a wildly inconsistent one (dvips/PK bitmap fonts sit at ~159) is renormalized. Band widened to [0.25, 4.0]. Corpus effect: 12 -> 7 documents change. The 5 that drop out were being wrongly rescaled — including Data-Processing-Agreement, whose phantom-table fix turned out to come from this bug rather than from the width fallback, so it is correctly given up. - base14: all 14 width tables now covered by the sort-invariant test via an ALL_TABLES registry, not a hand-picked subset. - base14: identical tables share one static (all four Courier variants are monospace 600; the oblique Helvetica variants match their upright forms), removing 5 duplicate copies. * test: refresh Shannon snapshot after merging main CI checks out a merge of the PR head with main, and main advanced 8 commits since this branch was cut — including #201 (contextual digit runs), #240 and #253 (markdown fixes). Those change extraction output, so a snapshot generated on the unmerged branch could not match; the Test job failed on the merge commit while passing on the branch itself. The merged behaviour is better: the footnote marker '2' before 'Hartley, R. V. L.' is now recovered instead of dropped. 950 tests pass on the merged tree, clippy clean.
7.1 KiB
Reprinted with corrections from The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948.
A Mathematical Theory of Communication
By C. E. SHANNON
INTRODUCTION
HE recent development of various methods of modulation such as PCM and PPM which exchange
Tbandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A
basis for such a theory is contained in the important papers of Nyquist¹ and Hartley² on this subject. 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. The fundamental problem of communication is that of reproducing at one point either exactly or ap- proximately a message selected at another point. 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. 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. 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, all choices being equally likely. As was pointed out by Hartley the most natural choice is the logarithmic function. Although this definition must be generalized considerably when we consider the influence of the statistics of the message and when we have a continuous range of messages, we will in all cases use an essentially logarithmic measure. The logarithmic measure is more convenient for various reasons:
- It is practically more useful. Parameters of engineering importance such as time, bandwidth, number of relays, etc., tend to vary linearly with the logarithm of the number of possibilities. For example, adding one relay to a group doubles the number of possible states of the relays. It adds 1 to the base 2 logarithm of this number. Doubling the time roughly squares the number of possible messages, or doubles the logarithm, etc.
- It is nearer to our intuitive feeling as to the proper measure. This is closely related to (1) since we in- tuitively measures entities by linear comparison with common standards. One feels, for example, that two punched cards should have twice the capacity of one for information storage, and two identical channels twice the capacity of one for transmitting information.
- It is mathematically more suitable. Many of the limiting operations are simple in terms of the loga- rithm but would require clumsy restatement in terms of the number of possibilities. The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly bits, a word suggested by
J. W. Tukey. A device with two stable positions, such as a relay or a flip-flop circuit, can store one bit of information. N such devices can storeN bits, since the total number of possible states is 2 N and log₂2 N = N. If the base 10 is used the units may be called decimal digits. Since
log₂M = log₁₀M= log₁₀2 = 3:32 log₁₀M;
1 Nyquist, H., “Certain Factors Affecting Telegraph Speed,” Bell System Technical Journal, April 1924, p. 324; “Certain Topics in Telegraph Transmission Theory,” A.I.E.E. Trans., v. 47, April 1928, p. 617. 2 Hartley, R. V. L., “Transmission of Information,” Bell System Technical Journal, July 1928, p. 535.
INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION
SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE
NOISE SOURCE
Fig. 1 — Schematic diagram of a general communication system.
a decimal digit is about 3 13 bits. A digit wheel on a desk computing machine has ten stable positions and therefore has a storage capacity of one decimal digit. In analytical work where integration and differentiation are involved the base e is sometimes useful. The resulting units of information will be called natural units. Change from the base a to base b merely requires multiplication by logba. By a communication system we will mean a system of the type indicated schematically in Fig. 1. It consists of essentially five parts:
- An information source which produces a message or sequence of messages to be communicated to the receiving terminal. The message may be of various types: (a) A sequence of letters as in a telegraph of teletype system; (b) A single function of time f (t) as in radio or telephony; (c) A function of time and other variables as in black and white television — here the message may be thought of as a function f (x; y;t) of two space coordinates and time, the light intensity at point (x; y) and time t on a pickup tube plate; (d) Two or more functions of time, say f (t), g(t), h(t) — this is the case in “three- dimensional” sound transmission or if the system is intended to service several individual channels in multiplex; (e) Several functions of several variables — in color television the message consists of three functions f (x; y;t), g(x; y;t), h(x; y;t) defined in a three-dimensional continuum — we may also think of these three functions as components of a vector field defined in the region — similarly, several black and white television sources would produce “messages” consisting of a number of functions of three variables; (f) Various combinations also occur, for example in television with an associated audio channel.
- A transmitter which operates on the message in some way to produce a signal suitable for trans- mission over the channel. In telephony this operation consists merely of changing sound pressure into a proportional electrical current. In telegraphy we have an encoding operation which produces a sequence of dots, dashes and spaces on the channel corresponding to the message. In a multiplex PCM system the different speech functions must be sampled, compressed, quantized and encoded, and finally interleaved properly to construct the signal. Vocoder systems, television and frequency modulation are other examples of complex operations applied to the message to obtain the signal.
- The channel is merely the medium used to transmit the signal from transmitter to receiver. It may be a pair of wires, a coaxial cable, a band of radio frequencies, a beam of light, etc.
- The receiver ordinarily performs the inverse operation of that done by the transmitter, reconstructing the message from the signal.
- The destination is the person (or thing) for whom the message is intended. We wish to consider certain general problems involving communication systems. To do this it is first necessary to represent the various elements involved as mathematical entities, suitably idealized from their