The Mathematical Theory of Communication
415 NYQUIST: FACTORS AFFECTING TELEGRAPH SPEED Feb. 1924 the literature does not disclose that anything has been SUBMARINE CABLES published on the experimental side either to confirm In the case of submarine-cable telegraphy, there is or to oppose this result. a limitation on voltage which has not been emphasized The in the simple direct-current case discussed above. CHOICE OF CODES voltage which may be impressed on the cable is limited A formula will first be derived by means of which Moreover, for certain reasons, the to a definite value. of transmitting intelligence, using codes the speed cable has an impedance associated with it at the sending employing different numbers of current values, can be end which may make the voltage on the cable differ compared for a given line speed, i. e., rate of sending of from the voltage applied to the sending-end apparatus. Using this formula, it will then be signal elements. Inasmuch as the limitation in this case isvoltagelimita- shown that if the line speed can be kept constant and tion at the cable, the ideal wave is one which applies a the number of current values increased, the rate of rectangular wave to the cable rather than to the appara- transmission of intelligence can be materially increased. tus, because it insures that the area under the curve Comparison will then be made between the theoretical should be the maximum consistent with the imposed possibilities indicated by the formula and the results It would be possible to make the trans- limitations. obtained by various codes in common use, including the mitting-end impedance approximately proportional to Continental and American Morse codes as applied to the cable impedance throughout most of the important land lines, radio and carrier circuits, and the Continental This would insure that the wave applied to the range. It will be Morse code as applied to submarine cables. cable would have approximately the same shape as the shown that the Continental and American Morse codes It would probably be wave applied to the apparatus. applied to circuits using two current values are materi- desirable for practical reasons to make this impedance ally slower than the code which it is theoretically possi- infinite for direct current. ble to obtain because of the fact that these codes are In connection with the submarine cable a special arranged so as to be readily deciphered by the ear. On kind of interference is particularly important, namely, the other hand, the Continental Morse code, as applied that due to imperfect duplex balance. For a given to submarine cables, or other circuits where three cur- degree of unbalance, the interference due to this source rent values are employed, wMl be shown to produce may be reduced by putting networks either in the path results substantially on par with the ideal. Taking the of the outgoing current or in the path of the incoming above factors into account, it will be shown that if a These facts, together with the frequency dis- current. given telegraph circuit using Continental Morse code tributions deduced above for each of the several im- with two current values were rearranged so as to make pressed waves as exhibited in Fig. 2, make it apparent possible the use of a code employing three current that the beneficial reaction on the effect of duplex un- values, it would be possible to transmit over the re- balance, which can be obtained by the use of a half- Harry Nyquist arranged circuit about 2.2 times as much intelligence cycle sine wave instead of a rectangular wave, can be with a given number of signal elements. obtained more effectively by the use of a simple network, It will then be pointed out why it is not feasible on either in the path of the outgoing or in the path of the all telegraph circuits to replace the codes employing Either of these locations is equally incoming currents. two current values with others employing more than effective in reducing interferences from duplex un- two current values, so as to increase the rate of trans- balance, but the location of the network in the path of The circuits, for which the possi- the outgoing current has the advantage that it de- mitting intelligence. in speed appear of thus securing increases creases the interference into other circuits, whereas the bilities greatest, are pointed out, as well as those for which the location in the path of the incoming current has the possibilities appear least. effect of reducing the interference from other circuits. • Certain Factors Affecting Before leaving the matter of submarine telegraphy, WITH USING CODES it may be well to point out that it is common in practise THEORETICAL POSSIBILITIES Telegraph Speed . Bell Labs DIFFERENT NUMBERS OF CURRENT VALUES to shorten the period during which the battery is ap- Technical Journal. 1924 The speed at which intelligence can be transmitted plied so as to make it less than the total period allotted over a telegraph circuit with a given line speed, i. e., a to the signal element in question. For instance, if it given rate of sending of signal elements, may be deter- is desired to transmit an e the battery may be applied mined approximately by the following formula, the f or, say, 75 per cent of the time allotted to that e and derivation of which is given in Appendix B. during the remaining 25 per cent the circuit is grounded. W = K log m The resulting voltage is shown in Fig. 3F. From the Where W is the speed of transmission of intelligence, foregoing, it is concluded that this method is less ad- m is the number of current values, vantageous than the application of the voltage for the and, K is a constant. whole period, because while the shape of the received By the speed of transmission of intelligence is meant signal is substantially the same in the two cases, the different of characters, representing magnitude, being proportional to the area under the the number letters, figures, etc., which can be transmitted in agiven A cursory examination of voltage curve, will be less.
Ralph Hartley • Transmission of Information . Bell Labs Technical Journal. 1928
Claude Shannon • A Symbolic Analysis of Relay and Switching Circuits . Master’s Thesis. MIT. 1937
Claude Shannon
Claude Shannon • A Mathematical Theory of Communication . Bell Labs Technical Journal. 1948 ing in cell i of its phase call H ∑ p i log p i t H x for its entropy;
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE Text message written in NOISE SOURCE natural language Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE Message encoded NOISE in Morse code SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE Encoded message corrupted by noise from the transmission lines NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE Received message decoded from Morse code NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE Received message written in NOISE SOURCE natural language. May contain errors. Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e f SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model ˆ e = arg max p ( e | f ) e INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e f SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
The Noisy Channel Model ˆ e = arg max p ( e | f ) e INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION e f SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1—Schematic diagram of a general communication system.
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