The application of information theory to data-transmission systems, and the possible use of binary coding to increase channel capacity

摘要

The simple application of information theory to data transmission shows that when the proper scale-unit of an input signal X(t) has been established by the reference of all noise to the input, the smallest time-interval, ?t, in which one metron (i.e. a change of one scale-unit) must be transmitted is determined by the maximum possible rate of change of X(t); this determines the required bandwidth ?f ? 1/?t. Channel capacity is taken as the number of metrons that can be transmitted per unit bandwidth in unit time, and it is shown that, if provision is made for transmission of changes in X(t) at the maximum rate of one unit ?x in each basic interval of time ?t, there will be considerable waste of channel capacity, since, in general, the mean rate of change of X(t) will be much smaller than the maximum rate. It is shown that, provided a small delay for coding and decoding and some loss of fine structure in the received signal can be accepted, some of the time wasted, when X(t) is changing slowly, can be employed by integrating the changes in X(t) over a number of basic intervals ?t. The integrated change over the period ? = n?t can then be coded into binary form and transmitted during the following period while the current changes in X(t) are again being accumulated. In this way either the bandwidth can be reduced or the time saved can be used for transmission of other quantities, Y(t), Z(t), etc. It is shown that in this way the number of metrons transmitted can be increased by a factor M dependent on R, the ratio of the maximum rate of change to the mean rate of change without regard to sign, and n. There is some increase in the proper scale-unit, indicating some loss of accuracy, but M may have values of the order of 4 with an increase of proper scale-unit of less than 50%. It is then shown that in some cases provision is being made for transmission of more binary digits than are usually necessary, and by limiting the total change in X(t) that can be transmitted in -none period ?, a further saving can be effected with only a small increase in proper scale-unit when R is of the order of 10 or more.