the first sixteen stored waveforms. Table 2 is a print-out of the first page of the code book for the program. On the next page a r e t h e first sixteen signals correlated with the second sixteen correlators, and so on. There are sixteen code groups of the type in Table 2. Any one of these sixteen code groups could be used to encode four bits of data for a signal-to-noise-ratio improvement over a standard four-bit code. Table 3 illustrates the correlation between groups. It is interesting to note that a cyclic variation of the four-bit sequences does not generate any new codes. It only rearranges the order in the two code groups. In the eight-bit case, however, new codes are generated; in fact, a tremendous number of new codes can be made not only by cyclically varying the bit locationsof the signal and stored waveformsbut also by interchanging the order of the bits in all possible combinations. The process may be carried to the sixteen-bit case, for which there are over 4 x lo9 crosscorrelation coefficients. Sanders has described the Digilock coded binary PCM telemeter, which encodes sixteen-bit words to represent five-bit samples (Reference 11). This system has been flown on an Air Force Blue Scout rocket.,
Parity CodesA simple error-detecting parity code is constructed by adding one bit to an n-bit sequence to indicate whether the total word has an even or an odd number of 2eYo.s It is most interesting to
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This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
note that group 1 of the four-bit correiaLon table can be made from a three-bit sequence by adding an even parity bit; group 2 is generated by adding an odd parity bit. The eight-bit code of Table 2 may be thought of as a four-bit code with four bits for error-detecting and error-correcting.
PFM Correlation TableIn the eight-bit correlation table (Table 2) the second sequence, 00001111, is the same as the second sequence of the four-bit table of Table l(a), 0011, if the words of each are of the same duration. The second word of the two-bit table of Table l(c), 01, is also the same as these two if the time T for the words is the same. Since identical words can be found on different correlation tables, the possibility might be considered that a new table could be constructed from sequences taken from a number of tables. These sequences should have orthogonal properties. The most obvious one is
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