Recurrent Codes: Easily Mechanized, Burst-Correcting, Binary Codes

In adapting the existing telephone network to high-speed digital data transmission, an error control problem arises. Most of the circuits were designed primarily for voice-type signals and considerable attention was given to control of thermal noise. Because of the high redundancy of speech, impulse noise on the lines is usually not even noticed by the telephone users, and hence has not been a serious problem. On the other hand, high-speed digital data (especially numerical data) contain little redundancy, and the noise pulses may resemble the signal pulses and thus cause errors. The deliberate introduction of redundancy to detect and correct transmission errors has been used for some time. Early systems 1 used repetition of characters and duplication of channels. There were two schemes which sent pictures of the characters using raster scans. By the late 1930's a radio telegraph system 2 using a 3-out-of-7 code for error detection had been patented and telephone apparatus using 2-out-of-5 codes3 was being designed. Most, if not all, of the recent work on error-detecting or error-correcting codes stems from Hamming's Systematic Parity Check codes.4 These codes will correct a single error per block of digits. Since then, much work has been done on codes for multiple errors (see Refs. 5 through 16). The 969