A Statistical Evaluation of Error Detection Cyclic Codes for Data Transmission

Error data from about 350 hours of 1200-baud data transmission tests are used to evaluate cyclic error detection codes. For polynomials of low degree (<7), the ratio of undetected erroneous messages to total erroneous messages is inversely proportional to the period of the coding polynomial. In a commercial synchronous operation, the typical optimum block length (>4,000 digits) is such that a Bose-Chaudhuri-Hocquenghem polynomial requires an excessive number of check digits when its period exceeds the block length. In this case, codes aimed at burst detection are considered superior. A figure of merit is defined and used as one of the criteria for polynomial selection. This figure is obtained, on the basis of these tests, for primitive, LRC, multiplex, fire, and other polynomials. For a typical error detection and retransmission system, transmission efficiency, turn-around time, and number of check digits are related to the data obtained from the tests.