Double and triple error detecting capability of Internet checksum and estimation of probability of undetectable error

The Internet checksum is calculated by 16-bit one's complement arithmetic. The occurrence of two or more errors, however, may not be detected. In this manuscript, we formulate the checksum procedure as a nonlinear code. Part of distance distribution of the nonlinear code is calculated. By using the results, we derived lower and upper bounds on the probability of an undetectable error when the nonlinear code is used for error detection on a binary symmetric channel. For the IP header with no optional fields, the lower bound is almost equal to the upper bound when the bit error rate is less than about 1.0/spl times/10/sup -3/.