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

Author

Desaki, Yoshihisa ; Iwasaki, Kazuhiko ; Miura, Yukiva ; Yokota, Daisuke

Author_Institution

Graduate Sch. of Eng., Tokyo Metropolitan Univ., Japan

fYear

1997

fDate

15-16 Dec 1997

Firstpage

47

Lastpage

52

Abstract

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 1.0×10^-3

Keywords

Internet; cyclic codes; digital arithmetic; error correction codes; error detection codes; fault tolerant computing; Internet checksum; binary symmetric channel; bit error rate; error detecting capability; lower bounds; nonlinear code; one´s complement arithmetic; probability estimation; undetectable error; upper bounds; Arithmetic; Computer errors; Cyclic redundancy check; Cyclic redundancy check codes; Fault detection; Fault tolerant systems; Internet; Probability; TCPIP; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Fault-Tolerant Systems, 1997. Proceedings., Pacific Rim International Symposium on

Conference_Location

Taipei

Print_ISBN

0-8186-8212-4

Type

conf

DOI

10.1109/PRFTS.1997.640124

Filename

640124