Research in Mathematics and Computer Science: Calculation of the Probability ofUndetected Error for Certain Error Detection Codes. Phase 2

摘要

Cyclic Redundancy Check (CRC) codes have become the standard means for detectingerror in messages that have been transmitted over a noisy communications channel. Unfortunately, even the very best CRC codes cannot detect all transmission errors. In this report,we first describe a hardware device capable of evaluating the random error performance of an important class of CRC codes that are generated by polynomials of the form g(x) = (x+1) p(x), where p(x) is a primitive polynomial of degree (R-1). We then introduce a new burst error model and establish an equivalence between the burst and random error performance of cyclic codes. From this, we can extend the random error test results obtained from the hardware device to include burst errors. Also included in this report is an intuitive look at the factors which lead to good code performance, and an overview of a supplemental hardware device to measure the performance of cyclic codes that are generated by arbitrary polynomials.