THE SYNDROME DISTRIBUTION OF M-BIT ERROR PATTERNS AND THE ANALYSIS OFATM FORWARD ERROR-CORRECTION CODES

The error detection and correction capability of a linear block code i s usually analyzed by its minimum distance and weight distribution fun ction. A different analysis tool, the syndrome distribution of m-bit e rror patterns, is introduced in this paper. Additional detailed inform ation about the capability of a code can be obtained from the syndrome distribution, e.g., undetected percentages, miscorrected percentages, as well as the weight distribution function. A fast algorithm is prov ided to compute the syndrome distribution vectors of m-bit error patte rns for all m. The cyclic codes defined in asynchronous transfer mode (ATM) for broadband ISDN are used as examples to show the strength of this new analysis tool. A rough, but simple, estimation of the undetec ted percentages is also introduced in the paper.