The syndrome distribution of m-bit error patterns and the analysis of ATM forward error correction codes

The error detection and correction capability of a linear block code is usually analyzed by its minimum distance and weight distribution function. A different analysis tool, the syndrome distribution of m-bit error patterns, is introduced in the paper. Additional detailed information 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 provided to compute the syndrome distribution vectors of m-bit error patterns 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 undetected percentages is also introduced in the paper