Packet Error Control System Performance Analysis And The Best Error Correction Code

An important parameter evaluating error control systems is the undetected error probability of the used codes that is studied in theoretical analysis and computer simulation. It is proven that the extended double-error-correcting BCH codes are proper for pure error-detection, and the (2m.2.m) nonlinear constant weight code for m>4 are not.Some results on the undetected error probability of linear codes for pure error-detection are, at present, generalized for both error detection and correction. An analytic formula is obtained to calculate the undetected error probability of linear block codes for simultaneous error detection and correction. The concept of good codes and proper codes for both error detection and correction is presented. It is shown that the binary perfect codes and the primitive double-error-correcting BCH codes and their extended codes are proper for both error detection and correction. The primitive triple-error-correcting BCH codes with length 2"' -1 and their extended codes are proper for odd m > 5 , not for even m > 6.Importance sample method has the potential applied value in computer simulation of error control systems. A simulation model using the 0-1 distribution as the bias probability distribution for both error detection and correction is put forward. The problem of optimum bias probability is solved in theoretical respect. The simulation efficiency at optimum bias probability is derived. The presented method is shown to be right through computer simulation for the (23.12) Golay code and the (15,7) BCH code.In this paper proposed and solved are some theoretical problems on the block code' performance analysis and simulation that have important significance for evaluating practical error control systems.