Almost sure convergence of relative frequency of occurrence of burst errors on channels with memory

摘要

Motivated by intention to evaluate asymptot- icallymultiple-error-correcting codes on channels with memory, we willderive the following fact. Let{Z_i}be a hidden Markov process, i.e.,a functional of a Markov chain with a finite State space, andW_b(Z_1Z_2...Z_n)denote the number of burst Error that appear inZ_1Z_2...Z_n, where the number of burst er- Rors is counted usingGabidulin's burst metric1, 1971. As the Main result, we will provethe almost sure convergence of relative Burst weightW_b(Z_1Z_2...Z_n)/n, i.e., the relative frequency of Occurrence ofburst errors, for a broad class of functionals{Z_i} Of finite Markovchains.