A generalized permutation entropy for noisy dynamics and random processes

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting rank vectors called ordinal patterns or just permutations. The reasons for increasing popularity this in analysis include that (i) it converges to Kolmogorov-Sinai underlying dynamics limit ever longer permutations, and (ii) its computation dispenses with generating ad hoc partitions. However, permutation diverges when number allowed permutations grows super-exponentially their length, as is usually case are output by random processes. In Letter we propose generalized finite processes, including discrete-time dynamical systems observational noise.