An Efficient Coding Technique for Stochastic Processes

Abstract

In the framework of coding theory, under the assumption of a Markov process (Xt) on a finite alphabet A, the compressed representation of the data will be composed of a description of the model used to code the data and the encoded data. Given the model, the Huffman’s algorithm is optimal for the number of bits needed to encode the data. On the other hand, modeling (Xt) through a Partition Markov Model (PMM) promotes a reduction in the number of transition probabilities needed to define the model. This paper shows how the use of Huffman code with a PMM reduces the number of bits needed in this process. We prove the estimation of a PMM allows for estimating the entropy of (Xt), providing an estimator of the minimum expected codeword length per symbol. We show the efficiency of the new methodology on a simulation study and, through a real problem of compression of DNA sequences of SARS-CoV-2, obtaining in the real data at least a reduction of 10.4%.

A Metric Based on the Efficient Determination Criterion

“…Partition Markov models, commonly referred to as those delineated by Definition 2, have found application in diverse realms. For instance, they have been employed in data compression in conjunction with Huffman coding, as exemplified in [ 3 ]. Across these investigations, the utilization of the BIC-based metric has proven indispensable.…”