In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.

Source coding for random processes Optimal coding of process Let X = (X1,... XN) be a vector of N symbols from a random process. Use an optimal source code to encode the vector. Then H(X1...XN) L(N) H(X1...XN)+1 which gives the average codeword length per symbol, L = 1 N L (N), 1 N H (X1...XN) L 1 N H X1...XN)+ 1 N

Markov Discrete Information Sources The entropy of a Markov Source is given as follows: H = N å i=1 Pr(s i).H i bits symbol (25) where N = number of states Pr(s i) = Probability to be on the ithstate s i H i = entropy of the ith state (considered as a DMS) Example: Consider a two-state Markov source which gives the symbols A,B,C according to ...

We use the state of a Markov chain to represent the \memory" of the source, and use the transitions between states to represent the next symbol out of the source. Thus, for example, the state could be the previous symbol from the source, or could be the previous 300 symbols.

Markov sources are of little importance in simple In-formation Theory, but are crucial to more advanced applications, and data compression. 2.4 Structure of Language A good example of a Markov source is ordinary text. Consider an alphabet of 27 symbols (26 letters and space). 1. Zero memory source with equiprobable sym-bols. Then H(S) = log 2

In this paper we rst formalize a a measure of information: entropy. In doing so, we explore various related measures such as conditional or joint entropy, and several foundational inequalities such as Jensen’s Inequality and the log-sum inequality. The rst major result we cover is the

Nov 10, 2002 · A Markov information source satisfies the condition Pr (X t ∈B | X u, u⩽s)= Pr (X t ∈B | X s) for every s<t and every Borel set B, where Pr (X t ∈B | Y) denotes the conditional probability of {X t ∈B} given Y.

Topics covered: Markov sources and Lempel-Ziv universal codes. Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Markov sources form a basic part of discrete mathematics both from the theoretical and practical point of view. For example, in cryptography, one needs to know how much redundancy is carried by a language such as English to ensure that encryption is secure.

Nov 10, 2002 · This paper discusses the classical entropy and entropy rate for discrete or continuous Markov sources, with finite or continuous alphabets, and their relations to program-size complexity and algorithmic probability.