Optimal Encoders Maximizing Directed Information of Channels with Memory and Feedback: Stochastic Control and Dynamic Programming
نویسندگان
چکیده
This paper is concerned with the stochastic control formulation of the capacity of channel with memory and feedback. The pay-off is the directed information from the source sequence to the channel output sequence, while the objective is to find the optimal encoder which maximizes this quantity. By invoking a change of measure technique this problem is reformulated in terms of controlling the a posteriori probability via the choice of the encoder strategies to maximize the directed information. A principle of optimality is derived and a dynamic programming equation is obtained which describe how the optimal encoder strategy should be selected. Further, a generalization of posterior matching scheme is presented.
منابع مشابه
Stochastic Dynamic Programming with Markov Chains for Optimal Sustainable Control of the Forest Sector with Continuous Cover Forestry
We present a stochastic dynamic programming approach with Markov chains for optimal control of the forest sector. The forest is managed via continuous cover forestry and the complete system is sustainable. Forest industry production, logistic solutions and harvest levels are optimized based on the sequentially revealed states of the markets. Adaptive full system optimization is necessary for co...
متن کاملA Multi-Stage Single-Machine Replacement Strategy Using Stochastic Dynamic Programming
In this paper, the single machine replacement problem is being modeled into the frameworks of stochastic dynamic programming and control threshold policy, where some properties of the optimal values of the control thresholds are derived. Using these properties and by minimizing a cost function, the optimal values of two control thresholds for the time between productions of two successive nonco...
متن کاملCapacity Achieving Distributions & Information Lossless Randomized Strategies for Feedback Channels with Memory: The LQG Theory of Directed Information-Part II
A methodology is developed to realized optimal channel input conditional distributions, which maximize the finite-time horizon directed information, for channels with memory and feedback, by information lossless randomized strategies. The methodology is applied to general Time-Varying Multiple Input Multiple Output (MIMO) Gaussian Linear Channel Models (G-LCMs) with memory, subject to average t...
متن کاملDynamic Facility Location with Stochastic Demand
Determination of facilities, such as factories or warehouses, location and availability conditions is one of the important and strategic decisions for an organization to make. Transportation costs that form a major part of goods price are dependent to this decision making. There are verity of methods have been presented to achieve the optimal locations of these facilities which are generally de...
متن کاملControl Problem and its Application in Management and Economic
The control problem and Dynamic programming is a powerful tool in economics and management. We review the dynamic programming problem from its beginning up to its present stages. A problem which was involved in physics and mathematics in I 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...
متن کامل