Vector Flows That Compute the Capacity of Discrete Memoryless Channels

Area of Science:

• Information Theory
• Dynamical Systems
• Computational Science

Background:

• The computation of channel capacity is a fundamental, long-standing problem in information theory.
• Existing methods like the Blahut-Arimoto algorithm provide a basis for capacity computation.

Purpose of the Study:

• To investigate a novel continuous-time dynamical system for computing channel capacity.
• To analyze the convergence properties of this new approach.
• To present a circuit design for analog computation of channel capacity.

Main Methods:

• Development of a continuous-time dynamical system.
• Mathematical proof of convergence properties.
• Circuit design for analog implementation.

Main Results:

• The proposed dynamical system is a continuous-time analog of the Blahut-Arimoto algorithm.
• The system demonstrates an exponential rate of convergence under specific conditions.
• A circuit design is presented for practical analog estimation of channel capacity.

Conclusions:

• The novel continuous-time dynamical system offers an efficient method for estimating channel capacity.
• This approach enables analog computation, potentially speeding up capacity estimation.
• The system's convergence properties make it a viable alternative to existing algorithms.