Variable-Length Lossy Source Code Using a Constrained-Random-Number Generator

A variable-length lossy source code is introduced with a rate-distortion pair close to the rate-distortion function. Random numbers that satisfy a condition specified by a function and its value are used to construct a stochastic encoder. The proof of the theorem is based on the balanced-coloring property of an ensemble of functions. Since an ensemble of systematic sparse matrices has this property, we can construct a tractable code for a memoryless source. Some algorithms for implementing the code are introduced and compared by simulation.