Achieving the Rate-Distortion Bound with Linear Codes

We show that linear codes can achieve the rate-distortion bound of a discrete memoryless source with arbitrary distortion measure if the size of finite field is sufficiently large. An alternative approach based on multilevel quantization is proposed. The optimality of this approach and the sufficiency of binary linear codes are established. Linear codes are also shown to be able to achieve a simplified version of the El Gamal-Cover (EGC) region for multiple description coding.