Design and analysis of lossy source coding of Gaussian sources with finite-length polar codes

Polar codes are proven to achieve the rate distortion bound of Gaussian sources under the condition that the size of reconstruction alphabet and code length grow to infinity. However, this condition cannot be satisfied in practice. In this paper, we propose a practical source coding scheme based on multilevel polar codes, called polar coded quantization (PCQ). In this scheme, extended reconstruction alphabet, set-partition (SP) labeling and successive cancellation (SC) (or its improved) encoding algorithm are combined to approach the rate distortion bound. Furthermore, an efficient upper bound of encoding rate for a given distortion is derived to guide the practical design of PCQ. Simulation results show that PCQ provides a flexible and constructive framework to efficiently approximate the rate distortion bound of Gaussian sources.