Non-binary Polar Coded Quantization for Lossy Source Coding

This paper presents a new vector quantization approach based on non-binary polar codes. Specifically, we use the non-binary polar code soft-input decoder as the encoder for vector quantization to realize source compression, while the non-binary polar encoder as the vector quantization decoder for source reconstruction. Further, we optimize the design of the reconstruction constellation set and the transition probability of the test channel. Our proposed scheme not only effectively mitigates the loss associated with the binary-to-multilevel mapping process, but is also adaptable to various sources with different distributions. Our scheme exhibits superior performance compared to the baseline binary polar coded method. Numerical evaluations under both continuous Gaussian and discrete multilevel source conditions demonstrate that the rate-distortion performance is close to the theoretical bound.