Scalar Quantizers with Uniform Encoders and Channel-Optimized Decoders for M-PSK Schemes

In this paper, the problem of index assignments for quantizers with uniform encoders and channel-optimized decoders for M-PSK schemes is studied. The analytical expressions of MSD (Mean-Squared Distortion) for such quantizers with the natural, zigzag and NBC-Gray mappings, respectively, have been derived. An interesting result is that at a wide range of MSD levels, the zigzag mapping can offer a significant gain in SNR over the other two mappings when used in such quantizers, especially when the alphabet size M gets larger, which is agreed by simulation results.