The design of binary shaping filter of binary code

In information theory, in order to maximize the total throughput, it is required that the codebook has an empirical distribution that maximizes the mutual information over the channel. In coding theory, however, most codes we can generate have Bernoulli (1 over 2) distribution. In this paper, we present a new coding scheme to efficiently generate binary codes with different distributions. Our main approach is to first encode the information bits by a linear code C, and then quantized the codeword to the closest codeword in another linear code Cs. The quantization error is then treated as the encoded codeword in our coding scheme. We discuss the practicality and advantage of such codes and give a design example.