On quantization of log-likelihood ratios for maximum mutual information

We consider mutual-information-optimal quantization of log-likelihood ratios (LLRs). An efficient algorithm is presented for the design of LLR quantizers based either on the unconditional LLR distribution or on LLR samples. In the latter case, a small number of samples is sufficient and no training data are required. Therefore, our algorithm can be used to design LLR quantizers during data transmission. The proposed algorithm is reminiscent of the famous Lloyd-Max algorithm and is not restricted to any particular LLR distribution.