A Lloyd-Max based quantizer of L-values for AWGN and Rayleigh fading channel

L-values have been widely adopted due to their outstanding features in many scenarios of digital communication systems, for instance, in channel decoders or in cooperative relays, where in the latter L-values could be exchanged between physically separated relays. However, an L-value is a real number, and for this reason, it must be quantized before being processed in any finite state machine. This irreversible process reduces the mutual information contained implicitly in the L-value. Therefore the quantizer must be designed carefully to jeopardize the mutual information contained in the L-value as little as possible. In literature, solutions for such a quantizer are proposed only for systems considering AWGN channels. In this paper a new method for the design of a quantizer of L-values is proposed which allows us to consider systems with both AWGN and flat Rayleigh fading channels. To this end, an optimized Lloyd-Max based quantizer of L-values is developed. It is shown that the cost function suitable for the Lloyd-Max algorithm can be designed in terms of the information loss instead of the mutual information.