Practical quantizer design for half-duplex estimate-and-forward relaying

We propose a quantizer design method for practical half-duplex estimate-and-forward (EF) relaying. First, we identify the regime in which EF relaying yields substantial gains - where the SNR is low and the relay-destination link is strong. Then we discover design simplifications that reduce complexity with little loss in the above regime. For relay quantizer design, we first consider mean-squared distortion minimization. To illustrate the unsuitability of the approach, we present an example with AWGN links and a BPSK source where the quantizer with worst mean squared distortion in a given set maximizes achievable rate. A distortion-minimizing quantizer attempts to preserve the received signal at the relay. The quantizer should instead preserve source information. In information theoretical terms, the quantizer should maximize the mutual information between the source transmission and the quantizer output conditioned on the side information at the destination subject to a rate constraint. The above conclusion, derived from information theoretical principles, is then translated to a quantizer design method for the low SNR regime. Using LDPC codes of blocklength 100000, BPSK modulation, and quantizers designed using the proposed criterion, we observe performance less than a decibel away from the achievable rate at a BER of 10^-4.