MMSE Scaling Enhances Performance in Practical Lattice Codes

We investigate the value of MMSE scaling for practical lattice codes. For ideal lattices, MMSE scaling has been shown to be a key ingredient in achieving the capacity of the AWGN channel. We demonstrate that MMSE scaling enhances the performance, particularly at low SNR, for practical lattice codes. For example, a dimension n = 10000 LDLC lattice exhibits approximately 0.6 dB gain when MMSE scaling is used for a rate of 1 bit/dimension. Furthermore, we provide a novel derivation of the MMSE scaling rule, showing that it emerges naturally from principles of belief propagation decoders which account for the transmit power constraint.