Achieving the AWGN channel capacity with lattice Gaussian coding

We propose a new coding scheme using only one lattice that, under lattice decoding, achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel, when the signal-to-noise ratio SNR > 3. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which additionally involves a quantization-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error (MMSE) lattice decoding is almost the same as that of Poltyrev´s coding over an infinite lattice, for any rate up to the AWGN channel capacity.