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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 &gt; 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.

Achieving the AWGN channel capacity with lattice Gaussian coding