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Reflecting on the AWGN error exponent
 IEEE Transactions on Information Theory
"... Recently it was shown that a lattice code with lattice decoding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This was achieved by using a minimum meansquare error (MMSE) scaling and dithering to transform the AWGN channel into a modulolattice additive noise (modΛ) ..."
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Recently it was shown that a lattice code with lattice decoding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This was achieved by using a minimum meansquare error (MMSE) scaling and dithering to transform the AWGN channel into a modulolattice additive noise (modΛ) channel. Further, Liu et. al. have shown that lattice decoding can achieve the error exponent of the AWGN channel using a scaling other than the MMSE scaling at rates above the critical rate of the channel. We present a simple geometric explanation for this result. 1
log(1 + SNR) on the AWGN Channel With Lattice Encoding and Decoding
"... Abstract—We address an open question, regarding whether a lattice code with lattice decoding (as opposed to maximumlikelihood (ML) decoding) can achieve the additive white Gaussian noise (AWGN) channel capacity. We first demonstrate how minimum meansquare error (MMSE) scaling along with ditherin ..."
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Abstract—We address an open question, regarding whether a lattice code with lattice decoding (as opposed to maximumlikelihood (ML) decoding) can achieve the additive white Gaussian noise (AWGN) channel capacity. We first demonstrate how minimum meansquare error (MMSE) scaling along with dithering (lattice randomization) techniques can transform the powerconstrained AWGN channel into a modulolattice additive noise channel, whose effective noise is reduced by a factor of 1+SNR SNR For the resulting channel, a uniform input maximizes mutual information, which in the limit of large lattice dimension becomes 1 2 log(1 + SNR), i.e., the full capacity of the original power constrained AWGN channel. We then show that capacity may also be achieved using nested lattice codes, the coarse lattice serving for shaping via the modulolattice transformation, the fine lattice for channel coding. We show that such pairs exist for any desired nesting ratio, i.e., for any signaltonoise ratio (SNR). Furthermore, for the modulolattice additive noise channel lattice decoding is optimal. Finally, we show that the error exponent of the proposed scheme is lower bounded by the Poltyrev exponent. Index Terms—Additive white Gaussian noise (AWGN) channel, dirty paper channel, dither, Euclidean distance, lattice decoding, minimum meansquare error (MMSE) estimation, nested codes, Poltyrev exponent, random lattice ensemble, shaping. I.