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An Error Exponent for the AWGN Channel with Decision Feedback and Lattice Coding

Abstract:

We present achievable error exponents for the AWGN channel with one bit noiseless feedback and an almost-sure power constraint. As in Forney's decision feedback approach for discrete memoryless channels, the backward channel is used to request retransmissions from the transmitter whenever an erasure is declared at the decoder. Our erasure/re-transmission-request scheme introduces a novel erasure decoding rule built on top of a lattice-based code inspired by De Buda. Numerically, our scheme is seen to outperform the sphere packing bound (valid for block codes) at lower rates and higher SNRs.