A Simplified Approach to Achieving the Capacity of the AWGN Channel With Erasures Using Nested Lattice Codes
Saifur Rahman, Chen Feng, Anas Chaaban · IEEE Communications Letters · 2021
We consider an additive white Gaussian noise (AWGN) channel with erasures. This channel behaves as an AWGN channel with probability$1-\alpha $, and produces an erased output with probability$\alpha $. The capacity of this channel is$1-\alpha $times the capacity of the underlying AWGN channel without erasures. It is shown in the literature that the capacity of the underlying AWGN channel without erasures is achievable using nested lattice code with Construction A. Here, we extend the proof to show that the same code achieves the capacity of the channel with erasures, with a simplified decoder that drops erasures. Our approach provides a simpler decoder and a simpler proof than related works in the literature.