Concatenated Coding Using Linear Schemes for Gaussian Broadcast Channels With Noisy Channel Output Feedback

Linear coding schemes have been the main choice of coding for the additive white Gaussian noise broadcast channel (AWGN-BC) with noiseless feedback in the literature. The achievable rate regions of these schemes go well beyond the capacity region of the AWGN-BC without feedback. In this paper, a concatenated coding design for the K-user AWGN-BC with noisy feedback is proposed that relies on linear schemes as inner codes to achieve rate tuples outside the no-feedback capacity region. The boundary of an achievable rate region of purely linear coding schemes for noiseless feedback is shown to be arbitrarily closely approached by the concatenated coding scheme for sufficiently small feedback noise levels. Then, a linear coding scheme for the K-user symmetric AWGN-BC with noisy feedback is presented and optimized for use in the concatenated coding scheme. For noiseless feedback, the presented linear coding scheme achieves the optimal sum-rate of linear-feedback coding. An upper bound on the inner code blocklength needed to achieve a sum-rate above no-feedback sum-capacity is derived.