Coding for Additive White Noise Channels With Feedback Corrupted by Quantization or Bounded Noise

We present coding strategies, which are variants of the Schalkwijk-Kailath scheme, for communicating reliably over additive white noise channels in the presence of corrupted feedback. Our framework comprises an additive white forward channel and a feedback link. We consider two types of corruption mechanisms in the feedback link. The first is quantization noise, i.e., the encoder receives the quantized values of the past outputs of the forward channel. The quantization is uniform, memoryless and time invariant. The second corruption mechanism is an arbitrarily distributed additive bounded noise. Here we allow symbol-by-symbol encoding at the input to the feedback link. We propose explicit schemes featuring positive information rate and positive error exponent. If the forward channel is additive white Gaussian (AWGN) then, as the amplitude of the noise at the feedback link decreases to zero, the rate of our schemes converges to the capacity of the channel. Moreover, the probability of error is shown to converge to zero at a doubly exponential rate. If the forward channel is AWGN and the feedback link consists of an additive bounded noise channel, with signal-to-noise ratio (SNR) constrained symbol-by-symbol encoding, then our schemes achieve rates arbitrarily close to capacity, in the limit of high SNR (at the feedback link).