Error Exponent for Gaussian Channels with Partial Sequential Feedback

We consider an additive white Gaussian noise (AWGN) channel with partial sequential feedback. Namely, for every fixed-length block of forward transmissions a fraction of the received symbols are fed back sequentially to the transmitter through a noiseless feedback link. It is well known that complete noiseless feedback can provide a dramatic improvement in reliability (i.e., double-exponential error rate with block length). We show that partial feedback can also provide a substantial improvement in error rate. Specifically, we propose a capacity- achieving coding scheme with partial feedback, in which the feedback is used to induce a prior distribution for the decoding of random forward error control (FEC) codewords. The error- exponent for this scheme is larger than the error-exponent with FEC coding only at all rates. For rates greater than those achieved by transmissions with feedback alone, we give an upper bound on the error exponent. Exponents close to this bound can be achieved with both the proposed scheme and a simple rate- splitting scheme. With finite block lengths, the proposed coding scheme achieves lower error rates than rate-splitting.