An efficient scheme for reliable error correction with limited feedback

This paper proposes a practical scheme to transmit reliable information through a noisy symmetric DMC using limited noiseless feedback. The ratio of feedback rate to feedforward rate is a design parameter that can be selected from zero to 1 - C, where C is the capacity of the channel. The proposed scheme uses a concatenation of low-density parity-check codes, belief propagation, and a noisy version of the closed-loop iterative doping algorithm, previously proposed by the authors for data compression using linear codes. Our scheme takes advantage of the availability of a modicum of feedback to achieve very small block error rates