Feedback and Belief Propagation

We demonstrate that feedback in discrete memoryless channels has the capability of greatly lowering the block error rate of codes designed for open-loop operation. First we show how to use full feedback of the channel output to turn any capacity achieving code into a reliability-function achieving code. Second, we propose a practical embodiment based on sparse-graph codes, belief propagation, and a variation of the closed-loop iterative doping algorithm. This scheme takes advantage of any available limited-rate feedback to bootstrap good block error rate from good bit error rate.