A class of capacity-achieving, low-complexity, high-reliability, variable-r
ate coding schemes is developed for communication over discrete memoryless
channels with noiseless feedback, Algorithms for encoding and decoding that
require computations growing linearly with the number of channel inputs us
ed are developed. The error exponent associated with the scheme is shown to
be optimal and implies that capacity is achievable. Simulations are perfor
med and support the analytically predicted high performance and low complex
ity.