Algebraic Coding for Reliable Computation using Unreliable Gates

We propose to study the algebraic coding problem in computing a logical-function through an unreliable logical gate-network, where unreliable means a small probability of failure at each logical-gate. We focus on suitable encoding of the input data to a probabilistic logic network such that the noisy output can be used to decode the actual output. This is very similar to the channel coding problem, except that general logic functions are much more complicated than an additive noise-channel. We note that these problems were proposed long ago, but a systematic algebraic coding strategy, except repetition, is unknown to the author.