A framework for coded computation

Error-correcting codes have been very successful in protecting against errors in data transmission. Computing on encoded data, however, has proved more difficult. In this paper we extend a framework introduced by Spielman [14] for computing on encoded data. This new formulation offers significantly more design flexibility, reduced overhead, and simplicity. It allows for a larger variety of codes to be used in computation and makes explicit conditions on codes that are compatible with computation. We also provide a lower bound on the overhead required for a single step of coded computation.