Update efficient codes for error correction

An update efficient code is a mapping from messages to codewords such that small perturbations in the message induce only slight changes to the corresponding codeword. The parameter that captures this notion is called update-efficiency. In this paper we study update-efficient error-correcting codes and develop their basic properties. While update-efficiency and error-correction are two conflicting objectives, we deduce conditions for existence of such codes. In particular, logarithmically growing update-efficiency is achievable with a capacity-achieving linear code in both binary symmetric and binary erasure channels. On the other hand we show a tight converse result. Our result implies that it is not possible to have a capacity-achieving code in binary symmetric channel that has sub-logarithmic update-efficiency. This is true in the case of the binary erasure channel as well for linear codes. We also discuss a number of questions related to update-efficient adversarial error-correcting codes.