Erasure recovery matrices for encoder protection

Abstract

Abstract In this article, we investigate the privacy issues that arise from a new frame-based kernel analysis approach to reconstruct from frame coefficient erasures. We show that while an erasure recovery matrix is needed in addition to a decoding frame for a receiver to recover the erasures, the erasure recovery matrix can be designed in such a way that it protects the encoding frame. The set of such erasure recovery matrices is shown to be an open and dense subset of a certain matrix space. We present algorithms to construct concrete examples of encoding frame and erasure recovery matrix pairs for which the erasure reconstruction process is robust to additive channel noise. Using the Restricted Isometry Property, we also provide quantitative bounds on the amplification of sparse additive channel noise. Numerical experiments are presented on the amplification of additive normally distributed random channel noise. In both cases, the amplification factors are demonstrated to be quite small.