Syndrome-coupled rate-compatible error-correcting codes

Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs, thus proving the existence of good rate-compatible codes. Then, we propose a general framework for constructing rate-compatible ECCs based on cosets and syndromes of a set of nested linear codes. We evaluate our construction from two points of view. From a combinatorial perspective, we show that we can construct rate-compatible codes with increasing minimum distances. From a probabilistic point of view, we prove that we are able to construct capacity-achieving rate-compatible codes.