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