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Achievability bounds for rate-compatible codes

This paper considers finite-blocklength achievability for rate-compatible codes. For a fixed number of messages, random coding analysis determines a sequence of achievable error probabilities for a sequence of blocklengths. However, traditional random coding achievability draws each code independently so that it does not show that a family of rate-compatible codes achieves that same sequence of error probabilities. Using random code extension, this paper shows achievable error probabilities for rate-compatible channel codes with finite blocklengths. This paper also shows that for a class of input-invariant channels, the rate-compatible constraint does not affect the achievability bounds on error rates when a threshold decoder is used.