Guaranteed error correction rate for a simple concatenated coding scheme with single-trial decoding

We consider a concatenated coding scheme using a single inner code, a single outer code, and a fixed single-trial decoding strategy that maximizes the number of errors guaranteed to be corrected in a concatenated codeword. For this scheme, we investigate whether maximizing the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol, necessitates pushing the code rate to zero. We show that this is not always the case for a given inner or outer code. Furthermore, to maximize the guaranteed error correction rate over all inner and outer codes of fixed dimensions and alphabets, the code rate of one (but not both) of these two codes should be pushed to zero