On the unsuccessful decoding probability for a simple concatenated coding scheme with single-trial decoding

For a simple concatenated coding scheme using a single inner code and a single outer code, optimization issues for the single-trial decoding strategy are considered. Different decoding strategies can be distinguished by varying the radius of the error correction spheres of the inner decoder. Strategies maximizing the number of correctable errors and strategies minimizing the unsuccessful decoding probability are compared. For small channel error probabilities, an optimal strategy in the latter respect is also optimal in the former respect. However, for large channel error probabilities, an optimal strategy in one respect may be suboptimal in the other respect