Composite scheme LR+Th for decoding with erasures and its effective equivalence to Forney´s rule

For decoding with erasures, Forney´s scheme is known to be optimal in the sense that no other scheme can make the erasure probability P_ers and undetected error probability P_uer simultaneously smaller. We propose a scheme for erasure decision which tests the likelihood ratio as well as the likelihood itself and show that the attainable upper bounds on P_ers and P_uer are the same as those proved for the optimal scheme up to a constant factor. We also show that the scheme gives, when applied to convolutional codes, a bound which is related to the block-coding bound via Forney´s inverse concatenation construction. We show that this bound is the same as the one which naturally arises when we apply Raghavan and Baum´s (1998) optimal scheme to convolutional code