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

Abstract

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/sub ers/ and undetected error probability P/sub 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/sub ers/ and P/sub 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.