Convolutional Codes for the Unequal Message Protection Problem

Abstract

In the context of unequal message protection (UMP), this report investigates blind codebook detection for short-packet transmissions. Within the Neyman-Pearson (NP) framework, we considered the optimal likelihood ratio test (LRT) and its generalized variant, the generalized likelihood ratio test (GLRT), both implemented via exact trellis-based computations. Our analysis revealed a floor effect in the false alarm and missed detection probabilities, directly tied to intersections between codebooks: when overlap exists, both error rates saturate at non-zero values for a range of specific thresholds. At moderateto-high signal-to-noise ratio (SNR), however, LRT and GLRT exhibit near-equivalence, producing identical decisions up to a deterministic offset for the studied convolutional code construction. These findings highlight both the limits imposed by codebook geometry and the practical relevance of the lower-complexity GLRT approach.