Design of Convolutional Codes for Unequal Message Protection in the Short-Blocklength Regime

Kurzfassung

This thesis investigates the design of tail-biting convolutional codes (TBCCs) for the unequal message protection (UMP) problem in the short-blocklength regime, where two message classes subject to different reliability targets must be discriminated blindly at the receiver from the internal structure of their codebooks alone, without an explicit preamble. To this end, we propose a two-stage design methodology. First, a nested pair of convolutional codes is generated, either by expanding a low-rate parent encoder with an additional input line (nesting approach) or by repeating and concatenating the output of a high-rate parent encoder across two timesteps (repetition approach). Second, a binary offset vector is optimized via a random-restart greedy local search to maximize the Hamming distance separating the two closest codewords from the resulting disjoint codebooks. Numerical results show that the proposed TBCC constructions consistently outperform equal-memory zero-tail-terminated convolutional codes, that the achievable end-to-end performance depends more strongly on codebook disjointness than on the specific choice of offset, and that, at sufficiently large encoder memory, the repetition-based construction matches or exceeds the performance of CRC-aided polar codes.