Erasure decoding of convolutional codes using first order representations

The paper specifies a linear-systems-based low-delay erasure decoding algorithm and the concrete linear systems it solves (windowed constraints (5), state-augmented constraints (3), and terminal equations Ew), together with design properties that make these systems well-conditioned, but it does not present a formal correctness theorem. The model’s solution recasts each algorithmic step as solving a consistent linear system with a full-column-rank erased-column submatrix to guarantee uniqueness, and it explains backfilling via the reachability block Rl and termination via Ew. These arguments align with the paper’s constructions and intent, but are more explicit about rank conditions and uniqueness. Hence both are substantively consistent; the model supplies the missing proof skeleton.