On classes of convolutional codes that are not asymptotically catastrophic

The author denotes by w₀ the minimum average weight per edge over all nonzero cycles in the state diagram for a convolutional code, and assumes that a technique is available for generating canonical parity-check matrices for codes with increasing degree m. The obtained class of codes is asymptotically catastrophic if w₀ approaches zero for large m. We prove the existence of convolutional code classes that are not asymptotically catastrophic by providing explicit constructions of codes with nonzero w₀ for all m