On the Behavior of the Distance Spectrum of Convolutional Codes under a Minimal Trellis Complexity Measure

In this paper, we investigate the behavior of the distance spectrum of convolutional codes when the decoding complexity is measured by the total number of edge symbols per information bit in the minimal trellis module representing the code. We conduct a code search restricted to the recently introduced class of generalized punctured convolutional codes, which is broad enough to contain good codes and yet has structural properties that facilitate the code search. New good convolutional codes are tabulated. For the same decoding complexity and the same code rate, the new codes have slightly better distance spectrum than the best known punctured convolutional codes. When compared to the best known unit-memory convolutional codes of the same rate, the new codes typically have improved free distance for a given decoding complexity, or about the same distance spectrum is achieved with much lower decoding complexity. Under this decoding complexity measure, the behaviour that higher decoding complexity implies better distance spectrum remains valid.