Minimality for punctured convolutional codes

This paper investigates encoders optimization for Hamming weight after periodic puncturing, and discusses mini. mality issues that may affect the performance of the punctured encoders. Periodically puncturing a minimal encoder produces a higher rate encoder that may or may not be minimal. If it is not minimal, it may have a zero-output loop and it may be catastrophic. A code search can use a fast algorithm to determine whether an encoder's state diagram has a zero-output loop under periodic symbol puncturing, and a proposed method to assess the performance of codes with a zero-output loop that are not catastrophic. As an example, the paper optimizes rate-1/4 unpuctured codes for Hamming weight under both bit-wise and symbol-wise periodic puncturing. Code tables and simulation results are included.