Optimum slope convolutional codes

A new family of binary convolutional codes is introduced: the maximum slope (MS) code family. MS codes are defined such, that there exist no other rate R=b/c binary convolutional code with the same free distance d_f and overall constraint length v, whose lower bounds on the active distance family exhibit a larger slope. Tables for the rate R=1/2 maximum slope code family with memory m=1, 2,…,5 are given. Furthermore, tables for new rate R=(c-1)/c, c=2, 3,…, 5, punctured convolutional codes with optimum free distance codes and MS mother codes are given. Simulation results for woven convolutional codes with MS component codes are presented. It is shown, that the component code choice makes a tradeoff between d_f and α