Rate l/(l+1) convolutional encoders over rings with maximal free branch distance

When we consider convolutional coded CPFSK over fading channels, the primary design criterion (for high SNR) is to maximize the effective code length (ECL), where ECL is the minimal possible Hamming distance between any two distinct symbol sequences. We define the free branch distance (d/sub free/) as the minimal possible branch distance between any two (unlabeled) parallel paths in the code trellis. We show that d/sub free/ achieving the maximum value is a necessary condition for maximizing ECL.