On the error correcting capability of convolutional codes: Old and new

A brief introduction to convolutional coding is given. The active distances are reviewed and shown to be an important tool for analyzing the error correcting capability of maximum-likelihood (ML) decoding of convolutional codes when communicating over a binary symmetric channel (BSC). Due to memory and delay constraints in practical coding schemes, convolutional codes often are either terminated or decoded by a window decoder. When a window decoder is used, the convolutional code sequence is not terminated; instead, the window decoder estimates the information digits after receiving a finite number of noise corrupted code symbols, thereby keeping the decoding delay short. A characterization of the error correcting capability of window decoded convolutional codes is given by using the active distances.