Truncation Depth Rule-of-Thumb for Convolutional Codes

Abstract

In this innovation, it is shown that a commonly used rule of thumb (that the truncation depth of a convolutional code should be five times the memory length, m, of the code) is accurate only for rate 1/2 codes. In fact, the truncation depth should be 2.5 m/(1 - r), where r is the code rate. The accuracy of this new rule is demonstrated by tabulating the distance properties of a large set of known codes. This new rule was derived by bounding the losses due to truncation as a function of the code rate. With regard to particular codes, a good indicator of the required truncation depth is the path length at which all paths that diverge from a particular path have accumulated the minimum distance of the code. It is shown that the new rule of thumb provides an accurate prediction of this depth for codes of varying rates.