New unit-memory codes obtained by puncturing periodically time-varying convolutional codes

Abstract

New good high-rate punctured convolutional codes (PCC) are presented. While any previously known PCC was derived by puncturing a low-rate time-invariant mother code, the new PCC are shown to be derived by puncturing a periodically time-varying convolutional code (PTVCC) acting as the mother code. To find the new PCC, we first show that any PTVCC (hence, any PCC) is equivalent to a type of time-invariant convolutional code. Focusing on a fixed unit-memory (UM) code, we also show that under certain conditions there exists a PTVCC along with a puncturing pattern that is equivalent to that UM code. A combinatorial optimization algorithm is then used to search for the new good UM codes for which equivalent PCC do exist. We observe that the new PCC compare favorably to the previously known PCC in several respects.