In this study, we consider techniques for searching high-rate convolutional code (CC) encoders using dual code encoders. A low-rate (R = 1/n) CC is a dual code to a high-rate (R = (n - 1)/n) CC. According to our past studies, if a CC encoder has a high performance, a dual code encoder to the CC also tends to have a good performance. However, it is not guaranteed to have the highest performance. We consider a method to obtain a high-rate CC encoder with a high performance using good dual code encoders, namely, high-performance low-rate CC encoders. We also present some CC encoders obtained by searches using our method.

In this study, we consider techniques to search for high-rate punctured convolutional code (PCC) encoders by rearranging row vectors of identical-encoder generator matrices. One well-known method to obtain a good PCC encoder is to perform an exhaustive search of all candidates. However, this approach is time-intensive. An exhaustive search with a rate RG=1/2 original encoder requires a relatively short time, whereas that with an RG=1/3 or lower original encoder takes significantly longer. The encoders with lower-rate original encoders are expected to create better PCC encoders. Thus, this paper proposes a method that uses exhaustive search results with rate RG=1/2 original encoders, and rearranges row vectors of identical-encoder generator matrices to create PCCs with a lower rate original code. Further, we provide PCC encoders obtained by searches that utilize our method.

In this study, we consider techniques to search for high-rate punctured convolutional code (PCC) encoders using dual code encoders. A low-rate R=1/n convolutional code (CC) has a dual code that is identical to a PCC with rate R=(n-1)/n. This implies that a rate R=1/n convolutional code encoder can assist in searches for high-rate PCC encoders. On the other hand, we can derive a rate R=1/n CC encoder from good PCC encoders with rate R=(n-1)/n using dual code encoders. This paper proposes a method to obtain improved high-rate PCC encoders, using exhaustive search results of PCC encoders with rate R=1/3 original encoders, and dual code encoders. We also show some PCC encoders obtained by searches that utilized our method.

This paper considers a method for constructing good high-rate punctured convolutional codes through dual codes. A low-rate R=1/n convolutional code has a dual code identical to a punctured convolutional code with rate R=(n-1)/n. This implies that a low-rate R=1/n convolutional code encoder can help the search of punctured convolutional code encoders. This paper provides the procedures that obtain all the useful dual code encoders to a given CC with rate R=1/n easily, and the best PCC encoder with rate R=(n-1)/n among the encoders we derive from all the obtained dual code encoders. This paper also shows an example of the PCC the procedures obtain from some CC.

In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

We consider two methods for constructing high rate punctured convolutional codes. First, we present the best high rate R=(n-1)/n punctured convolutional codes, for n=5,6,…,16, which are obtained by exhaustive searches. To obtain the best code, we use a regular convolutional code whose weight spectrum is equivalent to that of each punctured convolutional code. We search these equivalent codes for the best one. Next, we present a method that searches for good punctured convolutional codes by partial searches. This method searches the codes that are derived from rate 1/2 original codes obtained in the first method. By this method, we obtain some good punctured convolutional codes relatively faster than the case in which we search for the best codes.

An improved bidirectional search algorithm for computing the weight spectrum of convolutional codes is presented. This algorithm does not employ the column distance function of a code which plays an important role in the original bidirectional search algorithm. We show the proposed algorithm can reduce computaion time for obtaining the weigth spectrum of convolutional codes significantly compared with that of the bidirectional search algorithm.