Search and determination of convolutional self-doubly orthogonal codes for iterative threshold decoding

In this paper, we present new results on the search and determination of wide-sense convolutional self-doubly orthogonal codes (CSO²C-WS) which can be decoded using a simple iterative threshold decoding algorithm without interleaving. For their iterative decoding, in order to ensure the independence of observables over the first two iterations without the presence of interleavers, these CSO²C must satisfy specific orthogonal properties of their generator connections. The error performances of CSO²C, depend essentially on the number of taps J of the code generators but not on the code memory length. Since the overall latency of the iterative threshold decoding process is proportional to the memory length of the codes, therefore, when searching for the best CSO²C-WS of a given J value, the memory length of the codes should be chosen to be as small as possible. In this paper, we present a code-searching technique based on heuristic computer searching algorithms which have yielded the best known CSO²C-WS. The construction method for CSO²C-WS has provided the best known r=1/2 codes with the shortest memory length having J≤30. Although not very complex to implement, the search method presented here is quite efficient especially in reducing very substantially the execution time required to determine the codes with the shortest spans. Furthermore, in addition to presenting the search results for the codes, error performances obtained by simulation are also provided.