Efficient Search Algorithm for Determining Optimal R=1/2 Systematic Convolutional Self-Doubly Orthogonal Codes

A novel implicitly-exhaustive search algorithm for finding, in systematic form, rate R=frac{1}{2} optimal-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified Convolutional Self-Doubly Orthogonal (S-CDO) codes is presented. In order to build high-performance low-latency codecs with these codes, it is important to minimize their constraint length (or "span") for a given J number of generator connections. The proposed algorithm is exhaustive in nature and its improvements over the best previously published searching techniques allowed it to yield new optimal-span CDO/S-CDO codes (having order J ∈ {6,7,8} and J ∈ {9} respectively), as well as a span reduction for codes with a higher J value (J ∈ {10,11} and J ∈ {14,15} for CDO and S-CDO respectively).