Orthogonal Tree Codes for Communication in the Presence of White Gaussian Noise

This paper describes a convolutional encoder for generating tree codes whose distinct codewords are orthogonal over the constraint length of the code. The performance of this class of codes is analyzed and the error probability is shown to decrease exponentially with the energy-to-noise ratio over the constraint length period of the code. The performance is compared with wellknown results for orthogonal block codes and shown to be considerably superior to the latter. Asymptotic results are also obtained which coincide with results for the class of very noisy memoryless channels.