Shape nature of error-control codes

Abstract

In this paper we demonstrate that the perception of a shape property within error-control codes provides an alternative insight to their error-control capability. This insight may lead to the development of a new class of error-control codes based on shapes. To demonstrate the concept of shape, we illustrate the shape nature of convolutional codes within the Viterbi, maximum a posteriori, and Turbo decoding algorithms. We also introduce the concept of shape codes, in which binary information digits are mapped onto predefined imaginary shapes within a given signal constellation, and make use of these predefined shapes to provide a coding gain at very low signal-to-noise ratios, with a penalty of a reduction in the information throughput.