Non-commutative convolutional codes over the infinite dihedral group
by Marion Candau; Roland Gautier; Johannes Huisman
International Journal of Information and Coding Theory (IJICOT), Vol. 3, No. 1, 2015

Abstract: Classic convolutional codes are defined as the convolution of a message and a transfer function over ℤ. In this paper, we study convolutional codes over the infinite dihedral group D_∞. The goal of this study is to design convolutional codes with good and interesting properties and intended to be more resistant to code recognition. Convolution of two functions on D_∞ corresponds to the product of two polynomials in the non-commutative polynomial algebra 𝔽₂{X,Y}/{X² − 1, Y² − 1}. We show how encoding over D_∞ can be represented by two classical convolutions over ℤ. Furthermore, we adapt the Viterbi algorithm to decode these codes using two different trellises. Finally, we show that these codes have performances similar to classic convolutional codes, but are not more resistant to code recognition. However, we get more optimal codes in terms of free distance than conventional.

Online publication date: Thu, 09-Apr-2015

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