A Connection Between Block and Convolutional Codes

Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed–Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) OR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding we now have a new maximum likelihood decoding algorithm for many block codes. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.