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Trellis-canonical generator matrices for convolutional codes

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3 Author(s)
Wei Lin ; Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA ; McEliece, R.J. ; Meina Xu

It was asserted in McEliece without proof, that a canonical generator matrix G(D) is trellis-canonical if and only if G(D) has the property that the span-length of the corresponding scalar matrix “G¯” cannot be reduced by a row operation of the form Row[m]=Row[n]Ds+Row[m], where s is an integer in the range 0⩽s⩽L and m≠n. In this paper, we prove a stronger result, viz., a basic PGM is trellis-canonical if and only if it is “row-reduced”. An efficient algorithm for converting a basic PGM into a trellis-canonical PGM is presented. We also correct an error in the general algorithm given in Lin and McEliece (1995)

Published in:

Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on

Date of Conference:

29 Jun-4 Jul 1997