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Computation of the right-inverse of G(D) and the left-inverse of Ht(D)

Computation of the right-inverse of G(D) and the left-inverse of Ht(D)

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Useful column and row operations are given for the computation of the right-inverse G−(D) of an k × n generator matrix G(D) and the left-inverse [H(D)]−1 of the transpose of an (n — k) × n parity-check matrix H(D). The methods are illustrated with two examples.

Inspec keywords: encoding; codes; matrix algebra

Other keywords: binary coded digital communication; row operations; left inverse computation; column operations; encoder; parity-check matrix; right inverse computation; error-protection; coding; convolutional codes

Subjects: Codes; Algebra

References

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      • G.D. Forney . Convolutional codes I: Algebraic structure. IEEE Trans. , 720 - 738
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      • S. Lin , D.J. Costello , Jun . (1983) , Error control coding: Fundamentals and applications.
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      • I.S. Reed , T.K. Truong . New syndrome decoding techniques for the (n, k) convolutional codes. IEE Proc. F , 4 , 412 - 416
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      • Lee, L.H.C.: `Convolutional code design and performance', July 1987, Ph.D. Thesis, Victoria University of Manchester, UK.
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      • F.R. Gantmacher . (1960) , Matrix theory.
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Erratum: Computation of the right-inverse of G(D) and the left-inverse of Ht(D)
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