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Cosets of convolutional codes with least possible maximum zero- and one-run lengths

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2 Author(s)
K. J. Hole ; Dept. of Inf., Bergen Univ., Norway ; O. Ytrehus

A communication or storage system may use a coset of a binary convolutional code for both symbol synchronization and error control. To facilitate symbol synchronization, the coset must have a short maximum zero-run length Lmax. General upper and lower bounds on Lmax were given previously by Hole. In this correspondence we use these bounds to identify which convolutional codes have cosets with short Lmax. For such a code, we then show how to determine a coset with the least possible Lmax among all cosets of the code. Exact expressions for the least possible Lmax of convolutional code cosets are given, and examples of such cosets with large free distances are tabulated. Bounds on Lmax for cosets of block codes are also provided. It is indicated how to tighten the bounds for block codes satisfying the one-way chain condition. We show that the cosets obtained from traditional high-rate block code constructions have larger Lmax than cosets of convolutional codes with approximately the same rates. In some systems the convolutional code cosets must have short maximum one-run lengths as well as short maximum zero-run lengths to avoid loss of symbol synchronization. It is shown how to determine convolutional codes whose cosets with least possible maximum zero-run lengths also have least possible maximum one-run lengths

Published in:

IEEE Transactions on Information Theory  (Volume:44 ,  Issue: 1 )