Abstract
The sensitivity of a binary block code to loss of synchronism (misplacement of the "commas" separating codewords) can be characterized by a pair of numbers <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[s, \delta]</tex> such that any synchronization slip of s bits or less produces an overlap sequence differing from a legitimate codeword in at least <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta</tex> places. This definition is broader than that of comma freedom of index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta</tex> , which is included as the special case of s equal to the integer part of half the code block length. For codes having the slip-detecting characteristic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[s, \delta]</tex> there exists the possibility of implementation to restore synchronism during an interval relatively free from bit errors. It is shown that certain error-correcting binary cyclic block codes can be altered to obtain the characteristic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[s, \delta]</tex> by the addition of a fixed binary vector to each codeword prior to transmission. These altered cyclic codes retain the full error-correcting power of the original cyclic codes. An error-detecting/correcting data format providing protection against the acceptance of misframed data is thus obtained without the insertion of special synchronizing sequences into the bit stream.
Published Version
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