Further results on binary convolutional codes with an optimum distance profile (Corresp.)

Fixed binary convolutional codes are considered which are simultaneously optimal or near-optimal according to three criteria: namely, distance profile <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> , free distance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d∞</tex> , and minimum number of weight <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d∞</tex> paths. It is shown how the optimum distance profile criterion can be used to limit the search for codes with a large value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d∞</tex> . We present extensive lists of such robustly optimal codes containing rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = l/2</tex> nonsystematic codes, several with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d∞</tex> superior to that of any previously known code of the same rate and memory; rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = 2/3</tex> systematic codes; and rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = 2/3</tex> nonsystematic codes. As a counterpart to quick-look-in (QLI) codes which are not "transparent," we introduce rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R = 1/2</tex> easy-look-in-transparent (ELIT) codes with a feedforward inverse <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1 + D,D)</tex> . In general, ELIT codes have <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d∞</tex> superior to that of QLI codes.