Abstract

We introduce general sphere packing bounds for convolutional codes. These improve upon the Heller bound [J.L.Heller (1968)] for high rate convolutional codes. For example, based on the Heller bound, McEliece [2, p. 1114] suggested that for a rate (n-1)/n code of free distance 5 with /spl nu/ memory elements in its minimum encoder, asymptotically as /spl nu/ /spl rarr/ /spl infin/ it holds that n /spl les/ 2/sup (/spl nu/+1)/2/. a simple corollary of our bounds shows that in this case, n /spl lsim/2/sup /spl nu//2/, an improvement by a factor of /spl radic/2. The bound can be further strengthened.

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