UPPER BOUNDS ON THE MINIMUM DISTANCE OF TRELLIS CODES.
A trellis code is a 'sliding window' method of encoding a binary data stream into a sequence of real numbers that are input to a noisy transmission channel. When a trellis code is used to encode data at the rate of k bits/channel symbol, each channel input will depend not only on the most recent block of k data bits to enter the encoder but will also depend on, say, the nu bits preceding this block. The performance of trellis codes, like that of block codes, depends on a suitably defined minimum-distance property of the code. This paper obtains upper bounds on this minimum distance that are simple functions of k and nu . These results also provide a lower bound on the number of states required to achieve a specific coding gain.
Calderbank, AR; Mazo, JE; Shapiro, HM
The Bell System Technical Journal
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