Calderbank, AR; Mazo, JE; Shapiro, HM, *UPPER BOUNDS ON THE MINIMUM DISTANCE OF TRELLIS CODES.*,
The Bell System technical journal, vol. 62 no. 8 pt 1
(1983),
pp. 2617-2646 [doi] .
**Abstract:**

*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.*