Calderbank, AR; Mazo, JE; Wei, VK, *ASYMPTOTIC UPPER BOUNDS ON THE MINIMUM DISTANCE OF TRELLIS CODES.*,
IEEE Transactions on Communications, vol. COM-33 no. 4
(1985),
pp. 305-309 .
**Abstract:**

*A trellis code is a 'sliding window' method of encoding a binary data stream as a sequence of signal points. When a trellis code is used to encode data at the rate of k bits/channel symbol, each channel input depends not only on the most recent block of k bits to enter the encoder, but will also depend on a set of upsilon bits preceding this block. The upsilon bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state. The performance of a trellis code depends on a suitably defined minimum distance property of that code. This paper obtained upper bounds on this minimum distance that are better than any previously known.*