Publications [#235788] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. 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, Institute of Electrical and Electronics Engineers (IEEE) [doi]
   (last updated on 2026/01/18)

   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.