Calderbank, AR; Sloane, NJA, *Four-Dimensional Modulation With an Eight-State Trellis Code*,
At&T Technical Journal, vol. 64 no. 5
(1985),
pp. 1005-1018, Institute of Electrical and Electronics Engineers (IEEE) [doi] .
**Abstract:**

*A trellis code is a 'sliding window' method for encoding a binary data stream left brace a**i right brace , a**i equals 0, 1, as a sequence of signal points drawn from R**n. The rule for assigning signal points depends on the state of the encoder. In this paper n equals 4, and the signal points are 4-tuples of odd integers. The authors describe an infinite family of eight-state trellis codes. For k equals 3, 4, 5, . . . they construct a trellis encoder with a rate of k bits/four-dimensional signal. They propose that the codes with rates k equals 8 and 12 be considered for use in modems designed to achieve data rates of 9. 6 kb/s and 14. 4 kb/s, respectively.*