Four-dimensional modulation with an eight-state trellis code

A trellis code is a “sliding window” method for encoding a binary data stream {a
ⁱ
}, a
ⁱ
= 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 = 4, and the signal points are 4-tuples of odd integers. We describe an infinite family of eight-state trellis codes. For k = 3, 4, 5, … we construct a trellis encoder with a rate of k bits/four-dimensional signal. We propose that the codes with rates k = 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.