Trellis complexity versus the coding gain of lattices. I

The best possible tradeoff between the coding gain and trellis complexity for lattices is studied. Three trellis complexity functions are defined for lattices as a measure of minimum trellis decoding complexity per dimension required for achieving a coding gain γ. The properties of these functions are studied from an analytic perspective. It is also shown that the trellis decoding complexity per dimension is lower-bounded by an explicit power of γ