TRELLIS COMPLEXITY VERSUS THE CODING GAIN OF LATTICES .2.

For an arbitrary rational lattice L with gain gamma, the average numbe r of states (respectively, branches) in any given trellis diagram of L is bounded below by a function of gamma, It is proved that this funct ion grows exponentially in gamma, In the reverse direction, it is prov ed that given epsilon > 0, for arbitrarily large values of gamma, ther e exist lattices of gain gamma with an average number of branches and states less than exp (gamma((1+epsilon))).