On the error probability of general trellis codes with applications to sequential decoding (Corresp.)

An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random
L
-branch binary trellis codes of rate
R = 1/n
is given which separates the effects of the tail length
T
and the memory length
M
of the code. It is shown that the bound is independent of the length
L
of the information Sequence when
M \geq T + [nE_{VU}(R)]^{-1} \log_{2} L
. The implication that the actual error probability behaves similarly is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication which can thus be taken as a design rule for choosing
M
so that the error probability is reduced to its minimum value for a given
T
.