Decoding method for trellis codes with large free distances

DETAILED DESCRIPTION This invention is a decoding method for the trellis code T of which the encoding can be implemented by first using the encoder of a binary convolutional code C.
sup.
(1) to map a message u(t) into v.
sup.
(1) (t) that is sequentially converted into v.
sup.
(2) (t), v.
sup.
(3) (t), .
.
.
, and v.
sup.
(L+1) (t) through L processors R.
sup.
(1), R.
sup.
(2), .
.
.
, and R.
sup.
(L) as illustrated in FIG.
3, where v.
sup.
(l) (t) is a binary m-tuple, 1.
ltoreq.
l.
ltoreq.
L and v.
sup.
(L+1) (t) is the encoded output.
Referring to FIG.
4, the decoding method consists of using L+1 processors P.
sup.
(L), P.
sup.
(L-1), .
.
.
, P.
sup.
(1), P.
sup.
(0).
Let .
LAMBDA.
.
sup.
(l) be a nonnegative constant, where 1.
ltoreq.
l.
ltoreq.
L.
Let the received symbol which is the noise-corrupted form of the symbol v.
sup.
(L+1) (t) be denoted by y(t).
The processor P.
sup.
(L) takes the received sequence { .
.
.
,y(t-1),y(t),y(t+1), .
.
.
} as input.
Based on v.
sup.
(L) (t-j), j.
gtoreq.
.
lambda.
, where .
lambda.
is the truncation length used in decoding the binary convolutional code C.
sup.
(1), which have been recovered in earlier decoding and {y(t+j): j.
ltoreq.
.
LAMBDA.
.
sup.
(1) + .
.
.
+.
LAMBDA.
.
sup.
(L) }, the processor P.
sup.
(L) determines the metric M.
sub.
v.
spsb.
(L).
sub.
(t+.
LAMBDA.
.
spsb.
(1).
sub.
+ .
.
.
+.
LAMBDA.
.
spsb.
(L-1).
sub.
) for each of the 2.
sup.
m possible values of v.
sup.
(L) (t+.
LAMBDA.
.
sup.
(1) + .
.
.
+.
LAMBDA.
.
sup.
(L-1)).
Then the set T.
sub.
M.
sup.
(L) (t+.
LAMBDA.
.
sup.
(1) + .
.
.
+.
LAMBDA.
.
sup.
(L-1))={M.
sub.
v.
spsb.
(L).
sub.
(t+.
LAMBDA.
.
spsb.
(1).
sub.
+ .
.
.
+.
LAMBDA.
.
spsb.
(L-1).
sub.
) : v.
sup.
(L) (t+.
LAMBDA.
.
sup.
(1) + .
.
.
+.
LAMBDA.
.
sup.
(L-1)) .
epsilon.
{0,1}.
sup.
m } is fed into the processor P.
sup.
(L-1).
For l=L-1,L-2, .
.
.
,1, the processor P.
sup.
(l) takes the metric sequence { .
.
.
, T.
sub.
M.
sup.
(l+1) (t-1), T.
sub.
M.
sup.
(l+1) (t), .
.
.
} as input.
Based on v.
sup.
(l) (t-j), j.
gtoreq.
.
lambda.
which have been recovered in earlier decoding and {T.
sub.
M.
sup.
(l+1) (t+j): j.
ltoreq.
.
LAMBDA.
.
sup.
(1) + .
.
.
+.
LAMBDA.
.
sup.
(l) }, the processor P