Iterative Decoding of Binary
Block and Convolutional Codes
and Lutz Papke
codes has been termed
we show that any decoder can he used
which accepts soft inputs-including
a priori values-and
soft outputs that can he split into three terms: the soft channel and
a priori inputs, and the extrinsic value. The extrinsic value is used
as an a priori value for the next iteration.
are given not only for convolutional
by a stop criterion
which results in a minimal
decoders with reduced complexity
results show that very simple component
codes are sufficient,
block codes are appropriate
for high rates
rates less than
213 . Any
possible. Several interleaving
techniques are described. At a bit
around the bounds given by the cutoff rate for reasonably simple
sizes less than
1000 and for three to six iterations.
INCE the early days of information and coding theory the
goal has always been to come close to the Shannon limit
performance with a tolerable complexity. The results achieved
so far show that it is relatively
easy to operate at signal-
to-noise ratios of &/No
above the value determined by the
channel cutoff rate. For a rate l/2
code and soft decisions on
a binary input additive white Gaussian noise (AWGN) channel
the cutoff rate bound is at 2.5 dB, as opposed to the capacity
limit which for rate l/2
is at 0.2 dB. It is generally held that
between those two values of &/No
the task becomes very
complex. Previously known methods of breaking this barrier
were a) sequential decoding with the drawback of time and/or
storage overflow and b) concatenated coding using Viterbi and
decoders which achieve 1.6 dB at the cost of
a large interleaver and feedback between two decoders [ 11.
Recently, interest has focused on iterative decoding of prod-
uct or concatenated codes using
Manuscript received September 7, 1994; revised August 20, 1995.
J. Hagenauer is with the Technical University of Munich, D-80290 Munich,
E. Offer and L. Papke are with the Institute for Communications Technol-
ogy, German Aerospace Research Establishment (DLR), Oberpfaffenhofen,
D-82230 Wessling, P.O. Box 1116, Germany.
Publisher Item Identifier S 0018-9448(96)01474-5.
with fairly simple component codes in an interleaved scheme.