Performance optimisation for bit-interleaved
coded modulation with iterative demapping
with max-log- maximum a posterior detection
ISSN 1751-8628
Received on 11th October 2014
Revised on 13th April 2015
Accepted on 25th May 2015
doi: 10.1049/iet-com.2014.0971
www.ietdl.org
Chen Qian
1
✉
, Qiuliang Xie
2
, Peiyao Zhao
1
, Zhaocheng Wang
1
1
Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Electronic Engineering, Tsinghua
University, Beijing 100084, People’s Republic of China
2
Chinese National Engineering Laboratory for Digital TV at Beijing (DTVNEL), Beijing 100191, People’s Republic of China
✉ E-mail: qc8802@gmail.com
Abstract: Max-log-maximum a posterior (MAP) detection is preferred in practical systems rather than log-MAP because of
its lower complexity, but also suffers from a considerable performance loss. In this study, the authors focus on the
performance optimisation for (doped) bit-interleaved coded modulation with iterative demapping schemes where max-
log-MAP detection is employed. First, they study the effects of max-log-MAP detection to the extrinsic information
transfer curves of the (doped) demapper and decoder, and reselect the constellation labelling. Second, they find that
the small difference between max-log-MAP and log-MAP detection in each iteration would be accumulated during the
whole iterative procedure referred to as error accumulation, which causes a large performance loss, and consequently
they prop ose som e metho ds to control th e erro r accumu lation. Owing to the labelling reselection and error-
accumulation control, the proposed scheme exhibits several tenths to 1 dB gains, compared with the conventional
schemes, while maintaining low complexity.
1 Introduction
Bit-interleaved coded modulation (BICM) has become a widely used
coded modulation technique [1], which simply consists of a channel
code, a bit-wise interleaver and a bit-to-symbol constellation mapper.
The iterative version of BICM, that is, BICM with iterative
demapping (BICM-ID) was introduced by Li and Ritcey [2] and
ten Brink et al. [3].
It was soon recognised that finding a specific constellation
labelling, that is, bit-to-symbol mapping, to match the outer
channel code is an open challenge for BICM-ID designs [4, 5].
Previously, we proposed a method referred to as adaptive binary
switching algorithm (ABSA) for finding the constellation labelling
with the aid of extrinsic information transfer (EXIT) chart analysis
[6, 7]. EXIT chart is a powerful tool for analysing the convergence
behaviour of iterative schemes such as BICM-ID [8]. Our regular
BICM-ID schemes operate closely to the Shannon capacity limit
as the irregular ones, while the complexity is lower.
Nevertheless, we only addressed the logarithm-domain maximum
a posterior (log-MAP) detection algorithms in [6, 7]. Log-MAP is
optimal in the sense of bit error rate (BER) performance, but
suffers from two disadvantages: (i) its complexity is still relatively
high because therein exponential and logarithm operations are
required and (ii) its performance is sensitive to the noise
measurement [9]. Therefore, the max–sum approximation of
log-MAP (max-log-MAP) is preferred for practical systems, which
overcome these two disadvantages at the cost of some BER
performance loss.
Indeed, there are numerous contributions addressing
max-log-MAP detection and its improved versions for iterative
systems in literatures [10, 11]. Most of them mainly focus on the
low-density parity-check (LDPC) or turbo decoding. For example,
to reduce the complexity of the standard sum–product algorithm
for LDPC decoding [12], the min–sum algorithm is proposed with
an error performance degradation from several tenths of decibels
to 1 dB or more. Thereafter, improved min–sum algorithms are
proposed, for example, the normalised min–sum algorithm [10]
and the offset belief-propagation [13]. To enhance the
performance of normalised min–sum algorithm, the normalisation
factor is adaptively selected for each iteration based on
generalised mutual information (GMI) [14]. The idea of
normalisation is also extended for max-log-MAP turbo decoding
[10, 11
], wherein it shows that in most cases, the soft values
generated by the max-log-MAP decoding are overestimated with
respect to those by the log-MAP decoding, and therefore the
decoding performance can be improved by normalisation. To
further improve the performance of the normalised max-log-MAP
decoding, in [15], variable scaling factor scheme is proposed,
where the normalisation factor adaptively updated over all the
iterative stages and is determined by the variance of a priori
information. In [16], a very low-complexity log-MAP decoder is
proposed based on a pre-defined correction term, which is used
for turbo decoding.
Besides the max-log-MAP decoding for binary codes, there are
also other works related to max-log-MAP detection for BICM. For
example, Martinez et.al [17] paid a revisit to BICM using the tool
of GMI by modelling BICM as a mismatched decoder, whereby
BICM-ID was also revisited from the GMI point of view.
However, they assumed correct a priori information to the
BICM-ID demapper therein. In [18], an online numerical search is
proposed for linear Log-likelihood Ratio (LLR) optimisation also
based on GMI.
In this paper, we focus on improving the performance of
BICM-ID with max-log-MAP detection. We consider a BICM-ID
scheme with doping [19], also referred to as unity-rate precoding.
The doping technique was originally proposed by ten Brink [20]
for serially concatenated codes, and later introduced into BICM-ID
by Pfletschinger and Sanzi [19]. The doping code introduces
dependencies between adjacent bits. If perfect a priori information
is input to the doping decoder, perfect extrinsic information can be
produced at its output, which means that perfect convergence can
be achieved in the EXIT chart. As a result, the high error floor of
traditional BICM-ID can be removed for an infinite block length,
or be lowered down for a finite block length.
Our contributions can be summarised as follows.
First, we study the effects of max-log-MAP detection to the EXIT
curves of the demapper and decoder. We find that a good
constellation labelling function for the conventional log-MAP may
IET Communications
Research Article
IET Commun., 2015, Vol. 9, Iss. 14, pp. 1746–1753
1746
&
The Institution of Engineering and Technology 2015
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