A Further Research on Two-phase Decoding for
GC-LDPC Codes
Wei Zhou, Lijun Zhang, Qiang Sun
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China
{16120194, ljzhang, qsun}@bjtu.edu.cn
Abstract—For GC-LDPC code, a targeted decoding scheme is
the two-phase decoding scheme, i.e., the local decoding phase and
the global decoding phase. For both the phases, we find the direct
application of log-domin belief propagation (BP) algorithm will
lead to error. Hence, we propose an improved log-domin BP
algorithm and it will be used in the two-phase decoding scheme.
Since the two-phase decoding scheme has a large gain loss, we
present a modified two-phase decoding scheme in order to
further accelerate the convergence rate. Simulation results show
that the modified two-phase decoder has a gain of about 0.2 dB
compared to the two-phase decoder. Moreover, it also can reduce
complexity by 33.4% in high SNR compared with the whole
decoder.
Keywords—GC-LDPC code, BP algorithm, the two-phase
decoding algorithm, the local decoder, the global decoder
I. INTRODUCTION
Globally coupled low-density parity-check (GC-LPDC)
codes were first proposed by Shu Lin
[1, 2]
. For GC-LDPC code,
its parity-check matrix consists of a number of small disjoint
blocks which are connected together by a coupled block. There
are two types of GC-LDPC code. One is based on check-nodes
GC-LDPC code (CN-based GC-LDPC), the other is based on
variable-nodes GC-LDPC code (VN-based GC-LDPC). For
CN-based GC-LDPC code, a group of overall check-nodes can
give the only links between any two disjoint blocks denoted by
global CNs. For VN-based GC-LDPC code, a group of overall
variable-nodes can give the only links between any two disjoint
blocks denoted by global VNs.
In 2016, finite fields (FF) based GC-LDPC codes were
proposed in [1]. In 2017, the GC-LDPC codes were
constructed based on RS codes
[3-5]
. A two-phase decoding
scheme can be applied to decode these GC-LDPC codes. With
intuition, this two-phase decoding algorithm can significantly
reduce the complexity of decoding. However, in [1], the two-
phase decoding scheme has not been specifically implemented.
Therefore, in this paper, we will use the two-phase decoding
algorithm to decode and prove that it can reduce complexity,
and propose a modified two-phase decoding algorithm.
As we know, compared to the min-sum algorithm (MSA),
the log-domin belief propagation (BP) algorithm has the better
performance
[5-8]
. Hence, we choose log-domin BP algorithm as
the basic algorithm of decoding. When using the two-phase
decoding scheme to decode the CN-based GC-LDPC code, we
find that the direct application of the log-domin BP algorithm
leads to errors. Hence, we propose an improved log-domin BP
(imp-BP) algorithm. Based on the imp-BP algorithm, the two-
phase decoding scheme can be applied to decode CN-based
GC-LDPC code. In order to further accelerate the convergence
rate and approach to Shannon limit
[8]
, we presented a modified
two-phase decoding algorithm.
II. P
RELIMINARIES
In general, the parity-check matrix H of GC-LDPC codes
can be divided into two parts, the upper matrix and the lower
matrix or the left matrix and the right matrix, as shown in (1)
and (2), respectively. We call R the local matrix, X the global
matrix, and H the whole matrix. They correspond to the local
decoder, the global decoder, and the whole decoder,
respectively.
In (1), if R is an
mnu
matrix and X is an
matrix,
H
gc,cn
is an
()mk s nku
matrix. There are k copies of the
matrix R which are independent of each other and they can
only be connected through the s check nodes of the matrix X.
In (2), if R is an
mnu
matrix and X is an
mk su
matrix, H
gc,vn
is an
()mk nk su
matrix. There are k copies of the matrix R
which are independent of each other and they can only be
connected through the s variable nodes of the matrix X.But in
this paper, we only further research on (1).
,
ªº
«»
«»
«»
«»
«»
«»
¬¼
gc cn
R
R
H
R
X
(1)
,
ªº
«»
«»
«»
«»
¬¼
gc vn
R
RX
H
R
(2)
III. A F
URTHER RESEARCH OF TWO-PHASE DECODING
A. The Improved Log-domin Belief Propagation Algorithm
According to (1), the local matrix and the global matrix are
This work is supported by NSFC under grant number U1534201.
978-1-5386-6063-8/18/$31.00 ©2018 IEEE