Efficient HARQ Scheme based on Rate-Compatible
Punctured Polar Codes
Sha Wang, Jian Jiao, Bowen Feng, Shaohua Wu, Shushi Gu, and Qinyu Zhang
Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), Guangdong, China
{wangsha0701@foxmail.com; hitfbw@hotmail.com; {jiaojian, hitwush, gushushi, zqy}@hit.edu.cn}
Abstract—In this paper, an optimized parallel concatenated
punctured polar (OPCPP) coding scheme is designed to realise
the rate-compatible property of polar codes. First, an improved
random puncturing pattern of polar codes is proposed to achieve
better performance than the random puncturing scheme, which
can obtain about 0.2-1dB better than the random puncturing
scheme. Then, by analyzing the performance of HARQ transmis-
sion scheme via OPCPP coding blocks over slow fading channels,
the optimal initial code rate of each new OPCPP coding block can
be determined by the overhead of the previous successful decoded
coding block. Simulation results show that the mean number of
retransmissions in our proposed rate-compatible HARQ scheme
is about 1.5 times with the encoding construct of a 2-level OPCPP
codes, which can reduce half of the number of retransmissions
than the existing rate-compatible polar coding scheme.
Index Terms—Polar codes; puncturing; rate-compatible; re-
transmissions.
I. INTRODUCTION
Polar codes are a new type channel code introduced by
Arikan [1] which can achieve the capacity of any memory-less
symmetric channel [2]; the encoding and decoding complexity
are O(Nlog
2
N), where N is block length [3]. Polar codes will
be applied in fifth-generation (5G) communication systems
due to these attractive features [4].
Due to the time-varying nature of wireless channels in
the future 5G communications, the quality of the channel is
unknown to the transmitter in many communication scenarios
[5] and the conventional fixed-rate coding [6] schemes can not
perform well. In particular, polar codes need to be constructed
according to the channel capacity to have good approaching
performance [7], [8], and the original polar coding scheme can
not perform well over an unknown channel [9]. Moreover, the
block length of original polar codes is restricted to the power
of 2. Polar codes with any arbitrary lengths and rates can
be constructed by puncturing [10], [11], [12], [13]. However,
the performance of these punctured codes is worse than the
conventional polar codes.
Recently, a capacity-achieving rateless polar coding scheme
has been proposed in [14] to realise the polar codes over
an unknown channel by transmitting incrementally more and
more coded bits, until all the information bits are decod-
ed reliably by the receiver, and the receiver decodes by a
backward strategy according to the nesting property of the
information sets among polar codes [14]. However, the rate
in each transmission is such that R
m
= R
1
/m, where R
1
is the rate of the first transmission and m is the number
of retransmissions, so the scheme is not truly rateless. [15]
proposed a capacity-achieving rate-compatible polar codes, but
a sequential encoders and decoders are required to construct
different block length polar codes which cause an expense of
a complex system structure.
In this paper, we proposed an optimized parallel concate-
nated punctured polar (OPCPP) coding scheme and designed
a rate-compatible HARQ transmission scheme for multiple
OPCPP code blocks. In Section II we present preliminaries
of polar codes, and propose our system model. We present
our improve random puncturing polar coding algorithm that
limited the puncturing patterns in the frozen bits in Section
III, which provide better performance than original random
puncturing scheme. Furthermore, by analyzing the perfor-
mance of HARQ transmission scheme via OPCPP coding
blocks over slow fading channels in Section IV, we determine
the optimal initial code rate of each new OPCPP coding
block by the overhead of the previous successful decoded
coding block. Section V presents the simulation results of our
proposed puncturing methods and OPPCP scheme. Conclusion
is provided in Section VI.
II. P
RELIMINARIES AND SYSTEM MODEL
N polarized sub-channels {W
(i)
N
} (i =1, 2, ...N) can be
obtained by channel combining and splitting operation on
N independent discrete memoryless channels (DMCs). Let
C(N,R, A) denote a polar code of block length N =2
n
(n ≥ 0) and rate R with information set A, where R =
K
N
and K is the number of information bits. For a source message
vector u
N
1
=(u
1
,u
2
, ...u
N
), K information bits are transmit-
ted in “good” sub-channels with indices A while frozen bits
are transmitted in “bad” sub-channels with indices in comple-
mentary set A
c
. A polar codeword x
N
1
=(x
1
,x
2
, ..., x
N
) is
generated as
x
N
1
= u
N
1
G
N
(1)
where the generator matrix G
N
= B
N
F
⊗n
and B
N
is the
permutation matrix, F =
10
11
is known as standard
kernel and F
⊗n
is the nth Kronecker.
A sequence of nested polar codes C =
{C(N,R
i
, A
i
)}|
i∈{1,2,...,J}
can be constructed in a degraded
channel sequence {W
1
,W
2
, ..., W
J
}, where all codes have
the same block that are restricted to 2
n
and their respective
are nested such that A
1
⊇ A
2
⊇ ...⊇ A
J
.
2017 IEEE/CIC International Conference on Communications in China (ICCC)
978-1-5386-4502-4/17/$31.00 ©2017 IEEE