IEEE COMMUNICATIONS LETTERS, VOL. 21, NO. 8, AUGUST 2017 1811
On Optimizing Multicarrier-Low-Density Codebook
for GMAC With Finite Alphabet Inputs
Kexin Xiao, Bin Xia, Zhiyong Chen, Jinglun Wang, Dageng Chen, and Shaodan Ma
Abstract—Multicarrier-low-density spreading multiple access
(MC-LDSMA) is a novel non-orthogonal multiple access scheme,
which exploits a multidimensional codebook based on the sparse
spreading technique. In this letter, instead of assuming the ideal
Gaussian inputs, we contribute to design the sparse spreading
codebook with the finite alphabet inputs in an information-
theoretic framework. Single user mutual information (SMI) for
the system with a generic detection is first derived. Different
from the traditional method for maximizing the sum rate, we
propose a fairness balanced criterion to maximize the minimal
SMI in Gaussian multiple access channels. The modified multi-
start interior-point algorithm is proposed to obtain the optimal
codebook. With the proposed codebook, MC-LDSMA achieves
significant performance gains over the previously known schemes
in terms of the SMI and bit-error rate.
Index Terms—Low density spreading, multi-dimensional
codebook, single user mutual information, fairness.
I. INTRODUCTION
T
HE rapidly growing need of high spectral efficiency
and ubiquitous coverage for overloaded communication
networks has stimulated interest in developing Multicarrier-
Low Density Spreading Multiple Access (MC-LDSMA) [1].
The basic mechanism of MC-LDSMA is that the coded bits
for each user are transmitted via multi-dimensional codewords
and codewords from different users are spreading over a small
subset of the subcarriers [2]–[6]. Therefore, each user suffers
less interference from a small number of users on a given
sub-carrier. And the receiver can employ the near optimal
message passing algorithm (MPA) to recover the transmitted
user information [2]. Thus, satisfactory performance could be
achieved by optimizing the sparse spreading codebook when
multiuser codewords are superimposed simultaneously [4].
Sequence design for sparse spreading has been studied
in [2], where transmitted symbol is multiplied with a sparse
sequence generated by trial-and-error searches. Safavi et al. [3]
Manuscript received April 4, 2017; accepted April 27, 2017. Date of
publication May 4, 2017; date of current version August 10, 2017. This
work was supported in part by the National Key Research and Development
Program of China under Grant 2016YFE0121100, the Huawei HIRP Project
under Grant YB2015040062, the Key Laboratory of Wireless Sensor Network
and Communication, Chinese Academy of Sciences under Grant 2015002, the
National Nature Science Foundation of China under Grants 61601524 and
61401274 and the Macau Science and Technology Development Fund under
Grants 091/2015/A3 and 020/2015/AMJ. The associate editor coordinating
the review of this letter and approving it for publication was L. Dai.
(Corresponding author: Bin Xia.)
K. Xiao, B. Xia, Z. Chen, and J. Wang are with the Department of Elec-
tronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
(e-mail: kexin.xiao@sjtu.edu.cn; bxia@sjtu.edu.cn; zhiyongchen@sjtu.edu.cn;
wangjinglun@sjtu.edu.cn).
D. Chen is with the Communications Technology Lab Huawei Technologies
Co., Ltd. Shanghai 201206, China (e-mail: chendageng@huawei.com).
S. Ma is with the Department of Electrical and Computer Engineering,
University of Macau, Taipa, Macau (e-mail: shaodanma@umac.mo).
Digital Object Identifier 10.1109/LCOMM.2017.2701801
and Song et al. [4] propose a sparse sequence design
rule to maximize the minimum squared Euclidean distance.
In addition, Qi et al. [5] analyze the sparsity of the
sum capacity-achieving sequence and propose a construction
method with the help of the frame theory. However, the
assumption of the Gaussian distributed input signals lead
to non-optimal rate when inputs are actually substituted by
discrete constellations. Furthermore, Alishahi et al. [6] derive
the bounds on the sum rate and design the sequence matrices
for overloaded CDMA. Nevertheless, the schemes based on
maximizing the sum rate may introduce unfairness among
users.
To the best of the authors’ knowledge, few works has been
done considering both the finite alphabet inputs and the user
fairness to design the sparse spreading codebook. To this end,
we present a novel design method based on the maximization
of the minimal user rate with the finite alphabet inputs. Our
contribution can be summarized as follows:
• Information-theoretic framework: We provide a basis for
the information-theoretic evaluation by means of the
constellation constrained capacity for the MC-LDSMA
systems. Exploiting the unique transmitter and receiver
structures, we analytically derive the single user mutual
information (SMI), which corresponds to the channel
capacity for each user.
• Codebook optimization with fairness constraints: Consid-
ering the users’ QoS requirements, we propose a fairness
balanced criterion that maximizes the minimum SMI.
Since the mutual information is a nonlinear and non-
convex function of the sequence parameters, a modified
multi-start interior-point algorithm is proposed to obtain
the optimal codebook. Finally, simulation results show
that the proposed codebook outperforms the existing
schemes from the fairness and reliability point of view.
For the sake of clarity, deterministic and random vari-
ables are denoted by lowercase and uppercase letters,
respectively. And scalars, vectors and matrices are dis-
tinguished using normal, bold and underlined bold fonts,
respectively.
II. MC-LDSMA S
YSTEM MODEL
Consider the overloaded uplink systems for Gaussian
Multiple Access Channels (GMAC), where J users convey
information to a destination via K orthogonal subcarriers
(J > K ). By multiplexing J layers over K subcarriers, the
overloading factor is defined as λ = J/K . On the transmit
side, for the j-th user, j = 1, 2,...,J, the binary information
data stream is encoded and interleaved separately. Every
log
2
(M) coded binary bits are firstly grouped together and
then modulated into a complex symbol, under the mapping
relationship : f
j
:B
log
2
(M)
→ Z
j
∈ Z
j
⊂ C with the cardinality
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