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Seek and Decode: Random Multiple Access with Multiuser Detection and Physical-Layer Network Coding



We present a novel random multiple access scheme that combines joint multiuser detection (MUD) with physical-layer network coding (PLNC) over extended Galois fields (EGF). We derive an analytical bound to the throughput at the system level and present simulation results for the decoding at the physical level in both fast fading and block fading channels. We adopt a cross layer approach in which a non-binary joint multiuser decoder is used in combination with PLNC at slot level, while the use of EGF increases the system diversity at frame level. The results we present are encouraging and suggest that the combination of these two interference management techniques can significantly enhance the performance of random multiple access systems.
Seek and Decode: Random Multiple Access with
Multiuser Detection and Physical-Layer Network
Giuseppe Cocco, Stephan Pfletschinger
German Aerospace Center - DLR
Oberpfaffenhofen, D-82234, Wessling, Germany
Centre Tecnol`
ogic de Telecomunicacions de Catalunya – CTTC
Parc Mediterrani de la Tecnologia, Av. Carl Friedrich Gauss 7 08860, Castelldefels, Spain,
Abstract—We present a novel random multiple access scheme
that combines joint multiuser detection (MUD) with physical-
layer network coding (PLNC) over extended Galois fields (EGF).
We derive an analytical bound on the throughput at the system
level and present simulation results for the decoding at the
physical level in both fast fading and block fading channels.
We adopt a cross layer approach in which a non-binary joint
multiuser decoder is used in combination with PLNC at slot level,
while the use of EGF aims at increasing the system diversity at
frame level. The results we present are encouraging and suggest
that the combination of these two interference management
techniques can significantly enhance the performance of random
multiple access systems.
Random access systems (RAS) are at the same time an
opportunity and a challenge. Opportunity because they do not
require (or require little) coordination among the transmitters,
which, among other advantages, makes it possible to live
together with large delays, typical, for instance, of satellite
communication networks. However, if on the one hand the
lack of coordination can be seen as an asset, on the other hand
it brings about the issue of signals from different transmitters
interfering at the receiver. The problem of collisions in RAS
has been tackled in different ways like exploiting the differ-
ence in the power of the received signals [1] or the application
of multiuser detection (MUD) methods as in the code-division
multiple access (CDMA) systems [2]. Multi-packet reception,
i.e., the capability for the receiver to decode more than one
packet from a collision, has been and still is an active research
field. In [3], an overview of the main multiuser detection
techniques is presented. The impact of multi-packets reception
capability in slotted ALOHA systems has been studied in
[4]. Another approach proposed in the literature consists in
having each transmitter sending multiple replicas of the same
packet within a frame. The receiver tries to decode the packets
that do not experience collision [5] or subtracts the decoded
packets from the slots where their replicas are [6][7]. The
scheme proposed in [6] has been enhanced in [8] by inducing
fluctuations in the received power in order to allow iterative
hard interference cancelation within single slots. Recently the
possibility of decoding functions of colliding signals has been
studied in [9], where the linearity of error correction codes
has been applied for the decoding of the bitwise XOR of
the colliding signals in the two-way relay channel (TWRC)
under the assumption of equal codes at both end nodes. This
approach is one of the possible implementations of the wider
concept known as physical-layer network coding (PLNC). The
performance limits for the decoding of the sum of colliding
signals have been studied from an information theoretical
perspective and assuming lattice codes in [10][11]. Most part
of the literature on PLNC focuses on the TWRC. In [12]
a generalized sum-product algorithm has been proposed for
PLNC in the MAC phase of the TWRC. In [13] a quaternary
decoding approach for the MAC phase of the two-way relay
channel has been proposed, showing that there is an advantage
in obtaining the bitwise sum by combining the previously
estimated individual messages rather than directly decoding
the sum from the analog signal. In [14] it has been proposed
to apply PLNC in slotted random access systems by decoding
the bitwise XOR of all colliding signals within a slot and then
trying to recover all transmitted packets within a frame using
matrix manipulations in GF (2). In [15] and [16] an enhanced
scheme based on PLNC over extended Galois fields has been
proposed, showing an increased system diversity.
In the present paper we propose a random multiple ac-
cess scheme for symbol-synchronous slotted ALOHA systems
named Seek and Decode (S&D) in which the transmitters
pre-encode their information messages multiplying them by
a random coefficient in an extended Galois field while the
receiver tries to decode any linear combination in GF (2)
from the set of colliding bursts within each slot. The receiver
employs a hybrid between a joint multiuser decoder and a
PLNC decoder. Once the whole frame has been processed at
the physical layer, the receiver uses the whole set of linear
combinations available to retrieve all messages transmitted
within the frame by using matrix manipulation techniques over
the same extended Galois field used in the pre-coding stage.
The use of an extended Galois field in the pre-coding stage
increases system diversity. We derive an upper bound on the
throughput at the system level and present numerical results
for the number of innovative messages decoded within a slot in
a block fading channel. FER curves for the fast fading channel
are also presented.
Let us consider a random multiple access network with a
population of Mtransmitting terminals T1,...,TM, and one
receiver R. In the rest of the paper we will use interchangeably
the terms “transmitting node”, “terminal node” and “transmit-
ter”. Time is divided into slots. We define a packet uas a
block of RN information bits. Each terminal generates packets
according to a Poisson process of intensity G
Mpackets per
slot, where Gis the overall load offered to the network in
packets per slot. Each time a packet ui=[ui,1,...,u
i,RN ]
is generated at terminal Ti, it is channel encoded using an
encoder of rate Rcreating a codeword ci=[ci,1,...,c
i,N ]of
Nsymbols. The same channel code is used by all transmitting
nodes. The codeword ciis then mapped to a binary phase-shift
keying (BPSK)-modulated burst xiand transmitted over the
channel. We consider BPSK modulation for simplicity, but
other kinds of modulations can also be used. We assume that
the burst duration is approximately equal to that of a slot.
Transmissions are organized in frames of Sslots each. We
further assume that the transmitters are synchronized such
that all signals transmitted within a slot add up with symbol
synchronism at the receiver. At the receiver side, Rtries to
decode as many linearly independent messages as possible
by applying both joint multi-user detection and physical layer
network coding. In order to increase system diversity at the
frame level, we assume that a pre-coding, such as the one in
[16], is applied by each of the terminals before the channel
encoding. The main innovation in the present work is in the
type of decoder used and in the fact that the receiver tries
to obtain all possible linear combinations in GF (2) from the
signals colliding within a slot. Such linear combinations are
then used by the receiver to recover the whole frame, treating
the set of decoded linear combinations as a system of equations
in GF (2n).
In the present section we describe the proposed random
access scheme named Seek and Decode (S&D). The trans-
mitter side is the same as in [16]. The main innovation is
in the decoding process at both slot level and frame level.
The receiver processes one slot at a time in the analog
domain trying to decode either single messages or some linear
combination of the colliding signals. We briefly recall the
operations at the transmitter side presented in [16] and then
move to the description of the receiver side.
A. Transmitter Side
Each message is transmitted more than once within a frame,
i.e., several replicas of the same message (bursts) are trans-
mitted. Assume that node ihas a message uito deliver to R
during a given frame, i.e., node Tiis an active terminal. Before
each transmission, node ipre-encodes uias depicted in Fig. 1.
The message to be transmitted is divided into sub-blocks.
Fig. 1. Pre-coding, channel coding and modulation scheme at the transmitter
side. Pre-coding consists in dividing the message into blocks of nbits
(indicated as ur
iin the figure) and multiply each of these blocks by the same
coefficient randomly chosen in GF (2n). The sub index jindicates the slot
within a frame in which the replica of message uiis transmitted. A different
coefficient αij is used for each replica.
Each sub-block is multiplied by a coefficient αij GF (2n).
Coefficient αij,j∈{1,...,S}is chosen at random in each
time slot jwhile it is fixed for all sub-blocks within a message.
Note that the pre-coding does not have any impact on the
decoding process at the physical layer. The multiplication of
uiby αij is needed to increase diversity at the frame level and
does not modify the number of information bits transmitted.
After the multiplication, the message is channel-encoded, a
header is attached and the modulation takes place. The header
can be generated using a pseudonoise sequence generator such
as the ones used in CDMA. In practice the coefficients αij can
be generated using a pseudo-random number generator. In a
given frame the active node chooses a different seed and uses
as many outputs of the generator as the number of replicas
transmitted within the frame. Each seed is associated to a
certain header, which is assumed to be detected by the receiver
using the cross-correlation properties of the header 1. The same
header is used within a given frame by an active node. In this
way the receiver can detect in which slots a certain node is
transmitting and derive the coefficients used in the different
replicas from the header. The header is also used to perform
the channel estimation of each of the transmitters. A more
detailed analysis of the issues related to header detection and
channel estimation can be found in [16] and [17].
B. Receiver Side
The main innovation of the proposed scheme with respect to
previous works is at the receiver side. In the literature of ran-
dom access, and up to our knowledge, when a receiver receives
two or more interfering signal, it can either use some kind
of interference cancelation or, as in physical layer network
1Note that other signatures can also be used by the nodes to allow Rfor
the identification of the transmitters.
coding, try to decode a function of the colliding messages 2.
Most of the multiuser detection techniques found in literature
can be categorized as parallel (PIC) or serial (SIC). Often
such methods are iterative and alternate a detection phase
to an estimation phase. In the proposed scheme the receiver
applies a joint decoder which tries to recover simultaneously
all messages involved in the collision. An FFT-based belief
propagation decoder over the vectorial combination of all
message bits, which is described in detail in the companion
paper [19], has been adopted. The decoder jointly estimates all
the single messages and then calculates the bitwise XOR of
any subset of the estimated messages. It is important to notice
that, as shown in [13], the sum in GF (2) of a set of estimated
messages can be correct even if the estimated messages taken
individually contain errors. A cyclic redundancy check (CRC)
can be used for error detection. Note that, due to the linearity
of the code, the XOR of the CRCs relative to a set of messages
is a valid CRC for the XOR of the messages in the set. Here
we assume ideal error detection at the receiver for ease of
Given a slot with a collision of size k, the receiver tries to
decode kindependent linear combinations in GF (2) of the
colliding signals. One possible way to proceed, although not
necessarily the optimal one, can be the following. For each
slot with a collision of size k, the decoder tries to decode
single messages. If less than kmessages are decoded correctly,
the decoder tries to decode the sum in GF (2) of pairs of
messages (there are k
2possible combinations) stopping when
a total of klinearly independent combinations are decoded. If
still less than klinear combinations have been decoded, sums
of three messages are considered. The process goes on until
either enough linear combinations have been decoded or all
possible combinations have been exhausted. The total number
of linear combinations that the decoder can try to recover is
i=1 k
C. Example
In the following we illustrate the S&D scheme with a toy
example. Let us consider a frame with S=2slots and four
active nodes. Let us assume that nodes 1and 2transmit in
both slots, each time choosing at random their pre-coding
coefficients. Node 3only transmits in the first slot while node
4transmits only in the second, as illustrated in Fig. 2. Let us
assume that the S&D decoder is able to output only two linear
combinations in each of the two slots as shown in the picture.
The receiver tries, then, to recover all information messages
u1...,u4. The decoding is possible if the coefficient matrix
2In [18] a practical implementation of a system using both PNC and MUD
in the multiple access channel of a WLAN has been presented. Unlike in the
present work, in [18] only the case of two colliding signals is considered, a
relaying setup is assumed and a different multi-user detector (in which joint
detection is performed but not joint decoding) is adopted.
Fig. 2. Example of decoding at the physical layer in S&D with a two-slots
frame and four active terminals. Nodes 1and 2transmit in both slots, each
time choosing at random their pre-coding coefficients. Node 3only transmits
in the first slot while node 4transmits only in the second.
Ain GF (2n)(shown below) has full rank.
Note that matrix Ais rank deficient if coefficients are chosen
in GF (2) (i.e., all coefficients shown in the matrix above are
equal to 1), while it can be full rank in some extended Galois
field. For instance, in GF (4) the matrix
is full rank. If, by choosing the coefficients at random, the
above matrix is obtained it would be possible to decode the
whole frame. The probability of obtaining a full rank matrix
increases with the field size. Finally, we note that in the
example the average number of packets decoded per slot is
In the present section we derive an upper bound to the
system throughput, defined as the average number of de-
coded messages per time slot, for the proposed scheme. The
throughput depends on the repetition strategy chosen. For
mathematical tractability we assume a general scheme in
which each active node transmits in each slot with probability
p, fixed for all nodes.
A. Upper Bound to Decoding Probability
In our simulation results we observed that the probability
of correct decoding for the sum of a subset of messages with
cardinality ifrom a collision of size k,0<ik, is a function
of both iand kin both fast fading and block fading channels.
We define:
Pr{decode sum of imessages form collision of k}pk,i.
pk,i can be upper bounded as follows:
pk,i ¨pk,i ˜pk,i,
¨pk,i max
Sk,i being one of the k
isubsets of imessages among the k,
We found through simulations that pk,i is lower than or equal
to the probability to decode the sum of the istrongest signals
among the k. Thus, ˜pkis the maximum across all subset sizes
i,i∈{1,...,k}, of the probability to decode the sum of
the istrongest signals. ˜pkis used in the following for the
derivation of the upper bound on the throughput. By applying
both joint MUD and PLNC, the receiver can obtain up to
ηk2k1different linear combinations in a slot with a
collision of size k. At most kof the decoded combinations
are linearly independent. For ease of calculation we assume
in the following that the decodability of a given combination
is independent of the decoding of any other within the same
slot3. The number of combinations (linearly independent or
not) decoded in a slot is a random variable. We indicate such
variable with . Let us now indicate with kthe number of
combinations decoded in a slot when the collision size is k.
kis a Binomial random variable with parameters ˜pk,i and ηk,
i.e., kB(ηk,˜pk). The mean and variance of kare ηk˜pk
and ηk˜pk(1˜pk), respectively. The mean value of ,E[]=,
is then:
k=1 Ntx
kpk(1 p)Ntxkηk˜pk,(1)
while the mean squared value of is:
k=1 Ntx
kpk(1 p)Ntxk×
×ηk˜pk(1 ˜pk)+(ηk˜pk)2.(2)
Finally, the variance of σ
can be calculated using expres-
sions (1) and (2) as σ2
=E[2]2. The total number of
combinations decoded in the whole frame is a random variable
given by the sum of the numbers of combinations decoded
in all slots, which are i.i.d. random variables and for which
we just calculated the mean and the variance. Practical values
for Scan be on the order of 100, which is large enough to
approximate the sum of Si.i.d. random variables as a Gaussian
3In general this is only an approximation, since giving the correct decoding
of a subset of individual messages, any combination of such messages can
also be decoded. However, it can happen that the single messages can not be
decoded while the sum can (e.g., this is true for certain code rates and if two
signals have the same channel amplitude as shown in [13].)
variable having mean Sand variance . From expressions
(1) and (2) it can be seen that the mean and the variance of
depend on the number of active terminals in the frame. For
this we indicate with (Ntx)fr and σ(Ntx )2
the mean and
the variance of , respectively. As mentioned in Section II
we assume Poisson arrivals with an overall offered load of G
packets per slot. An upper bound on the normalized throughput
can be calculated by assuming p=2
n1,nbeing the size of
the Galois field of the coefficients used in the pre-coding step,
and assuming that all combinations decoded within a frame
are obtained using independently drawn coefficients for each
message in each equation4.Ifnis large, the probability pNtx
to decode a number of combinations larger than or equal to
the number of active nodes within a frame is given by (3)
(GS)Ntx eGS
S(2Ntx 1)
Using (3) we can obtain an upper bound on the normalized
system throughput ΦUB when a large field size is used. The
expression for ΦUB is given by Eqn. 4 at the top of next page.
A. Joint Decoding in the Fast Fading Channel
For a first evaluation of the joint decoding approach, we
considered the simultaneous decoding of k∈{2,3,...,8}
packets in a fast Rayleigh fading symmetric multiple-access
channel, given by
hi,n ·xi,n +wn,w
The fading coefficients hi,n are i.i.d. Rayleigh distributed
with average signal-to-noise ratio SNR = E[h2
i,n]and the
decoder employs joint decoding of all kmessages as described
in [19]. Due to the fast fading and the symmetric channel,
the ktransmitted packets experience approximately the same
channel quality and we consider the word error rate of the
combined messages. In other words, we count a word error if
any of the kmessages is not correctly decoded. Fig. 3 shows
the simulation results for the CCSDS LDPC code [20] of rate
R=0.4and message length RN = 1024 bits. In Fig. 3
we can see that the simultaneous decoding of several packets
is possible and requires only a moderate SNR increase for a
growing collision size.
While these results verify the functioning of the joint
decoding approach, for a practical random access scheme the
assumption of fast fading is not realistic and we therefore
apply block fading for the following throughput evaluations.
4Note that in practice each message has the same coefficient for all
combinations within a given slot.
ΦUB =1
Ntx (GS)Ntx eGS
(GS)Ntx eGS
2 4 6 8 10 12 14 16 18 20
k=2 k=3 k=4 k=5 k=6 k=7 k=8
SNR [dB]
Fig. 3. Word error rate for joint decoding in symmetric fast Rayleigh fading
channel. An error occurs when one of the kmessages can not be correctly
B. Seek & Decode in the Block Fading Channel
As described in the previous sections, in the S&D scheme
the receiver uses a joint decoder to recover as many linearly
independent combinations of colliding signal as possible in
each slot and then, exploiting the pre-coding of the transmitted
messages at the receiver side, try to decode the whole frame
using standard matrix manipulations techniques. The linearly
independent combinations may be either single messages or
sums in GF (2) of any number of messages from 2to k,k
being the collision size in the slot. One could guess that it
might not be necessary to decode sums of messages since the
joint decoder is highly efficient and thus all messages could
be directly decoded from each slot. However, our simulation
results show that for a range of SNR and collision sizes of
practical interest, decoding sums of messages does increase
significantly the number of linearly independent combinations
decoded in a slot. This is shown in Fig. 4, where the average
number of innovative packets decoded in a slot is plotted
against the average SNR for the proposed seek and decode
method (S&D in the figure) and for a plain joint decoding
scheme (JD in the figure), in which only single messages are
decoded. For these simulations, we assumed block Rayleigh
fading where the fading coefficients are constant during a
packet transmission. A packet is said to be innovative if it can
not be obtained as a linear combination in GF (2) of previously
decoded packets. Different curves for different collision sizes
kare shown. It can be seen how for larger kand mid-low SNR
values the gain of S&D with respect to JD is significant (more
than 25% gain at about 11 dB for k=6). The gain derives
from the fact that, in a non negligible number of cases, it is
possible do decode correctly the sum of two or more messages
from a collision even if the single messages can not be decoded
5 0 5 10 15 20 25 30
SNR [dB]
Innovative packets per slot
Fig. 4. Average number of innovative packets decoded in a slot plotted
against the average SNR for the proposed seek and decode, S&D, and for
joint decoding, JD. Different curves for different collision sizes kare shown.
It can be seen how for larger kand mid-low SNR values the gain of S&D
with respect to JD is significant (gain of around 20% at 10 dB for k=4).
with a joint decoder. Note also that, once the decoding at the
physical layer is finished, the receiver is left with Ssets of
equations. Each of these sets derives from the decoding at the
physical layer of each slot. Note also that, even if some (or all)
of the sets of equations have not a full rank associated matrix,
(i.e., not all of the colliding signals within a block can be
decoded), it may still be possible to recover all the messages
transmitted in a frame by applying matrix manipulations over
the equivalent associated matrix in GF (2n).
We proposed a new random multiple access scheme for
symbol-synchronous slotted aloha random access systems.
Each node transmits several replicas of the same message
within a frame after a pre-multiplication by a (pseudo)-
randomly chosen coefficient in GF (2n). The receiver tries
to decode as many linear combination in GF (2) of signals
colliding in each slot as possible and then tries to recover all
the messages transmitted within a frame treating the linear
combinations decoded in the whole frame as a single system
of equations in GF (2n). We presented analytical results for
the throughput at system level and simulation results for the
decoding process at the physical level. As future work we plan
to optimize the multiple access scheme taking into account the
decoder performance, which is a function of the collision size
and the specific linear combination within a collision, with the
aim of maximizing the system throughput and minimizing the
packet error rate. At the physical level we plan to consider
higher order modulations and different decoding approaches.
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... Beyond SIC, another promising strategy, which is inspired by physical-layer network coding (PLNC), consists in encoding and decoding linear combinations of packets [14]- [17]. By collecting enough linearly independent packet combinations within a contention period (frame), the receiver might be able to resolve all individual packets. ...
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Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear combinations of colliding packets, whenever the decoding of individual packets fails. The resulting linear combinations are then temporarily stored in the hope of gathering enough linearly independent combinations so as to eventually recover all individual packets through the resolution of a linear system at the end of the contention frame. However, it is unclear which among the numerous linear combinations---whose number grows exponentially with the degree of collision---will have low probability of decoding error. Since no analytical framework exists to determine which combinations are easiest to decode, this makes the case for a machine learning algorithm to assist the receiver in deciding which linear combinations to target. For this purpose, we train neural networks that approximate the error probability for every possible linear combination based on the estimated channel gains and demonstrate the effectiveness of our approach by numerical simulations.
... The solution falls under the category of coded random access [36], where features of channel coding are exploited both at the slot and frame level. In particular, the scheme partially presented in [37], [38] is extended for massive access, with emphasis on the transmission of short packets. The proposed scheme assumes a minimum coordination that ensures packet synchronization. ...
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The fifth generation of cellular communication systems is foreseen to enable a multitude of new applications and use cases with very different requirements. A new 5G multiservice air interface needs to enhance broadband performance as well as provide new levels of reliability, latency and supported number of users. In this paper we focus on the massive Machine Type Communications (mMTC) service within a multi-service air interface. Specifically, we present an overview of different physical and medium access techniques to address the problem of a massive number of access attempts in mMTC and discuss the protocol performance of these solutions in a common evaluation framework.
... where R, λ h , and F Proof: The theorem follows from Lemma 3 and Lemma 4 by considering p i = F s (F u ( p i−1 )), where F u (·) and F s (·) are given by Eq. (26) and Eq. (23), respectively. ...
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In this paper, we investigate the design and analysis of coded slotted ALOHA (CSA) schemes in the presence of channel erasure. We design the code probability distributions for CSA schemes with repetition codes and maximum distance separable (MDS) codes to maximize the expected traffic load, under both packet erasure channels and slot erasure channels.We derive the extrinsic information transfer (EXIT) functions of CSA schemes over erasure channels. By optimizing the convergence behavior of the derived EXIT functions, the code probability distributions to achieve the maximum expected traffic load are obtained. Then, we derive the asymptotic throughput of CSA schemes over erasure channels. In addition, we validate that the asymptotic throughput can give a good approximation to the throughput of CSA schemes over erasure channels.
This paper presents a cross-layer design of backbone-assisted wireless local area network (WLAN) for dense WLAN deployment. With dense access points (AP), an AP could overhear packets destined for other APs. Backbone-assisted WLAN is a new system architecture where cooperative APs share the overheard packets through a backbone network, thereby reducing packet retransmission. Conventional WLAN uses Stop-and-Wait ARQ. This paper argues that Stop-and-Wait does not work well with backbone-assisted WLAN because of large backbone delays. We first show that with a variant of Selective Repeat ARQ, a single-user backbone-assisted WLAN system can achieve substantial throughput improvement over that with Stop-and-Wait ARQ. Then, we put forth a new system architecture, referred to as network-coded backbone-assisted WLAN, in which multiple users are allowed to transmit simultaneously. A distinguishing feature of this system is the joint use of physical-layer network-coding (PNC) decoding and multiuser-decoding in multipacket reception. This paper is the first attempt to design an ARQ for multiuser backbone-assisted WLAN. Our overall system design solves a PNC sequence obfuscation problem and addresses long packet latency. Experiments indicate network-coded Ethernet-backbone-assisted WLAN can achieve high system throughput and low packet latency. Overall, we believe network-coded backbone-assisted WLAN is a viable solution for boosting throughput and reducing latency in dense WLAN environments.
In this paper, we propose an enhanced low-complexity binary physical-layer network coding (PNC) based decoding scheme for random access systems with binary phase-shift keying modulation to improve the system throughput. In the proposed scheme, the linear combinations of collided users’ messages in each time slot are first obtained by exploiting a low-complexity PNC decoding scheme. Based on the decoded linear combinations within a MAC frame, we then propose an enhanced message-level successive interference cancellation algorithm to recover more users’ messages. We propose an analytical framework for the PNC-based decoding scheme and derive a tight approximation of the system throughput for the proposed scheme. Subsequently, the number of repeated transmissions of a message, i.e., the number of replicas transmitted by each user, is optimized to further improve the system throughput and energy efficiency. Interestingly, the optimization results show that the optimal number of replicas for maximizing the energy efficiency is a constant for all offered loads. On the other hand, the optimal number of replicas that maximizes the system throughput decreases as the offered load increases. Numerical results show that the derived analytical results closely match with the simulation results. Furthermore, the proposed scheme achieves a considerable throughput improvement, compared to the CRDSA++ scheme.
A recently proposed network-coded multiple access (NCMA), consisting of XOR-based channel decoding (XOR-CD) and multi-user complete decoding (MUD-CD), can significantly improve throughput over conventional successive interference cancellation (SIC) decoding under near power-balanced channels. In this paper, we propose an improved NCMA (I-NCMA) for non-orthogonal multiple access (NOMA) in the 5G wireless communications, consisting of multiple users and a single base station (BS). At the transmitter side, the proposed scheme enables all users to simultaneously transmit messages to the BS in the same time and frequency. At the receiver side, we propose a joint-user channel decoding (JU-CD) to jointly decode all user messages by a single decoder. Then, the extrinsic messages from JU-CD can be jointly utilized by MUD-CD for decoding all user messages. Also, other than conventional NCMA that mainly deals with two users, I-NCMA is adapt to the NOMA networks with an arbitrary number of users. Simulation results indicate that the proposed I-NCMA achieves a better decoding performance than both SIC and conventional NCMA over near power-balanced channels in the low-to-medium SNR regime, while retaining a performance closed to conventional NCMA in the high SNR regime.
Conference Paper
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Machine-to-machine (M2M) communications have a very large potential market growth, particularly in the low-end segment. Current satellite systems are not adequate to serve very large populations of low cost devices, with low bandwidth requirements, and severe cost and energy constraints. A satellite system can bring unique advantages in terms of cross-border coverage, availability, and security of the communication. However, it must compete in cost with cellular and unlicensed devices, which are rapidly evolving. The high cost of the space segment can be compensated by the high scalability of the system if the terminal cost can be kept sufficiently low. Moreover, the low bandwidth requirements of M2M systems make reusing current infrastructure possible. In this paper we analyze the feasibility of such M2M satellite system. We define a satellite architecture and multiple access technique appropriate for low-cost, energy-constrained devices, and evaluate its performance in terms of system capacity and energy usage.
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In this paper, we consider the two-way relay channel with the two-phase protocol. In the first phase, two terminals simultaneously transmit their packets to the relay, creating a multiple-access channel (MAC), while in the second phase the relay sends a network-coded combination of the two packets to both terminals. We focus on the multiple-access phase and propose a practical decoding scheme based on practical binary block codes in order to obtain the combined packet at the relay. This scheme is found to perform well for a wide range of code rates and is superior to lattice coding at low rates.
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This paper proposes and experimentally demonstrates a first wireless local area network (WLAN) system that jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost system throughput. We refer to this multiple access mode as Network-Coded Multiple Access (NCMA). Prior studies on PNC mostly focused on relay networks. NCMA is the first realized multiple access scheme that establishes the usefulness of PNC in a non-relay setting. NCMA allows multiple nodes to transmit simultaneously to the access point (AP) to boost throughput. In the non-relay setting, when two nodes A and B transmit to the AP simultaneously, the AP aims to obtain both packet A and packet B rather than their network-coded packet. An interesting question is whether network coding, specifically PNC which extracts packet (A XOR B), can still be useful in such a setting. We provide an affirmative answer to this question with a novel two-layer decoding approach amenable to real-time implementation. Our USRP prototype indicates that NCMA can boost throughput by 100% in the medium-high SNR regime (>=10dB). We believe further throughput enhancement is possible by allowing more than two users to transmit together.
Conference Paper
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We address several implementation issues related to multi-user physical layer network coding, in which the symbol synchronous collision of an arbitrary number of signals is decoded. In particular we study the effect of frequency and phase offsets, the imperfect symbol synchronization of the colliding signals and the estimation of frequency and phase offsets and amplitudes in the presence of more than two colliding signals.
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This paper was originally distributed informally as ARPA Satellite System Note 8 on June 26, 1972. The paper is an important one and since its initial limited distribution, the paper has been frequently referenced in the open literature, but the paper itself has been unavailable in the open literature. Publication here is meant to correct the previous gap in the literature. As the paper was originally distributed only to other researchers intimately familiar with the area covered by the paper, the paper makes few concessions to the reader along the lines of introductory or tutorial material. Therefore, a bit of background material follows. ALOHA packet systems were originally described by Abramson ("The ALOHA System--Another Alternative for Computer Communication," Proceedings of the AFIPS Fall Joint Computer Conference, Vol. 37, 1970, pp. 281--285). In an ALOHA a single broadcast channel is shared by a number of communicating devices. In the version originally described by Abramson, every device transmits its packets independent of any other device or any specific time. That is, the device transmits the whole packet at a random point in time; the device then times out for receiving an acknowledgment. If an acknowledgment is not received, it is assumed that a collision occured with a packet transmitted by some other device and the packet is retransmitted after a random additional waiting time (to avoid repeated collisions). Under a certain set of assumptions, Abramson showed that the effective capacity of such a channel is 1/(2e). Roberts in the present paper investigates methods of increasing the effective channel capacity of such a channel. One method he proposes to gain in capacity is to consider the channel to be slotted into segments of time whose duration is equal to the packet transmission time, and to require the devices to begin a packet transmission at the beginning of a time slot. Another method Roberts proposes to gain in capacity is to take advantage of the fact that even though packets from two devices collide in the channel (i.e., they are transmitted so they pass through the channel at overlapping times), it may be possible for the receiver(s) to "capture" the signal of one of the transmitters, and thus correctly receive one of the conflicting packets, if one of the transmitters has a sufficiently greater signal than the other. Roberts considers the cases of both satellite and ground radio channels.
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We propose a collision recovery scheme for symbol-synchronous slotted ALOHA based on physical layer network coding over extended Galois fields. Information is extracted from colliding bursts allowing to achieve higher maximum throughput with respect to previously proposed collision recovery schemes. An energy efficiency analysis is also performed, and it is shown that by adjusting the transmission probability, high energy efficiency can be achieved. A performance evaluation is carried out using the proposed algorithms, revealing remarkable performance in terms of normalized throughput. [Invited Paper]
Conference Paper
We develop a belief-propagation (BP) decoder for the joint decoding of multiple codewords which belong to the same non-binary LDPC code. Decoding is based on soft information in form of joint channel-posterior probabilities of all codeword symbols. We extend the BP algorithm for q-ary LDPC codes such that the FFT-based check node processing is preserved and the complexity remains manageable. This joint decoding is useful in settings in which multiple codewords are transmitted in a non-orthogonal way over the same channel, including multiple-access with packet collisions, physical-layer network coding and multi-resolution broadcasting. We show in an example that joint decoding can be far superior to separate decoding.
Contention resolution diversity slotted ALOHA (CRDSA) is a simple but effective improvement of slotted ALOHA. CRDSA relies on MAC bursts repetition and on interference cancellation (IC), achieving a peak throughput T ≅ 0.55, whereas for slotted ALOHA T ≅ 0.37. In this paper we show that the IC process of CRDSA can be conveniently described by a bipartite graph, establishing a bridge between the IC process and the iterative erasure decoding of graph-based codes. Exploiting this analogy, we show how a high throughput can be achieved by selecting variable burst repetition rates according to given probability distributions, leading to irregular graphs. A framework for the probability distribution optimization is provided. Based on that, we propose a novel scheme, named irregular repetition slotted ALOHA, that can achieve a throughput T ≅ 0.97 for large frames and near to T ≅ 0.8 in practical implementations, resulting in a gain of ~ 45% w.r.t. CRDSA. An analysis of the normalized efficiency is introduced, allowing performance comparisons under the constraint of equal average transmission power. Simulation results, including an IC mechanism described in the paper, substantiate the validity of the analysis and confirm the high efficiency of the proposed approach down to a signal-to-noise ratio as a low as E<sub>b</sub>/N<sub>0</sub>=2 dB.
A generalization of the slotted ALOHA random access scheme is considered in which a user transmits multiple copies of the same packet. The multiple copies can be either transmitted simultaneously on different frequency channels (frequency diversity) or they may be transmitted on a single high-speed channel but spaced apart by random time intervals (time diversity). In frequency diversity, two schemes employing channel selections with and without replacements have been considered. In time diversity, two schemes employing a fixed number of copies or a random number of copies for each packet have been considered. In frequency diversity, activity factor-throughput tradeoffs and in time diversity, delay-throughput tradeoffs for various diversity orders have been compared. It is found that under light traffic, multiple transmission gives better delay performance. If the probability that a packet fails a certain number or more times is specified not to exceed some time limit (realistic requirement for satellite systems having large round trip propagation delay), then usually multiple transmission gives higher throughput.