37 research outputs found
Multiuser non coherent massive MIMO schemes based on DPSK for future communication systems
The explosive usage of rich multimedia content in wireless devices has overloaded the
communication networks. Moreover, the fifth generation (5G) of wireless communications
involves new requirements in the radio access network (RAN) which require higher network
capacities and new capabilities such as ultra-reliable and low-latency communication
(URLLC), vehicular communications or augmented reality. All this has encouraged a remarkable
spectrum crisis in the RF bands. A need for searching alternative techniques
with more spectral efficiency to accommodate the needs of future emerging wireless communications
is emerging. In this context, massive MIMO (m-MIMO) systems have been
proposed as a promising solution for providing a substantial increase in the network capacity,
becoming one of the key enabling technologies for 5G and beyond. m-MIMO
provides high spectral- and energy-efficiency thanks to the deployment of a large number
of antennas at the BS. However, we have to take into account that the current communication
technologies are based on coherent transmission techniques so far, which require
the transmission of a huge amount of signaling. This drawback is escalating with the
excessive available number of antennas in m-MIMO. Therefore, the differential encoding
and non coherent (NC) detection are an alternative solution to circumvent the drawbacks
of m-MIMO in coherent systems. This Ph.D. Thesis is focused on signal processing
techniques for NC detection in conjunction with m-MIMO, proposing new constellation
designs and NC detection algorithms, where the information is transmitted in the signal
differential phase.
First, we design new constellation schemes for an uplink multiuser NC m-MIMO system
in Rayleigh fading channels. These designs allow us to separate the users' signals
at the receiver thanks to a one-to-one correspondence between the constellation for each
user and the received joint constellation. Two approaches are considered in terms of BER:
each user achieves a different performance and, on the other hand, the same performance
is provided for all users. We analyze the number of antennas needed for those designs
and compare to the required number by other designs in the literature. It is shown that
our designs based on DPSK require a lower number of antennas than that required by
their counterpart schemes based on energy. In addition, we compare the performance to
their coherent counterpart systems, resulting NC-m-MIMO based on DPSK capable of
outperforming the coherent systems with the suitable designs.
Second, in order to reduce the number of antennas required for a target performance
we propose a multi-user bit interleaved coded modulation - iterative decoding (BICM-ID) scheme as channel coding for a NC-m-MIMO system based on DPSK. We propose a novel
NC approach for calculating EXIT curves based on the number of antennas. Then using
the EXIT chart we find the best channel coding scheme for our NC-m-MIMO proposal.
We show that the number of users served by the BS can be increased with a 70% reduction
in the number of antennas with respect to the case without channel coding. In particular,
we show that with 100 antennas for error protection equal design for all users and a coding
rate of 1/2 we achieve the minimum probability of error.
Third, we consider that current scenarios such as backhaul wireless systems, rural
or suburban environments, and even new device-to-device (D2D) communications or the
communications in higher frequencies (millimeter and the emerging ones in terahertz frequencies)
can have a predominant line-of-sight (LOS) component, modeled by Rician
fading. For all these new possible scenarios in 5G, we analyze the behavior of the NC
m-MIMO systems when we have a Rician fading. We present a new constellation design
to overcome the problem of the LOS channel component, as well as an associated detection
algorithm to separate each user in reception taking into account the characterization
of the constellation. In addition, for contemplating a more realistic scenario, we propose
grouping users which experience a Rayleigh fading with those with Rician fading, analyzing
the SINR and the performance of such combination in a multi-user NC m-MIMO
system based on M-DPSK. The adequate user grouping allows unifying the constellation
for both groups of users and the detection algorithm, reducing the complexity of the
receiver. Also, the number of users that may be multiplexed may be further increased
thanks to the improved performance.
In the fourth part of this Thesis, we analyse the performance of multi-user NC m-
MIMO based on DPSK in real environments and practical channels defined for the current
standards such as LTE, the future technologies such as 5G and even for communications
in the terahertz band. For this purpose, we use a metric to model the time-varying characteristics
of the practical channels. We employ again the EXIT charts tool for analyzing
and designing iteratively decoded systems. This analysis allows us to obtain an estimate
of the degradation of the system's performance imposed by realistic channels. Hence, we
show that our proposed system is robust to temporal variations, thus it is more recommendable
the employment of NC-m-MIMO-DPSK in the future communication standards
such as 5G. In order to reduce he number of hardware resources required in terms of RF
chains, facilitating its implementation in a real system, we propose incorporating differential
spatial modulation (DSM). We present and analyze a novel multiuser scheme for
NC-m-MIMO combined with DSM with which we can see that the number of antennas
is not a
affected by the incorporation of DSM, even we have an improvement on the
performance with respect to the coherent case.
Finally, we study the viability of multiplexing users by constellation schemes against
classical multiplexing techniques such as time division multiple access (TDMA). In order
to fully characterize the system performance we analyze the block error rate (BLER)
and the throughput of a NC-m-MIMO system. The results show a significant advantage
regarding the number of antennas for multiplexing in the constellation against TDMA.
However, in some cases, the demodulation of multiple users in constellation could require
an excessively large number of antennas compared to TDMA. Therefore, it is necessary to
properly manage the tradeoff
between throughout and the number of antennas, to reach
an optimal operational point, as shown in this Thesis.El inmenso uso de contenido multimedia en los dispositivos inalámbricos ha sobrecargado
las redes de comunicaciones. Además, la quinta generación (5G) de sistemas de
comunicaciones demanda nuevos requisitos para la red de acceso radio, la cual requiere
ofrecer capacidades de red mayores y nuevas funcionalidades como comunicaciones ultra
fiables y con muy poca letancia (URLLC), comunicaciones vehiculares o aplicaciones
como la realidad aumentada. Todo esto ha propiciado una crisis notable en el espectro
electromagnético, lo que ha llevado a una necesidad por buscar técnicas alternativas con
más eficiencia espectral para acomodar todos los requisitos de las tecnologÃas de comunicaciones
emergentes y futuras. En este contexto, los sistemas multi antena masivos,
conocidos como massive MIMO, m-MIMO, han sido propuestos como una solución prometedora
que proporciona un incremento substancial de la capacidad de red, convirtiéndose
en una de las tecnologÃas claves para el 5G. Los sistemas m-MIMO elevan enormemente el
número de antenas en la estación base, lo que les permite ofrecer alta eficiencia espectral
y energética. No obstante, tenemos que tener en cuenta que las actuales tecnologÃas de comunicaciones
emplean técnicas coherentes, las cuales requieren de información del estado
del canal y por ello la transmisión de una enorme cantidad de información de señalización.
Este inconveniente se ve agravado en el caso del m-MIMO debido al enorme número de
antenas. Por ello, la codificación diferencial y la detección no coherente (NC) son una
solución alternativa para solventar el problema de m-MIMO en los sistemas coherentes.
Esta Tesis se centra en las técnicas de procesado de señal para detección NC junto con
m-MIMO, proponiendo nuevos esquemas de constelación y algoritmos de detección NC,
donde la información sea transmitida en la diferencia de fase de la señal.
Primero, diseñamos nuevas constelaciones para un sistema multi usuario NC en m-
MIMO en enlace ascendente (uplink) en canales con desvanecimiento tipo Rayleigh. Estos
diseños nos permiten separar las señales de los usuarios en el receptor gracias a la correspondencia
unÃvoca entre la constelación de cada usuario individual y la constelación
conjunta recibida en la estación base. Hemos considerado dos enfoques para el diseño en
términos de probabilidad de error: cada usuario consigue un rendimiento distinto, mientras
que por otro lado, todos los usuarios son capaces de recibir las mismas prestaciones
de probabilidad de error. Analizamos el número de antenas necesario para estos diseños y
comparamos con el número requerido por otros diseños propuestos en la literatura. Nuestro
diseño basado en DPSK requiere un número menor de antenas comparado con los
sistemas basados en detección de energÃa. También comparamos con su homólogo coherente, resultando que NC-m-MIMO basado en DPSK es capaz de superar a los sistemas
coherentes con los diseños adecuados.
En segundo lugar, para reducir el número de antenas requerido para un rendimiento
dado, proponemos incluir un esquema de codificación de canal. Hemos optado por un
esquema de modulación codificado por bit entrelazado y decodificación iterativa (BICMID).
Hemos empleado la herramienta EXIT chart para el diseño de la codificación de canal,
proponiendo un nuevo enfoque para calcular las curvas EXIT de forma NC y basadas en
el número de antenas. Los resultados muestran que el número de usuarios servidos por
la estación base puede ser incrementado reduciendo un 70% el número de antenas con
respecto al caso sin codificación de canal. En particular, para un array de 100 antenas
y un diseño que ofrezca iguales prestaciones a todos los usuarios, con un código de tasa
1=2, podemos conseguir la mÃnima probabilidad de error.
En tercer lugar, consideramos escenarios donde el canal tenga una componente predominante
de visión directa (LOS) con la estación base modelada mediante un desvanecimiento
tipo Rician. Por ejemplo, sistemas inalámbricos de backhaul, entornos rurales
o sub urbanos, comunicaciones entre dispositivos (D2D), también cuando nos movemos
hacia frecuencias superiores como son en la banda de milimétricas o más recientemente,
la banda de terahercios para buscar mayores anchos de banda. Todos estos escenarios
están contemplados en el futuro 5G. Los diseños presentados para canales Rayleigh ya no
son válidos debido a la componente LOS del canal, por ello presentamos un nuevo diseño de constelación que resuelve el problema de la componente LOS, asà como una guÃa para
diseñar nuevas constelaciones. También proponemos un algoritmo asociado al diseñno de
la constelación para poder separar a los usuarios en recepción. Además, para contemplar
un escenario más realista donde podamos encontrar tanto desvanecimiento Rayleigh como
Rice, proponemos agrupar usuarios de ambos grupos, analizando su rendimiento y relación
señal a interferencia en la combinación. El adecuado agrupamiento permite unificar el
diseño de la constelación para ambos desvanecimientos y por tanto reducir la complejidad
en el receptor. También, el número de usuarios multiplicados en la constelación podrÃa
ser incrementado, gracias a la mejora en el rendimiento.
El cuarto módulo de esta tesis es dedicado a analizar el rendimiento de los diseños
propuestos en presencia de canales reales, donde disponemos de variabilidad temporal y en
frecuencia. Proponemos usar una métrica que modela las caracterÃsticas de la variabilidad
temporal y, usando de nuevo la herramienta EXIT, analizamos los sistemas decodificados
iterativamente considerando ahora los parámetros prácticos del canal. Este análisis nos
permite obtener una estimación de la degradación que sufre el rendimiento del sistema
impuesto por canales reales. Los resultados muestran que los sistemas NC-m-MIMO basados
en DPSK son muy robustos a la variabilidad temporal por lo que son recomendables
para los nuevos escenarios propuestos por el 5G, donde el canal cambia rápidamente.
Otra consideración para introducir los sistemas NC con m-MIMO es la problemática
de necesitar muchas cadenas de radio frecuencia que llevarÃan a tamaños de dispositivos
enormes. Para reducir este número se propone la modulación espacial. En esta Tesis,
estudiamos su uso con los sistemas NC, proponiendo una solución de modulación espacial
diferencial para esquemas con múltiples usuarios combinado con NC-m-MIMO.
Finalmente, estudiamos la viabilidad de multiplexar usuarios en la constelación frente
a usar técnicas clásicas de multiplexación como TDMA. Para caracterizar completamente
el rendimiento del sistema, analizamos la tasa de error de bloque (BLER) y el throughput
de un sistema NC-m-MIMO. Los resultados muestran una ventaja significativa en cuanto
al número de antennas para multiplexar usuarios en la constelación frente al requerido
por TDMA. No obstante, en algunos casos, la demodulación de múltiples usuarios en
la constelación podrÃa requerir un número de antennas excesivamente grande comparado
con la multiplexación en el tiempo. Por ello, es necesario gestionar adecuadamente un
balance entre el throughput y el número de antenas para alcanzar un punto operacional
óptimo, como se muestra en esta Tesis.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ana Isabel Pérez Neira.- Secretario: Máximo Morales Céspedes.- Vocal: MarÃa del Carmen Aguayo Torre
Acceleration of High-Fidelity Wireless Network Simulations
Network simulation with bit-accurate modeling of modulation, coding and channel properties is typically computationally intensive. Simple link-layer models that are frequently used in network simulations sacrifice accuracy to decrease simulation time. We investigate the performance and simulation time of link models that use analytical bounds on link performance and bit-accurate link models executed in Graphical Processing Units (GPUs). We show that properly chosen analytical bounds on link performance can result in simulation results close to those using bit-level simulation while providing a significant reduction in simulation time. We also show that bit-accurate decoding in link models can be expedited using parallel processing in GPUs without compromising accuracy and decreasing the overall simulation time
D11.2 Consolidated results on the performance limits of wireless communications
Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin
High Capacity CDMA and Collaborative Techniques
The thesis investigates new approaches to increase the user capacity and improve the error
performance of Code Division Multiple Access (CDMA) by employing adaptive interference cancellation
and collaborative spreading and space diversity techniques. Collaborative Coding Multiple
Access (CCMA) is also investigated as a separate technique and combined with CDMA. The
advantages and shortcomings of CDMA and CCMA are analysed and new techniques for both the
uplink and downlink are proposed and evaluated.
Multiple access interference (MAI) problem in the uplink of CDMA is investigated first. The
practical issues of multiuser detection (MUD) techniques are reviewed and a novel blind adaptive
approach to interference cancellation (IC) is proposed. It exploits the constant modulus (CM)
property of digital signals to blindly suppress interference during the despreading process and obtain
amplitude estimation with minimum mean squared error for use in cancellation stages. Two
new blind adaptive receiver designs employing successive and parallel interference cancellation
architectures using the CM algorithm (CMA) referred to as ‘CMA-SIC’ and ‘BA-PIC’, respectively,
are presented. These techniques have shown to offer near single user performance for large
number of users. It is shown to increase the user capacity by approximately two fold compared
with conventional IC receivers. The spectral efficiency analysis of the techniques based on output
signal-to interference-and-noise ratio (SINR) also shows significant gain in data rate. Furthermore,
an effective and low complexity blind adaptive subcarrier combining (BASC) technique using a
simple gradient descent based algorithm is proposed for Multicarrier-CDMA. It suppresses MAI
without any knowledge of channel amplitudes and allows large number of users compared with
equal gain and maximum ratio combining techniques normally used in practice.
New user collaborative schemes are proposed and analysed theoretically and by simulations
in different channel conditions to achieve spatial diversity for uplink of CCMA and CDMA. First,
a simple transmitter diversity and its equivalent user collaborative diversity techniques for CCMA
are designed and analysed. Next, a new user collaborative scheme with successive interference
cancellation for uplink of CDMA referred to as collaborative SIC (C-SIC) is investigated to reduce
MAI and achieve improved diversity. To further improve the performance of C-SIC under high
system loading conditions, Collaborative Blind Adaptive SIC (C-BASIC) scheme is proposed.
It is shown to minimize the residual MAI, leading to improved user capacity and a more robust
system. It is known that collaborative diversity schemes incur loss in throughput due to the need of
orthogonal time/frequency slots for relaying source’s data. To address this problem, finally a novel
near-unity-rate scheme also referred to as bandwidth efficient collaborative diversity (BECD) is proposed and evaluated for CDMA. Under this scheme, pairs of users share a single spreading sequence to exchange and forward their data employing a simple superposition or space-time
encoding methods. At the receiver collaborative joint detection is performed to separate each
paired users’ data. It is shown that the scheme can achieve full diversity gain at no extra bandwidth
as inter-user channel SNR becomes high.
A novel approach of ‘User Collaboration’ is introduced to increase the user capacity of CDMA
for both the downlink and uplink. First, collaborative group spreading technique for the downlink
of overloaded CDMA system is introduced. It allows the sharing of the same single spreading
sequence for more than one user belonging to the same group. This technique is referred to as
Collaborative Spreading CDMA downlink (CS-CDMA-DL). In this technique T-user collaborative
coding is used for each group to form a composite codeword signal of the users and then a
single orthogonal sequence is used for the group. At each user’s receiver, decoding of composite
codeword is carried out to extract the user’s own information while maintaining a high SINR performance.
To improve the bit error performance of CS-CDMA-DL in Rayleigh fading conditions,
Collaborative Space-time Spreading (C-STS) technique is proposed by combining the collaborative
coding multiple access and space-time coding principles. A new scheme for uplink of CDMA
using the ‘User Collaboration’ approach, referred to as CS-CDMA-UL is presented next. When
users’ channels are independent (uncorrelated), significantly higher user capacity can be achieved
by grouping multiple users to share the same spreading sequence and performing MUD on per
group basis followed by a low complexity ML decoding at the receiver. This approach has shown
to support much higher number of users than the available sequences while also maintaining the
low receiver complexity. For improved performance under highly correlated channel conditions,
T-user collaborative coding is also investigated within the CS-CDMA-UL system
Transmission strategies for broadband wireless systems with MMSE turbo equalization
This monograph details efficient transmission strategies for single-carrier wireless broadband communication systems employing iterative (turbo) equalization. In particular, the first part focuses on the design and analysis of low complexity and robust MMSE-based turbo equalizers operating in the frequency domain. Accordingly, several novel receiver schemes are presented which improve the convergence properties and error performance over the existing turbo equalizers. The second part discusses concepts and algorithms that aim to increase the power and spectral efficiency of the communication system by efficiently exploiting the available resources at the transmitter side based upon the channel conditions. The challenging issue encountered in this context is how the transmission rate and power can be optimized, while a specific convergence constraint of the turbo equalizer is guaranteed.Die vorliegende Arbeit beschäftigt sich mit dem Entwurf und der Analyse von
effizienten Übertragungs-konzepten für drahtlose, breitbandige
Einträger-Kommunikationssysteme mit iterativer (Turbo-) Entzerrung und
Kanaldekodierung. Dies beinhaltet einerseits die Entwicklung von
empfängerseitigen Frequenzbereichs-entzerrern mit geringer Komplexität
basierend auf dem Prinzip der Soft Interference Cancellation Minimum-Mean
Squared-Error (SC-MMSE) Filterung und andererseits den Entwurf von
senderseitigen Algorithmen, die durch Ausnutzung von
Kanalzustandsinformationen die Bandbreiten- und Leistungseffizienz in Ein-
und Mehrnutzersystemen mit Mehrfachantennen (sog. Multiple-Input
Multiple-Output (MIMO)) verbessern.
Im ersten Teil dieser Arbeit wird ein allgemeiner Ansatz für Verfahren zur
Turbo-Entzerrung nach dem Prinzip der linearen MMSE-Schätzung, der
nichtlinearen MMSE-Schätzung sowie der kombinierten MMSE- und
Maximum-a-Posteriori (MAP)-Schätzung vorgestellt. In diesem Zusammenhang
werden zwei neue Empfängerkonzepte, die eine Steigerung der
Leistungsfähigkeit und Verbesserung der Konvergenz in Bezug auf
existierende SC-MMSE Turbo-Entzerrer in verschiedenen Kanalumgebungen
erzielen, eingeführt. Der erste Empfänger - PDA SC-MMSE - stellt eine
Kombination aus dem Probabilistic-Data-Association (PDA) Ansatz und dem
bekannten SC-MMSE Entzerrer dar. Im Gegensatz zum SC-MMSE nutzt der PDA
SC-MMSE eine interne Entscheidungsrückführung, so dass zur Unterdrückung
von Interferenzen neben den a priori Informationen der Kanaldekodierung
auch weiche Entscheidungen der vorherigen Detektions-schritte
berücksichtigt werden. Durch die zusätzlich interne
Entscheidungsrückführung erzielt der PDA SC-MMSE einen wesentlichen Gewinn
an Performance in räumlich unkorrelierten MIMO-Kanälen gegenüber dem
SC-MMSE, ohne dabei die Komplexität des Entzerrers wesentlich zu erhöhen.
Der zweite Empfänger - hybrid SC-MMSE - bildet eine Verknüpfung von
gruppenbasierter SC-MMSE Frequenzbereichsfilterung und MAP-Detektion.
Dieser Empfänger besitzt eine skalierbare Berechnungskomplexität und weist
eine hohe Robustheit gegenüber räumlichen Korrelationen in MIMO-Kanälen
auf. Die numerischen Ergebnisse von Simulationen basierend auf Messungen
mit einem Channel-Sounder in Mehrnutzerkanälen mit starken räumlichen
Korrelationen zeigen eindrucksvoll die Ãœberlegenheit des hybriden
SC-MMSE-Ansatzes gegenüber dem konventionellen SC-MMSE-basiertem Empfänger.
Im zweiten Teil wird der Einfluss von System- und Kanalmodellparametern auf
die Konvergenzeigenschaften der vorgestellten iterativen Empfänger mit
Hilfe sogenannter Korrelationsdiagramme untersucht. Durch semi-analytische
Berechnungen der Entzerrer- und Kanaldecoder-Korrelationsfunktionen wird
eine einfache Berechnungsvorschrift zur Vorhersage der
Bitfehlerwahrscheinlichkeit von SC-MMSE und PDA SC-MMSE Turbo Entzerrern
für MIMO-Fadingkanäle entwickelt. Des Weiteren werden zwei Fehlerschranken
für die Ausfallwahrscheinlichkeit der Empfänger vorgestellt. Die
semi-analytische Methode und die abgeleiteten Fehlerschranken ermöglichen
eine aufwandsgeringe Abschätzung sowie Optimierung der Leistungsfähigkeit
des iterativen Systems.
Im dritten und abschließenden Teil werden Strategien zur Raten- und
Leistungszuweisung in Kommunikationssystemen mit konventionellen iterativen
SC-MMSE Empfängern untersucht. Zunächst wird das Problem der Maximierung
der instantanen Summendatenrate unter der Berücksichtigung der Konvergenz
des iterativen Empfängers für einen Zweinutzerkanal mit fester
Leistungsallokation betrachtet. Mit Hilfe des Flächentheorems von
Extrinsic-Information-Transfer (EXIT)-Funktionen wird eine obere Schranke
für die erreichbare Ratenregion hergeleitet. Auf Grundlage dieser Schranke
wird ein einfacher Algorithmus entwickelt, der für jeden Nutzer aus einer
Menge von vorgegebenen Kanalcodes mit verschiedenen Codierraten denjenigen
auswählt, der den instantanen Datendurchsatz des Mehrnutzersystems
verbessert. Neben der instantanen Ratenzuweisung wird auch ein
ausfallbasierter Ansatz zur Ratenzuweisung entwickelt. Hierbei erfolgt die
Auswahl der Kanalcodes für die Nutzer unter Berücksichtigung der Einhaltung
einer bestimmten Ausfallwahrscheinlichkeit (outage probability) des
iterativen Empfängers. Des Weiteren wird ein neues Entwurfskriterium für
irreguläre Faltungscodes hergeleitet, das die Ausfallwahrscheinlichkeit von
Turbo SC-MMSE Systemen verringert und somit die Zuverlässigkeit der
Datenübertragung erhöht. Eine Reihe von Simulationsergebnissen von
Kapazitäts- und Durchsatzberechnungen werden vorgestellt, die die
Wirksamkeit der vorgeschlagenen Algorithmen und Optimierungsverfahren in
Mehrnutzerkanälen belegen. Abschließend werden außerdem verschiedene
Maßnahmen zur Minimierung der Sendeleistung in Einnutzersystemen mit
senderseitiger Singular-Value-Decomposition (SVD)-basierter Vorcodierung
untersucht. Es wird gezeigt, dass eine Methode, welche die Leistungspegel
des Senders hinsichtlich der Bitfehlerrate des iterativen Empfängers
optimiert, den konventionellen Verfahren zur Leistungszuweisung überlegen
ist
Fast Decoder for Overloaded Uniquely Decodable Synchronous CDMA
We consider the problem of designing a fast decoder for antipodal uniquely
decodable (errorless) code sets for overloaded synchronous code-division
multiple access (CDMA) systems where the number of signals K_{max}^a is the
largest known for the given code length L. The proposed decoder is designed in
a such a way that the users can uniquely recover the information bits with a
very simple decoder, which uses only a few comparisons. Compared to
maximum-likelihood (ML) decoder, which has a high computational complexity for
even moderate code length, the proposed decoder has a much lower computational
complexity. Simulation results in terms of bit error rate (BER) demonstrate
that the performance of the proposed decoder only has a 1-2 dB degradation at
BER of 10^{-3} when compared to ML