scholarly journals Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 581
Author(s):  
Yunus Can Gültekin ◽  
Tobias Fehenberger ◽  
Alex Alvarado ◽  
Frans M. J. Willems
Keyword(s):  
Gaussian Noise ◽  
Energy Efficient ◽  
Power Efficiency ◽  
Additive White Gaussian Noise ◽  
Constant Composition ◽  
Composition Distribution ◽  
Awgn Channel ◽  
Distribution Matching ◽  
Simulation Results ◽  
Rate Loss

In this paper, we provide a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. However, as the blocklength decreases, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths over the additive white Gaussian noise (AWGN) channel, the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM) and SpSh are reviewed as energy-efficient shaping techniques. Numerical results show that both have smaller rate losses than CCDM. SpSh—whose sole objective is to maximize the energy efficiency—is shown to have the minimum rate loss amongst all, which is particularly apparent for ultra short blocklengths. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspectives of latency, storage and computations.

scholarly journals BER Performance Analysis of Non-Coherent Q-Ary Pulse Position Modulation Receivers on AWGN Channel

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6102
Author(s):  
Xianhua Shi ◽  
Yimao Sun ◽  
Jie Tian ◽  
Maolin Chen ◽  
Youjiang Liu ◽  
...  
Keyword(s):  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Theoretical Formula ◽  
Pulse Position Modulation ◽  
Error Performance ◽  
Optimal Receiver ◽  
Awgn Channel ◽  
Simulation Results ◽  
The Relationship ◽  
Better Than

This paper introduces the structure of a Q-ary pulse position modulation (PPM) signal and presents a noncoherent suboptimal receiver and a noncoherent optimal receiver. Aiming at addressing the lack of an accurate theoretical formula of the bit error rate (BER) of a Q-ary PPM receiver in the additive white Gaussian noise (AWGN) channel in the existing literature, the theoretical formulas of the BER of a noncoherent suboptimal receiver and noncoherent optimal receiver are derived, respectively. The simulation results verify the correctness of the theoretical formulas. The theoretical formulas can be applied to a Q-ary PPM system including binary PPM. In addition, the analysis shows that the larger the Q, the better the error performance of the receiver and that the error performance of the optimal receiver is about 2 dB better than that of the suboptimal receiver. The relationship between the threshold coefficient of the suboptimal receiver and the error performance is also given.

scholarly journals Threshold Computation for Spatially Coupled Turbo-Like Codes on the AWGN Channel

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 240
Author(s):  
Muhammad Umar Farooq ◽  
Alexandre Graell i Amat ◽  
Michael Lentmaier
Keyword(s):  
Gaussian Noise ◽  
Belief Propagation ◽  
Additive White Gaussian Noise ◽  
Maximum A Posteriori ◽  
Prediction Methods ◽  
Threshold Analysis ◽  
A Posteriori ◽  
Awgn Channel ◽  
Efficient Prediction ◽  
Binary Erasure Channel

In this paper, we perform a belief propagation (BP) decoding threshold analysis of spatially coupled (SC) turbo-like codes (TCs) (SC-TCs) on the additive white Gaussian noise (AWGN) channel. We review Monte-Carlo density evolution (MC-DE) and efficient prediction methods, which determine the BP thresholds of SC-TCs over the AWGN channel. We demonstrate that instead of performing time-consuming MC-DE computations, the BP threshold of SC-TCs over the AWGN channel can be predicted very efficiently from their binary erasure channel (BEC) thresholds. From threshold results, we conjecture that the similarity of MC-DE and predicted thresholds is related to the threshold saturation capability as well as capacity-approaching maximum a posteriori (MAP) performance of an SC-TC ensemble.

scholarly journals A New Reliability Ratio Weighted Bit Flipping Algorithm for Decoding LDPC Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chakir Aqil ◽  
Ismail Akharraz ◽  
Abdelaziz Ahaitouf
Keyword(s):  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Ldpc Codes ◽  
Low Density ◽  
Parity Check ◽  
Coding Gain ◽  
Decoding Complexity ◽  
Low Density Parity Check ◽  
Awgn Channel ◽  
Infinite Loop

In this study, we propose a “New Reliability Ratio Weighted Bit Flipping” (NRRWBF) algorithm for Low-Density Parity-Check (LDPC) codes. This algorithm improves the “Reliability Ratio Weighted Bit Flipping” (RRWBF) algorithm by modifying the reliability ratio. It surpasses the RRWBF in performance, reaching a 0.6 dB coding gain at a Binary Error Rate (BER) of 10−4 over the Additive White Gaussian Noise (AWGN) channel, and presents a significant reduction in the decoding complexity. Furthermore, we improved NRRWBF using the sum of the syndromes as a criterion to avoid the infinite loop. This will enable the decoder to attain a more efficient and effective decoding performance.

scholarly journals Performance Comparison of Digitized Quaternion Modulation with other Modulation Schemes

2019 ◽  
Vol 27 ◽  
pp. 01004
Author(s):  
Anam Zahra ◽  
Qasim Umar Khan
Keyword(s):  
Global Positioning System ◽  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Performance Comparison ◽  
Superior Performance ◽  
Positioning System ◽  
Space Communication ◽  
Global Positioning ◽  
Simulation Results ◽  
Modulation Schemes

In wireless networks signal’s security from noise has been a very challenging issue, primarily because of the broadcast nature of communication. This paper focuses on digitized Quaternion Modulation (QM) which gives better performance as compared to QPSK, QAM and QFSK. We compare the performance of quaternion modulation with other modulation schemes in terms of BER using idealistic Additive White Gaussian Noise AWGN channel. This scheme can be used in applications such as Global Positioning System (GPS), satellite and space communication system to reduce errors. The simulation results show superior performance of the proposed digitized Quaternion Modulation over its counterparts. Thus one may trade off bandwidth for BER.

Parameter Estimation of Co-Channel AIS Signal Using Ambiguity Function

2014 ◽  
Vol 644-650 ◽  
pp. 4035-4039
Author(s):  
Hao Su Zhou ◽  
Jian Xin Wang
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Reference Signal ◽  
Two Dimensions ◽  
Ambiguity Function ◽  
Weak Signal ◽  
Strong Signal ◽  
Estimated Parameters ◽  
Simulation Results

A new data-aided algorithm for parameter estimation of the co-channel AIS signal transmitted over the additive white Gaussian noise channel is proposed in this paper. The co-channel signal consists of a strong signal with high power and a weak signal with low power. The parameters of the strong signal are estimated by searching the ambiguity function of the co-channel signal in two dimensions. A reference signal is therefore reconstructed with the estimated parameters and the aided data. By removing the ambiguity function of the reconstructed reference signal from that of the original co-channel signal, a new co-channel signal ambiguity function is obtained, from which the parameters of the weak signal are estimated. The simulation results illustrate that the proposed algorithm can estimate the parameters of the co-channel AIS signal effectively.

Research on Overlapped Time Division Multiplexing in the Amplify-and-Forward Cooperative Mode

2015 ◽  
Vol 713-715 ◽  
pp. 1103-1106
Author(s):  
Hong Zhang ◽  
Wei Ping Ma
Keyword(s):  
Cooperative Communication ◽  
Gaussian Noise ◽  
Communication System ◽  
Additive White Gaussian Noise ◽  
Spectrum Efficiency ◽  
Amplify And Forward ◽  
Time Division Multiplexing ◽  
Simulation Results ◽  
Time Division ◽  
New System

In order to improve spectrum efficiency of cooperative communication system, Overlapped Time Division Multiplexing (OVTDM) is applied to Amplify-and-Forward (AF) cooperative communication system. The simulation results under Additive White Gaussian Noise (AWGN) channel show that the performance of new system is superior to that of corresponding AF cooperative communication system.

scholarly journals Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

2021 ◽  
Author(s):  
Ramazan Duram ◽  
Murat Güzeltepe
Keyword(s):  
Gaussian Noise ◽  
Figure Of Merit ◽  
Residue Class ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Average Energy ◽  
Division Algorithm ◽  
Prime Integer ◽  
Awgn Channel ◽  
Signal Constellations

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

scholarly journals Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small division” property

2021 ◽  
Author(s):  
Ramazan Duram ◽  
Murat Güzeltepe
Keyword(s):  
Gaussian Noise ◽  
Figure Of Merit ◽  
Residue Class ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Average Energy ◽  
Division Algorithm ◽  
Prime Integer ◽  
Awgn Channel ◽  
Signal Constellations

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

scholarly journals Hierarchical Distribution Matching for Probabilistic Amplitude Shaping

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 958
Author(s):  
Stella Civelli ◽  
Marco Secondini
Keyword(s):  
Lower Layer ◽  
Minimum Energy ◽  
Single Layer ◽  
Low Complexity ◽  
Design Guidelines ◽  
Constant Composition ◽  
Distribution Matching ◽  
Practical Design ◽  
Rate Loss ◽  
Complexity Increase

Probabilistic amplitude shaping—implemented through a distribution matcher (DM)—is an effective approach to enhance the performance and the flexibility of bandwidth-efficient coded modulations. Different DM structures have been proposed in the literature. Typically, both their performance and their complexity increase with the block length. In this work, we present a hierarchical DM (Hi-DM) approach based on the combination of several DMs of different possible types, which provides the good performance of long DMs with the low complexity of several short DMs. The DMs are organized in layers. Each upper-layer DM encodes information on a sequence of lower-layer DMs, which are used as “virtual symbols”. First, we describe the Hi-DM structure, its properties, and the encoding and decoding procedures. Then, we present three particular Hi-DM configurations, providing some practical design guidelines, and investigating their performance in terms of rate loss and energy loss. Finally, we compare the system performance obtained with the proposed Hi-DM structures and with their single-layer counterparts: a 0.19dB SNR gain is obtained by a two-layer Hi-DM based on constant composition DMs (CCDM) compared to a single-layer CCDM with same complexity; a 0.12dB gain and a significant complexity reduction are obtained by a Hi-DM based on minimum-energy lookup tables compared to a single-layer DM based on enumerative sphere shaping with same memory requirements.

scholarly journals Encoder Lipschitz Integers: The Lipschitz integers that have the ”division with small remainder” property

2021 ◽  
Author(s):  
Ramazan Duran ◽  
Murat Güzeltepe
Keyword(s):  
Gaussian Noise ◽  
Figure Of Merit ◽  
Residue Class ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Average Energy ◽  
Division Algorithm ◽  
Prime Integer ◽  
Awgn Channel ◽  
Signal Constellations

Abstract The residue class set of a Lipschitz integer is constructed by modulo function with primitive Lipschitz integer whose norm is a prime integer, i.e. prime Lipschitz integer. In this study, we consider primitive Lipschitz integer whose norm is both a prime integer and not a prime integer. If the norm of each element of the residue class set of a Lipschitz integer is less than the norm of the primitive Lipschitz integer used to construct the residue class set of the Lipschitz integer, then, the Euclid division algorithm works for this primitive Lipschitz integer. The Euclid division algorithm always works for prime Lipschitz integers. In other words, the prime Lipschitz integers have the ”division with small remainder” property. However, this property is ignored in some studies that have a constructed Lipschitz residue class set that lies on primitive Lipschitz integers whose norm is not a prime integer. In this study, we solve this problem by defining Lipschitz integers that have the ”division with small remainder” property, namely, encoder Lipschitz integers set. Therefore, we can define appropriate metrics for codes over Lipschitz integers. Also, we investigate the performances of Lipschitz signal constellations (the left residue class set) obtained by modulo function with Lipschitz integers, which have the ”division with small remainder” property, over the additive white Gaussian noise (AWGN) channel by agency of the constellation figure of merit (CFM), average energy, and signal-to-noise ratio (SNR).

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