scholarly journals Design of Nonbinary LDPC Cycle Codes with Large Girth from Circulants and Finite Fields

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hengzhou Xu ◽  
Huaan Li ◽  
Jixun Gao ◽  
Guixiang Zhang ◽  
Hai Zhu ◽  
...  
Keyword(s):  
Finite Fields ◽  
Gaussian Noise ◽  
Iterative Decoding ◽  
Additive White Gaussian Noise ◽  
Ldpc Codes ◽  
Parity Check ◽  
Undirected Graphs ◽  
Awgn Channel ◽  
Exponent Matrix ◽  
Large Girth

In this paper, we study a class of nonbinary LDPC (NBLDPC) codes whose parity-check matrices have column weight 2, called NBLDPC cycle codes. We propose a design framework of 2 , ρ -regular binary quasi-cyclic (QC) LDPC codes and then construct NBLDPC cycle codes of large girth based on circulants and finite fields by randomly choosing the nonzero field elements in their parity-check matrices. For enlarging the girth values, our approach is twofold. First, we give an exhaustive search of circulants with column/row weight ρ and design a masking matrix with good cycle distribution based on the edge-node relation in undirected graphs. Second, according to the designed masking matrix, we construct the exponent matrix based on finite fields. The iterative decoding performances of the constructed codes on the additive white Gaussian noise (AWGN) channel are finally provided.

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 A Construction of High Performance Quasicyclic LDPC Codes: A Combinatoric Design Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Asif ◽  
Wuyang Zhou ◽  
Muhammad Ajmal ◽  
Zain ul Abiden Akhtar ◽  
Nauman Ali Khan
Keyword(s):  
Iterative Decoding ◽  
High Performance ◽  
Linear Complexity ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Ldpc Codes ◽  
Combinatorial Designs ◽  
Parity Check ◽  
Excellent Performance ◽  
Moderate Length

This correspondence presents a construction of quasicyclic (QC) low-density parity-check (LDPC) codes based on a special type of combinatorial designs known as block disjoint difference families (BDDFs). The proposed construction of QC-LDPC codes gives parity-check matrices with column weight three and Tanner graphs having a girth lower-bounded by 6. The proposed QC-LDPC codes provide an excellent performance with iterative decoding over an additive white Gaussian-noise (AWGN) channel. Performance analysis shows that the proposed short and moderate length QC-LDPC codes perform as well as their competitors in the lower signal-to-noise ratio (SNR) region but outperform in the higher SNR region. Also, the codes constructed are quasicyclic in nature, so the encoding can be done with simple shift-register circuits with linear complexity.

scholarly journals Iterative Soft Permutation Decoding of Product Codes

2016 ◽  
Vol 9 (1) ◽  
pp. 128 ◽  
Author(s):  
Mohamed Askali ◽  
Fouad Ayoub ◽  
Idriss Chana ◽  
Mostafa Belkasmi
Keyword(s):  
Gaussian Noise ◽  
Iterative Decoding ◽  
Additive White Gaussian Noise ◽  
Quadratic Residue ◽  
White Gaussian Noise ◽  
Permutation Decoding ◽  
Product Codes ◽  
Quadratic Residue Codes ◽  
Numerical Result ◽  
Awgn Channel

<p>In this paper the performance of product codes based on quadratic residue codes is investigated. Our Proposed<br />Iterative decoding SISO based on a soft permutation decoding algorithm (SPDA) as a component decoder.<br />Numerical result for the proposed algorithm over Additive White Gaussian Noise (AWGN) channel is provided.<br />Results show that the turbo effect of the proposed decoder algorithm is established for this family of quadratic<br />residue codes.</p>

Chase-Like Decoding of Arithmetic Codes with Applications

2013 ◽  
pp. 27-41
Author(s):  
Amin Zribi ◽  
Sonia Zaibi ◽  
Ramesh Pyndiah ◽  
Ammar Bouallègue
Keyword(s):  
Image Compression ◽  
Gaussian Noise ◽  
Iterative Decoding ◽  
Convolutional Code ◽  
Additive White Gaussian Noise ◽  
Error Rates ◽  
Sequence Estimation ◽  
Awgn Channel ◽  
Arithmetic Codes ◽  
Classical Arithmetic

Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

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 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 Rate-compatible LDPC convolutional codes over non-gaussian noise channel

2020 ◽  
Vol 309 ◽  
pp. 01010
Author(s):  
Qiang Liu
Keyword(s):  
Gaussian Noise ◽  
Iterative Decoding ◽  
Belief Propagation ◽  
Additive White Gaussian Noise ◽  
Convolutional Codes ◽  
Gaussian Mixture ◽  
Performance Study ◽  
Shift Keying ◽  
Non Gaussian ◽  
The Impact

This paper is aimed to study the characteristics of the underwater acoustic channel with non-Gaussian noise channel. And Gaussian mixture model (GMM) is utilized to fit the background noise over the non-Gaussian noise channel. Furthermore, coding techniques which use a sequence of rate-compatible low-density parity-check (RC-LDPC) convolutional codes with separate rates are constructed based on graph extension method. The performance study of RC-LDPC convolutional codes over non-Gaussian noise channel and the additive white Gaussian noise (AWGN) channel is performed. Study implementation of simulation is that modulation with binary phase shift keying (BPSK), and iterative decoding based on pipeline log-likelihood rate belief propagation (LLRBP) algorithm. Finally, it is shown that RC-LDPC convolutional codes have good bit-rate-error (BER) performance and can effectively reduce the impact of noise.

scholarly journals A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Asif ◽  
Wuyang Zhou ◽  
Qingping Yu ◽  
Xingwang Li ◽  
Nauman Ali Khan
Keyword(s):  
Fading Channels ◽  
Iterative Decoding ◽  
Rayleigh Fading ◽  
Additive White Gaussian Noise ◽  
Ldpc Codes ◽  
Destination Node ◽  
Relay Nodes ◽  
Binary Matrix ◽  
Relay Cooperation ◽  
Joint Iterative Decoding

This correspondence presents a jointly designed quasicyclic (QC) low-density parity-check (LDPC) coded-relay cooperation with joint-iterative decoding in the destination node. Firstly, a design-theoretic construction of QC-LDPC codes based on a combinatoric design approach known as optical orthogonal codes (OOC) is presented. Proposed OOC-based construction gives three classes of binary QC-LDPC codes with no length-4 cycles by utilizing some known ingredients including binary matrix dispersion of elements of finite field, incidence matrices, and circulant decomposition. Secondly, the proposed OOC-based construction gives an effective method to jointly design length-4 cycles free QC-LDPC codes for coded-relay cooperation, where sum-product algorithm- (SPA-) based joint-iterative decoding is used to decode the corrupted sequences coming from the source or relay nodes in different time frames over constituent Rayleigh fading channels. Based on the theoretical analysis and simulation results, proposed QC-LDPC coded-relay cooperations outperform their competitors under same conditions over the Rayleigh fading channel with additive white Gaussian noise.

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).

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