scholarly journals A Survey on Old and New Approximations to the Function ϕ(x) Involved in LDPC Codes Density Evolution Analysis Using a Gaussian Approximation

Information ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 212
Author(s):  
Francesca Vatta ◽  
Alessandro Soranzo ◽  
Massimiliano Comisso ◽  
Giulia Buttazzoni ◽  
Fulvio Babich
Keyword(s):  
Probability Distribution Function ◽  
Iterative Decoding ◽  
Gaussian Approximation ◽  
Ldpc Codes ◽  
Parity Check ◽  
Recurrent Sequence ◽  
Evolution Analysis ◽  
Low Density Parity Check ◽  
Log Likelihood ◽  
Convergence Performance

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution function of the decoder’s log-likelihood ratio messages is roughly Gaussian, a multiplicity of moderate entanglement strategies to this analysis has been suggested. The first of them was proposed in Chung et al.’s 2001 paper, where the recurrent sequence, characterizing the passage of messages between variable and check nodes, concerns the function ϕ(x), therein specified, and its inverse. In this paper, we review this old approximation to the function ϕ(x), one variant on it obtained in the same period (proposed in Ha et al.’s 2004 paper), and some new ones, recently published in two 2019 papers by Vatta et al. The objective of this review is to analyze the differences among them and their characteristics in terms of accuracy and computational complexity. In particular, the explicitly invertible, not piecewise defined approximation of the function ϕ(x), published in the second of the two abovementioned 2019 papers, is shown to have less relative error in any x than most of the other approximations. Moreover, its use conducts to an important complexity reduction, and allows better Gaussian approximated thresholds to be obtained.

Study on a New Joint Source-Channel Decoder Design

2013 ◽  
Vol 340 ◽  
pp. 471-475
Author(s):  
Fei Zhong ◽  
Shu Xu Guo
Keyword(s):  
Iterative Decoding ◽  
Ldpc Codes ◽  
Low Density ◽  
Parity Check ◽  
Information Redundancy ◽  
Low Density Parity Check ◽  
Error Ratio ◽  
Bit Error Ratio ◽  
Simulation Results ◽  
Decoder Design

To improve upon the Low-Density Parity-Check (LDPC) codes , incorporating compressed sensing (CS) and information redundancy, a new joint decoding algorithm frame is presented. The proposed system exploits the information redundancy by CS reconstruction during the iterative decoding process to correct decoding of LDPC codes. The simulation results show that the algorithm presented can improve system decoding performance and obviously make bit error ratio (BER) lower then traditional LDPC codes. In addition, a relatively short argument is given on different CS reconstructed algorithms in proposed system, the new design is shown to benefit from different CS reconstructed algorithms.

LDPC Codes with the Layered LLR-BP Algorithm for 3GPP

2013 ◽  
Vol 462-463 ◽  
pp. 720-723
Author(s):  
Miao Miao Li ◽  
Jian Ping Li ◽  
Chao Shi Cai
Keyword(s):  
Belief Propagation ◽  
Ldpc Codes ◽  
Bp Algorithm ◽  
Parity Check ◽  
Computation Complexity ◽  
Decoding Algorithm ◽  
Absolute Value ◽  
Low Density Parity Check ◽  
Variable Node ◽  
Log Likelihood

We propose a layered log-likelihood-ratio-based belief propagation(LLR-BP)algorithm for Low Density Parity Check (LDPC)codes. In the conventional decoding algorithm, the process of decoding would be terminated when it reaches the maximum iterative number or the near-convergence is achieved. The proposed algorithm is based on the variable node information quantification and stop updating criterion thought. By dividing the absolute value of the variable node to different layers, a part of the check nodes stop the iteration before reaching the maximum iterative number to save iterative time. From the simulation results, we know that the improved decoding algorithm successively achieves lower computation complexity than the conventional one .And the layered LLR-BP algorithm is a better scheme for LDPC codes.

scholarly journals Construction and Decoding of Rate-Compatible Globally Coupled LDPC Codes

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Ji Zhang ◽  
Baoming Bai ◽  
Xijin Mu ◽  
Hengzhou Xu ◽  
Zhen Liu ◽  
...  
Keyword(s):  
Iterative Decoding ◽  
Classical Method ◽  
Ldpc Codes ◽  
Algebraic Method ◽  
Parity Check ◽  
Rate Code ◽  
Algebraic Construction ◽  
Two Phase ◽  
Low Density Parity Check ◽  
Wide Range

This paper presents a family of rate-compatible (RC) globally coupled low-density parity-check (GC-LDPC) codes, which is constructed by combining algebraic construction method and graph extension. Specifically, the highest rate code is constructed using the algebraic method and the codes of lower rates are formed by successively extending the graph of the higher rate codes. The proposed rate-compatible codes provide more flexibility in code rate and guarantee the structural property of algebraic construction. It is confirmed, by numerical simulations over the AWGN channel, that the proposed codes have better performances than their counterpart GC-LDPC codes formed by the classical method and exhibit an approximately uniform gap to the capacity over a wide range of rates. Furthermore, a modified two-phase local/global iterative decoding scheme for GC-LDPC codes is proposed. Numerical results show that the proposed decoding scheme can reduce the unnecessary cost of local decoder at low and moderate SNRs, without any increase in the number of decoding iterations in the global decoder at high SNRs.

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.

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