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Turbo codes and turbo algorithms

Claude Berrou, Charlotte Langlais, Yi Yu
2017 Journal of Communications Software and Systems  
We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes  ...  We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance.  ...  This method is just a tool to gauge the quality of coding/decoding schemes and has no application in real systems.  ... 
doi:10.24138/jcomss.v2i3.282 fatcat:vbybemis3vgdhb7i7nru7obidq

Low-Complexity LP Decoding of Nonbinary Linear Codes

Mayur Punekar, Pascal O. Vontobel, Mark F. Flanagan
2013 IEEE Transactions on Communications  
It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.  ...  Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years.  ...  The authors would like to thank Maria José Canet Subiela for her valuable support in their simulation work.  ... 
doi:10.1109/tcomm.2013.070213.120801 fatcat:cibagfanqberbilffkp36724h4

Multicore implementation of LDPC decoders based on ADMM algorithm

Imen Debbabi, Nadia Khouja, Fethi Tlili, Bertrand Le Gal, Christophe Jego
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
two binary vectors of Hamming weight r and r + 2, for some even integer Error correction performance The ADMM LP decoding has proven its e ciency as an error correction approach [31] against traditional  ...  An adjustle precision floating point for both data and computaformed to improve the processing efficiency without the correction performance of the decoder.  ...  The parallelism levels available for SPMD parallelization ๏ INTEL Core-i7 has many physical cores having each a SIMD unit, ๏ Switching to many-core devices ?  ... 
doi:10.1109/icassp.2016.7471820 dblp:conf/icassp/DebbabiKTGJ16 fatcat:ntmo7fs6qjek5ay7lrhgfuf5yq

Design of LDPC Decoder Based On FPGA in Digital Image Watermarking Technology

Zhongxun Wang, Tiantian Tang
2017 TELKOMNIKA (Telecommunication Computing Electronics and Control)  
In this paper, MATLAB software and Qt development environment are combined to achieve the digital watermarking application software design. It could get real-time input data for the LDPC decoder.  ...  In order to realize FPGA design of LDPC decoder in the application scheme, an effective implementation method of digital watermarking application system must be found.  ...  It could get real-time input data for the LDPC decoder. The hardware of the LDPC decoder is primarily implemented by FPGA in digital image watermarking system.  ... 
doi:10.12928/telkomnika.v15i1.4044 fatcat:jqlpb5hdujh7ndrn6sftb7opfq

Parameter-free ℓ_p-Box Decoding of LDPC Codes [article]

Qiong Wu, Fan Zhang, Hao Wang, Jun Lin, Yang Liu
2018 arXiv   pre-print
The Alternating Direction Method of Multipliers (ADMM) decoding of Low Density Parity Check (LDPC) codes has received many attentions due to its excellent performance at the error floor region.  ...  In this paper, we develop a parameter-free decoder based on Linear Program (LP) decoding by replacing the binary constraint with the intersection of a box and an ℓ_p sphere.  ...  For binary LDPC codes over symmetric channels, Feldman introduced a relaxed version [3] , [4] of Maximum Likelihood (ML) decoding problem which can be interpreted as a Linear Program (LP) decoding,  ... 
arXiv:1711.10767v2 fatcat:h4rr2rtms5h6vjbhojd56q322a

Decomposition Methods for Large Scale LP Decoding [article]

Siddharth Barman and Xishuo Liu and Stark C. Draper and Benjamin Recht
2013 arXiv   pre-print
We present numerical results for LDPC codes of lengths more than 1000.  ...  However, LP decoding when implemented with standard LP solvers does not easily scale to the block lengths of modern error correcting codes.  ...  Acknowledgements The authors would like to thank Matthew Anderson, Eric Bach, Brian Butler, Alex Dimakis, Paul Sigel, Emre Telatar, Yige Wang, Jonathan Yedidia and Dalibor Zelený for useful discussions  ... 
arXiv:1204.0556v2 fatcat:jq4vql6kffcbhcmcgsvsmku35y

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Michael Helmling, Stefan Ruzika, Akın Tanatmis
2012 IEEE Transactions on Information Theory  
This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.  ...  Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory.  ...  Vontobel and Frank Kienle for their comments and suggestions. We also thank the anonymous referees for the helpful reviews.  ... 
doi:10.1109/tit.2012.2191697 fatcat:zyv2tbnkxvhlzps5mleuxln4va

Ultra-Low-Power Error Correction Circuits: Technology Scaling and Sub-$V_{ \rm T}$ Operation

Chris Winstead, Joachim Neves Rodrigues
2012 IEEE Transactions on Circuits and Systems - II - Express Briefs  
Techniques are evaluated for implementing error correction codes in wireless applications with severe power constraints, such as bio-implantable devices and energy harvesting motes.  ...  Index Terms-Analog decoders, biomedical implants, error correction codes (ECC), sub-threshold, ultra-low voltage.  ...  INTRODUCTION E RROR correction codes (ECC) are widely used to optimize performance in wireless communication devices.  ... 
doi:10.1109/tcsii.2012.2231040 fatcat:xywl3dnpizbt7lyno4rhpbofeq

Divide and Concur and Difference-Map BP Decoders for LDPC Codes

Jonathan S. Yedidia, Yige Wang, Stark C. Draper
2011 IEEE Transactions on Information Theory  
We investigate two decoders for low-density parity-check (LDPC) codes based on these ideas.  ...  We present simulation results for LDPC codes on the additive white Gaussian noise and binary symmetric channels, comparing DC and DMBP decoders with other decoders based on BP, linear programming, and  ...  Unfortunately, BP decoders of LDPC codes often suffer from "error floors" in the high SNR regime, which is a significant problem for applications that have extreme reliability requirements, including magnetic  ... 
doi:10.1109/tit.2010.2094815 fatcat:ozrfjglht5hedkpqqjzbcub6ta

Divide & Concur and Difference-Map BP Decoders for LDPC Codes [article]

Jonathan S. Yedidia, Yige Wang, Stark C. Draper
2010 arXiv   pre-print
We investigate two decoders for low-density parity-check (LDPC) codes based on these ideas.  ...  We present simulation results for LDPC codes on the additive white Gaussian noise and binary symmetric channels, comparing DC and DMBP decoders with other decoders based on BP, linear programming, and  ...  Unfortunately, BP decoders of LDPC codes often suffer from "error floors" in the high SNR regime, which is a significant problem for applications that have extreme reliability requirements, including magnetic  ... 
arXiv:1001.1730v1 fatcat:fnh7hx7vqzbjpjwzdkbv3ijnoe

Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes

Xiaojie Zhang, Paul H. Siegel
2012 IEEE Transactions on Information Theory  
Simulation results for several low-density parity-check (LDPC) codes demonstrate that the proposed decoding algorithms significantly narrow the performance gap between LP decoding and ML decoding.  ...  Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem  ...  When used with ALP decoding, the cuts have been found empirically to achieve near-ML decoding performance in the high SNR regime for several short-to-moderate length LDPC codes.  ... 
doi:10.1109/tit.2012.2204955 fatcat:fw7rttjlzrdejkor2fo3ekw2xe

Compressed sensing and linear codes over real numbers

Fan Zhang, Henry D. Pfister
2008 2008 Information Theory and Applications Workshop  
While coding theory does not typically deal with codes over real numbers, there is actually a very close relationship between CS and error-correcting codes over large discrete alphabets.  ...  In this paper, we analyze CS using tools from coding theory because CS can also be viewed as syndrome-based source coding of sparse vectors using linear codes over real numbers.  ...  In many applications, the two relevant performance measures are the oversampling ratio m/k required for good performance and the computational complexity of reconstruction.  ... 
doi:10.1109/ita.2008.4601055 fatcat:kodvzmq5fvbzpip6c7gibde3jm

An integer programming-based search technique for error-prone structures of LDPC codes

Abdullah Sarıduman, Ali E. Pusane, Z. Caner Taşkın
2014 AEU - International Journal of Electronics and Communications  
In this paper, an efficient, general framework is presented for finding common, devastating error-prone structures (EPS) of any finite-length low-density parity-check (LDPC) code.  ...  The smallest stopping set for the binary erasure channel (BEC), the smallest fully absorbing set, the smallest absorbing set, and the smallest elementary trapping set for the binary symmetric channel (  ...  In [25] , cycles of the parity-check matrix of an LDPC code are used to improve the LP decoder performance.  ... 
doi:10.1016/j.aeue.2014.05.012 fatcat:gn2xptz62vbrhh2uz2nxmhs4m4

Design of Distributed Network-Channel Codes for Wireless Sensor Networks

Kun Pang, Zihuai Lin, Yonghui Li, Branka Vucetic
2011 2011 IEEE International Conference on Communications (ICC)  
We formulate the code design and code search as a linear programming (LP) problem.  ...  Simulation results of the proposed irregular codes show that a considerable performance improvement can be achieved in the waterfall region compared with the existing codes.  ...  This research work is supported by Norman I Price Scholarship, School of Electrical and Information Engineering, The University of Sydney Postgraduate Award Scholarship, and Australian Research Council  ... 
doi:10.1109/icc.2011.5962869 dblp:conf/icc/PangLLV11 fatcat:fgsiin6cffbyloiegufu7otiqa

Hardware-Based Linear Program Decoding with the Alternating Direction Method of Multipliers

Mitchell Wasson, Mario Milicevic, Stark Draper, Patrick G. Gulak
2019 IEEE Transactions on Signal Processing  
This thesis is concerned with the hardware implementation of Linear Program (LP) decoding for Low-Density Parity-Check (LDPC) codes.  ...  Until recently, LDPC codes have been decoded exclusively by means of graphical inference using belief propagation (BP).  ...  In [13] it is proved that if (2.5) gives an all-integer solution, then it is the ML decoding. This certificate of correctness can be very attractive for high-reliability applications.  ... 
doi:10.1109/tsp.2019.2929944 fatcat:h7yprh5yd5fshhthnsslmckrc4
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