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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  ...  and double-binary turbo codes associated with Max-Log-MAP decoding.  ...  If we consider channel coding and LP as separate tasks, the optimal detector for the LP task is based on ML decoding.  ... 
doi:10.24138/jcomss.v2i3.282 fatcat:vbybemis3vgdhb7i7nru7obidq

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.  ...  Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message  ...  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

Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets [article]

Eirik Rosnes, Øyvind Ytrehus
2006 arXiv   pre-print
The solution is based on the algorithm proposed by Garello et al. in 2001 to compute an exhaustive list of all low-weight codewords in a turbo code.  ...  Finally, we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption, and an efficient enumeration algorithm of small-size turbo stopping sets for  ...  In [1] , an iterative decoding algorithm for LDPC codes over the BEC was proposed, and it was shown that this scheme approaches channel capacity arbitrarily close.  ... 
arXiv:cs/0602072v1 fatcat:3jyq5tvtrjainndz4y4s6c2ye4

Provably efficient instanton search algorithm for LP decoding of LDPC codes over the BSC [article]

Shashi Kiran Chilappagari, Michael Chertkov, Bane Vasic
2008 arXiv   pre-print
We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC).  ...  We prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice  ...  Vontobel for his comments and suggestions and D. Sridhara for his clarifications regarding Lemma 1. The work by S. K Chilappagari was performed when he was a summer GRA at LANL.  ... 
arXiv:0808.2515v2 fatcat:putveumgereslf4k776frr3rxy

An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSC

Shashi Kiran Chilappagari, Michael Chertkov, Bane Vasic
2011 IEEE Transactions on Information Theory  
We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC).  ...  We prove that: (a) the LP decoder fails for any error pattern with support that is a superset of the support of an instanton; (b) for any input, the ISA outputs an instanton in the number of steps upper-bounded  ...  flexibility and feasibility of an LP-based ML for moderately large codes [21] , [22] .  ... 
doi:10.1109/tit.2011.2146670 fatcat:vpcj74lywrgnvegq6niafrqruu

Deriving Good LDPC Convolutional Codes from LDPC Block Codes [article]

Ali E. Pusane, Roxana Smarandache, Pascal O. Vontobel, Daniel J. Costello Jr
2010 arXiv   pre-print
In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional  ...  We investigate some possible reasons for this "convolutional gain," and we also discuss the --- mostly moderate --- decoder cost increase that is incurred by going from LDPC block to LDPC convolutional  ...  ACKNOWLEDGMENTS The authors would like to thank Chris Jones, Michael Lentmaier, David Mitchell, Michael Tanner, and Kamil Zigangirov for their valuable discussions and comments.  ... 
arXiv:1004.5157v3 fatcat:x7viyypw7fhxvm4l7ujq75cmii

Towards combinatorial LP turbo decoding

Michael Helmling, Stefan Ruzika
2013 2013 IEEE International Symposium on Information Theory  
A numerical study shows that our algorithm clearly beats the running time, up to a factor of 100, of generic commercial LP solvers for medium-sized codes, especially for high SNR values.  ...  We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in  ...  University of Kaiserslautern for financial support.  ... 
doi:10.1109/isit.2013.6620475 dblp:conf/isit/HelmlingR13 fatcat:gkr2cwtxo5hutd67ysplawv6lu

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.  ...  Section IV introduces our proposed irregular distributed codes design based on EXIT chart and codes search by utilizing a LP algorithm. Section V presents the simulation results.  ... 
doi:10.1109/icc.2011.5962869 dblp:conf/icc/PangLLV11 fatcat:fgsiin6cffbyloiegufu7otiqa

Spatially coupled LDPC coding in cooperative wireless networks

Dushantha Nalin K. Jayakody, Vitaly Skachek, Bin Chen
2016 EURASIP Journal on Advances in Signal Processing  
We introduce an array-based optimized SC-LDPC codes in relay channels.  ...  It was observed in [12] that the so-called "convolutional LDPC codes" outperform classical LDPC block codes.  ...  Acknowledgment The authors wish to thank Eirik Rosnes, University of Bergen, Norway, and Michael Lentmaier, Lund University, Sweden, for the helpful discussions.  ... 
doi:10.1186/s13634-016-0311-9 fatcat:ip3w775rhnb2tevn4xmj4kaeai

Spatially-coupled LDPC coding in cooperative wireless networks

Dushantha Nalin K. Jayakody, Vitaly Skachek, Bin Chen
2016 2016 IEEE Wireless Communications and Networking Conference  
We introduce an array-based optimized SC-LDPC codes in relay channels.  ...  It was observed in [12] that the so-called "convolutional LDPC codes" outperform classical LDPC block codes.  ...  Acknowledgment The authors wish to thank Eirik Rosnes, University of Bergen, Norway, and Michael Lentmaier, Lund University, Sweden, for the helpful discussions.  ... 
doi:10.1109/wcnc.2016.7564992 dblp:conf/wcnc/JayakodySC16 fatcat:xvvraq5a3rgszc5a2jfkucuo5e

Introduction to Mathematical Programming-Based Error-Correction Decoding [article]

Michael Helmling
2015 arXiv   pre-print
At first celebrated mainly for its analytical powers, real-world applications of LP decoding are now within reach thanks to most recent research.  ...  Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods  ...  They are constructed by combining two or more (terminated) convolutional codes.  ... 
arXiv:1509.01117v1 fatcat:tifcrkwr2rcehaigpgyvlf4xhm

Error Bounds for Repeat-Accumulate Codes Decoded via Linear Programming [article]

Idan Goldenberg, David Burshtein
2010 arXiv   pre-print
For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a linear-programming based decoder which is an inverse polynomial in the block  ...  Our bound is valid for any memoryless, binary-input, output-symmetric (MBIOS) channel. This result generalizes the bound derived by Feldman et al., which was for regular RA(2) codes.  ...  While the first analytic result for LP decoding [13] has been for the case of RA codes, most of the results for LP decoding thereafter refer to LDPC codes.  ... 
arXiv:0904.1692v2 fatcat:3tpdselhpvb7vhfu75pvfiwpy4

Decoding Reed-Muller Codes Using Minimum-Weight Parity Checks [article]

Elia Santi, Christian Häger, Henry D. Pfister
2018 arXiv   pre-print
and BP decoding for the binary symmetric channel.  ...  As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping  ...  Promising contenders include modified polar codes, low-density parity-check (LDPC) codes, and tailbiting convolutional codes [1] - [3] .  ... 
arXiv:1804.10319v1 fatcat:dx6o3qq4kbbubiyqibnfxlunp4

Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks

Elia Santi, Christian Hager, Henry D. Pfister
2018 2018 IEEE International Symposium on Information Theory (ISIT)  
and BP decoding for the binary symmetric channel.  ...  As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping  ...  Promising contenders include modified polar codes, low-density parity-check (LDPC) codes, and tailbiting convolutional codes [1] - [3] .  ... 
doi:10.1109/isit.2018.8437637 dblp:conf/isit/SantiHP18 fatcat:4kvseoxu6jhfxls7ud53vq5hzm

Fifteen Years of Quantum LDPC Coding and Improved Decoding Strategies

Zunaira Babar, Panagiotis Botsinis, Dimitrios Alanis, Soon Xin Ng, Lajos Hanzo
2015 IEEE Access  
The near-capacity performance of classical low-density parity check (LDPC) codes and their efficient iterative decoding makes quantum LDPC (QLPDC) codes a promising candidate for quantum error correction  ...  Finally, we intricately amalgamate our modified decoder with the classic uniformly reweighted belief propagation for the sake of achieving an improved performance.  ...  We also review the syndrome-based iterative decoding algorithms invoked for QLDPC codes.  ... 
doi:10.1109/access.2015.2503267 fatcat:j2tsdl4dpvdkhpeglk56yh35om
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