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A Generalized Algebraic Approach to Optimizing SC-LDPC Codes [article]

Allison Beemer, Salman Habib, Christine A. Kelley, Joerg Kliewer
2017 arXiv   pre-print
In this paper, we unify all existing SC-LDPC code construction methods under a new generalized description of SC-LDPC codes based on algebraic lifts of graphs.  ...  We present an improved low-complexity counting method for the special case of (3,3)-absorbing sets for array-based SC-LDPC codes, which we then use to optimize permutation assignments in SC-LDPC code construction  ...  SC-LDPC Codes from Algebraic Lifts In the protograph approach to SC-LDPC code construction, a base Tanner graph is copied and coupled to form the SCprotograph.  ... 
arXiv:1710.03619v1 fatcat:5qgv6hjwkncyng6iszpzcyr2eu

Spatially-coupled codes for optical communications: state-of-the-art and open problems

Alexandre Graell i Amat, Christian Hager, Fredrik Brannstrom, Erik Agrell
2015 2015 Opto-Electronics and Communications Conference (OECC)  
We give a brief survey of a particularly interesting class of codes, called spatially-coupled codes, which are strong candidates for future optical communication systems.  ...  We discuss some recent research on this class of codes in the area of optical communications, and summarize some open research problems.  ...  In practice, however, SC-LDPC codes need to be terminated to operate with a finite block length.  ... 
doi:10.1109/oecc.2015.7340116 fatcat:xh4zbyh3srgqvgdeyefcns2obq

Algebraic Optimization of Binary Spatially Coupled Measurement Matrices for Interval Passing [article]

Salman Habib, Joerg Kliewer
2018 arXiv   pre-print
As a consequence, IPA-based reconstruction with SC measurement matrices is able to provide an almost error free reconstruction for significantly denser signal vectors compared to uncoupled AB LDPC measurement  ...  The IPA is known to fail due to the presence of harmful sub-structures in the Tanner graph of a binary sparse measurement matrix, so called termatiko sets.  ...  Note that AB SC LDPC codes can be constructed via an edge-spreading process applied to a base Tanner graph of the LDPC block code (BC), yielding an SC protograph.  ... 
arXiv:1809.05647v1 fatcat:d4akvtlaebf2vi643ejn2nchki

Memory Efficient Decoders using Spatially Coupled Quasi-Cyclic LDPC Codes [article]

Vikram Arkalgud Chandrasetty, Sarah J. Johnson, Gottfried Lechner
2013 arXiv   pre-print
In this paper we propose the construction of Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes using a periodic time-variant Quasi-Cyclic (QC) algorithm.  ...  It is shown that the proposed QC SC-LDPC code (with optimization) can be stored with reasonable logic resources and without the need of block memory in the FPGA.  ...  The staircase structure of the SC-LDPC codes offers a unique opportunity to optimize the QC based technique to further reduce the hardware resources required for the decoder.  ... 
arXiv:1305.5625v2 fatcat:v7oilymhovcalc55lg2dshd4ta

Message from the general chairs

Ramesh Jain, Mohan Kumar
2008 2008 International Symposium on a World of Wireless, Mobile and Multimedia Networks  
A unified approach to optimization of LDPC codes for various communication scenarios A unified approach to construct and optimize codes determined by their sparse parity-check matrices is presented.  ...  Several algebraic methods for constructing non-binary LDPC codes are presented.  ... 
doi:10.1109/wowmom.2008.4594797 dblp:conf/wowmom/JainK08 fatcat:ziu25issdvga7cmqjgbtqtdu7q

Nested Array-Based Spatially Coupled LDPC Codes [article]

Salman Habib, David G. M. Mitchell, Joerg Kliewer
2021 arXiv   pre-print
In this paper, we consider nested array-based spatially coupled low-density parity-check (SC-LDPC) codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing  ...  To tackle these constraints, a multi-step optimization process is applied first to one of the nested codes, then sequential optimization of the remaining nested codes is carried out based on the constraints  ...  Hence, the optimized nested QC-SC-LDPC codes are expected to have better error-floor performance when constructed via Method 1 or 2 compared to randomly generated QC-SC-LDPC codes. VI.  ... 
arXiv:2102.10623v1 fatcat:om5zrxdtjjf4lpv6babqusd4fa

FPGA implementation of rate-adaptive spatially coupled LDPC codes suitable for optical communications

Xiaole Sun, Ivan B. Djordjevic
2019 Optics Express  
The implemented unified structure can be employed for any template QC-LDPC code to achieve a spatially-coupling based code-rate adaptation scheme. K K QC J J J K  ...  In this paper, we propose a unified field-programmable gate array (FPGA) structure for a rate-adaptive forward error correction (FEC) scheme based on spatially coupled (SC) LDPC codes derived from quasi-cyclic  ...  A simple approach to construct a LDPC-CC from a standard LDPC block code (LDPC-BC) was given.  ... 
doi:10.1364/oe.27.003422 fatcat:rpoawzaxsreelkdftjrdpkbekm

Spatially coupled codes and optical fiber communications: An ideal match?

Laurent Schmalen, Detlef Suikat, Detlef Rosener, Vahid Aref, Andreas Leven, Stephan ten Brink
2015 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)  
We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an  ...  We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.  ...  The block code, which has a matrix that has been optimized for low error floors, is outperformed by both SC-LDPC codes.  ... 
doi:10.1109/spawc.2015.7227080 dblp:conf/spawc/SchmalenSRALB15 fatcat:rzzxtqewxndizenfxw5jdnrigm

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings

Christian Häger, Alexandre Graell i Amat, Fredrik Brännström, Alex Alvarado, Erik Agrell
2014 Optics Express  
The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder.  ...  In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation.  ...  Spatially coupled LDPC codes SC-LDPC codes have parity-check matrices with a band-diagonal structure (for a general definition see, e.g., [12] ).  ... 
doi:10.1364/oe.22.014544 pmid:24977550 fatcat:7g7vuqgd45gktkvnpu3fjctihi

Guest Editorial Recent Advances in Capacity Approaching Codes

Erdal Arikan, Daniel J. Costello, Joerg Kliewer, Michael Lentmaier, Paul Siegel, Ruediger Urbanke, Michael Pursley
2016 IEEE Journal on Selected Areas in Communications  
The encoding method is shown to be equivalent to spatial coupling of the generator matrix, and performance comparisons to SC-LDPC codes and ARJA-type LDPC block codes indicate excellent waterfall region  ...  SPATIALLY COUPLED CODES The paper by Liu et al. introduces a new algebraic construction method for spatially coupled (convolutional) LDPC (SC-LDPC) codes, called replicate-and-mask (R&M).  ... 
doi:10.1109/jsac.2015.2508219 fatcat:pq7svpzseza7ljrrz6rlzl2fw4

Performance Analysis of LDPC-Coded Diversity Combining on Rayleigh Fading Channels With Impulsive Noise

Zhen Mei, Martin Johnston, Stephane Le Goff, Li Chen
2017 IEEE Transactions on Communications  
A detector based on the bi-parameter Cauchy-Gaussian mixture model is used and shows near-optimal performance with a significant reduction in complexity when compared with the optimal detector.  ...  Noise added at each branch of the diversity combiner is generally assumed to be additive white Gaussian noise, but there are many applications where the received signal is impaired by noise with a non-Gaussian  ...  Alternatively, a simulation-based approach can be used to find the pdf of a egc using a histogram method. For MRC, a different approach is used to find the pdf of the initial LLR.  ... 
doi:10.1109/tcomm.2017.2683485 fatcat:zhx3fyk4jnfm3a2zejrhx6znae

Coded Cooperation for Multiway Relaying in Wireless Sensor Networks

Zhongwei Si, Junyang Ma, Ragnar Thobaben
2015 Sensors  
To obtain good performance with practical codes, we choose spatially-coupled LDPC (SC-LDPC) codes for the coded cooperation.  ...  Due to the capacity-achieving property of the SC-LDPC codes, we prove that the capacity region can theoretically be achieved by the proposed MET SC-LDPC codes.  ...  Acknowledgments This work was supported in part by the National Natural Science Foundation of China The authors would like to thank the editors and the anonymous reviewers for their valuable comments and  ... 
doi:10.3390/s150715265 pmid:26131675 pmcid:PMC4541830 fatcat:ctsdukok4jgkdozm5zpjks4lnm

Performance Analysis of Block Markov Superposition Transmission of Short Codes [article]

Kechao Huang, Xiao Ma
2015 arXiv   pre-print
with the generator matrices of short codes (referred to as basic codes) coupled.  ...  Then, we present a performance comparison of BMST codes and SC low-density parity-check (SC-LDPC) codes on the basis of equal decoding latency.  ...  ACKNOWLEDGMENT The authors would like to thank Prof. Daniel J. Costello, Jr. for his helpful comments, polishing this paper, and invaluable  ... 
arXiv:1504.02978v1 fatcat:qqdzlet6jbhlloeq43usquhica

Physical-Layer Network Coding for Wireless Cooperative Networks

Wen Chen, Xiaodai Dong, Pingyi Fan, Christoph Hausl, TiffanyJing Li, Petar Popovski, Meixia Tao
2010 EURASIP Journal on Wireless Communications and Networking  
As the (sparse) mixing operation of network coding finds natural connection to low-density parity-check (LDPC) codes, both make essential use of the LDPC coding structure.  ...  The inception of network coding provides a powerful remedy for improving the spectral efficiency and opens new possibilities for achieving the end-to-end throughput optimality by allowing intermediate  ... 
doi:10.1155/2010/693158 fatcat:lij2bybct5al5p2z3oy54r2ici

Systematic Convolutional Low Density Generator Matrix Code [article]

Suihua Cai, Wenchao Lin, Xinyuanmeng Yao, Baodian Wei, Xiao Ma
2020 arXiv   pre-print
The SC-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization.  ...  To improve the waterfall performance, we construct the systematic convolutional LDGM (SC-LDGM) codes by a random splitting process.  ...  An important feature of SC-LDPC codes is the threshold saturation [14] that the decoding performance of SC-LDPC codes under BP decoding approaches the MAP decoding performances of uncoupled LDPC block  ... 
arXiv:2001.02854v1 fatcat:omdiglj4vnazlpqdt5y4alxvqq
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