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Information Sets of Multiplicity Codes [article]

Daniel Augot, Françoise Levy-Dit-Vehel (ENSTA ParisTech UMA), Man Cuong Ngô
2015 arXiv   pre-print
We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions.  ...  We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party.  ...  We can now define information sets of Multiplicity Codes: Definition 4 (Information set of a Multiplicity Code): An information set of Mult s d is a set I ⊂ S × F m q such that the mapping φ : Mult s d  ... 
arXiv:1509.00279v1 fatcat:3tfeacyx7reh5com3atriomtvq

Information sets of Multiplicity codes

Daniel Augot, Francoise Levy-dit-Vehel, Cuong M. Ngo
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions.  ...  We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kopparty.  ...  We can now define information sets of Multiplicity Codes: Definition 4 (Information set of a Multiplicity Code): An information set of Mult s d is a set I ⊂ S × F m q such that the mapping φ : Mult s d  ... 
doi:10.1109/isit.2015.7282886 dblp:conf/isit/AugotLN15 fatcat:mqspqgf6kfbtrpprh77kkhhbom

Managing evolving code sets and integration of multiple data sources in health care analytics

James P. McGlothlin, Latifur Khan
2013 Proceedings of the 2013 international workshop on Data management & analytics for healthcare - DARE '13  
We will provide our solutions and experience addressing key challenges including code set integration and migration and patient identification.  ...  With the rapid advancement of medical record digitization, there is a very large amount of information available for analysis.  ...  We will focus primarily on the key challenges of dealing with multiple and evolving code sets and of integrating information from multiple data sources.  ... 
doi:10.1145/2512410.2512424 dblp:conf/cikm/McGlothlinK13 fatcat:l62aewxbjvd4xhz5vtkoyf3lve

Information Sets of Multiplicity Codes Information Sets of Multiplicity Codes Françoise Levy-dit-Vehel ENSTA ParisTech 828 boulevard des Maréchaux 91762 Palaiseau INRIA Saclay and LIX levy@ensta.fr

Daniel Augot, Françoise Levy-Dit-Vehel, Man Ngô, Daniel Augot, Inria Saclay, Lix Bâtiment, Alan Turing, Cuong Ngô, Alan Bâtiment, Turing
2015 2015 IEEE International Symposium on   unpublished
We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions.  ...  We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party.  ...  We can now define information sets of Multiplicity Codes: Definition 4 (Information set of a Multiplicity Code): An information set of Mult s d is a set I ⊂ S × F m q such that the mapping φ : Mult s d  ... 
fatcat:olm2kw4cgzh6bl55ffvt7l3iya

Multiple access analog fountain codes

Mahyar Shirvanimoghaddam, Yonghui Li, Branka Vucetic
2014 2014 IEEE International Symposium on Information Theory  
We show that the multiple access process will create an equivalent analog fountain code, referred to as the multiple access analog fountain code (MA-AFC), at the destination.  ...  We further analyse the asymptotic performance of the BP decoder by using a density evolution approach and show that the average log-likelihood ratio (LLR) of each user's information symbol is proportional  ...  Multiple Access Analog Fountain Codes Each coded symbol in AFC is a linear combination of modulated information symbols with real weight coefficients.  ... 
doi:10.1109/isit.2014.6875217 dblp:conf/isit/ShirvanimoghaddamLV14 fatcat:hkxn6g7zbrhvni2tw2uukzucrm

Polar Codes in Network Quantum Information Theory

Christoph Hirche, Ciara Morgan, Mark M. Wilde
2016 IEEE Transactions on Information Theory  
In the present work, we apply the polar coding method to network quantum information theory, by making use of recent advances for related classical tasks.  ...  Recently, this method has been generalized to the realm of quantum information processing, for tasks such as classical communication, private classical communication, and quantum communication.  ...  In the quantum setting polar coding has been generalized to the case of single user quantum channels for the task of sending classical [22, 23] and quantum information [24, 25] .  ... 
doi:10.1109/tit.2016.2514319 fatcat:3dpxnzzwd5fnbkywqeos457t5u

Bounding Multiple Unicasts through Index Coding and Locally Repairable Codes [article]

Karthikeyan Shanmugam, Alexandros G. Dimakis
2014 arXiv   pre-print
In a GLRC, every node is decodable from a specific set of other nodes and these sets induce a recoverability directed graph.  ...  We show that the dual linear subspace of a GLRC is a solution to an index coding instance where the side information graph is this GLRC recoverability graph.  ...  Consider any user i in the index coding problem. Let the side information set be S i .  ... 
arXiv:1402.3895v1 fatcat:z5c35n6sjjhg7puu6ugor4zgcy

Page 9445 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
The set of linear codes used has the property that the average probability of error over the set vanishes as the block length tends to infinity.  ...  In this case minimum entropy decoding can be used instead of typical set de- coding.  ... 

Distributed Video Coding with Multiple Side Information Sets

Jung Ah PARK, Doug Young SUH, Gwang-Hoon PARK
2010 IEICE transactions on information and systems  
This letter proposes a method to retrieve the original image X out of multiple sets of SI (Side Information) in distributed video coding (DVC).  ...  Using Turbo decoding methods, the most reliable segments from the decoded Y i 's were selected for the composition of Y ∞ , whose conditional entropy H(X|Y ∞ ) became much lower than any individual conditional  ...  This letter proposes the use of multiple sets of SI and a novel method to combine information from them.  ... 
doi:10.1587/transinf.e93.d.654 fatcat:yhv2c2jeknasfevactzaf53r54

Codes for multiple localized burst error correction

A. Mardjuadi, J.H. Weber
1998 IEEE Transactions on Information Theory  
A new construction method for codes correcting multiple localized burst errors is proposed.  ...  Unlike the Larsson codes, the proposed codes are also asymptotically optimal when the number of bursts to be corrected and the correctable burst length are both fixed.  ...  on the rate of conventional codes for multiple burst error correction.  ... 
doi:10.1109/18.705586 fatcat:3cxfnl3zx5hz3fwseg6pe3b6uu

Visual cryptography in single-pixel imaging [article]

Shuming Jiao, Jun Feng, Yang Gao, Ting Lei, Xiaocong Yuan
2019 arXiv   pre-print
In the first scheme, QR-code VC is designed by using opaque sheets instead of transparent sheets.  ...  It is pointed out that the overlapping of visual key images in VC is similar to the superposition of pixel intensities by a single-pixel detector in SPI.  ...  When multiple visual key images are illuminated by multiple sets of identical illumination patterns under the recording of only one single-pixel detector, the secret image can be reconstructed from the  ... 
arXiv:1911.05033v1 fatcat:wxw4eyc7szeitipgnnkvdzzzjq

Rate-Splitting Multiple Access for Downlink Multi-Antenna Communications: Physical Layer Design and Link-level Simulations [article]

Onur Dizdar, Yijie Mao, Wei Han, Bruno Clerckx
2020 arXiv   pre-print
In this work, we leverage recent results on the optimization of RSMA and design for the first time its physical layer, accounting for modulation, coding (using polar codes), message split, adaptive modulation  ...  and coding, and SIC receiver.  ...  The locations of information bits in the vector u are chosen from the set A, which is the set of indexes of K polarized channels with smallest Bhattacharyya parameters.  ... 
arXiv:2005.13257v3 fatcat:7236yspq7fdszlplqsmkjnyjta

Cuboid Partitioning for Hierarchical Coded Matrix Multiplication [article]

Shahrzad Kiani, Nuwan Ferdinand, Stark C. Draper
2019 arXiv   pre-print
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems.  ...  Building on this framework, we apply the idea of hierarchical coding (Ferdinand & Draper, 2018) to coded matrix multiplication.  ...  Polynomial codes: One way to achieve information dimen-1 rNxs " t1, . . . , Nxu is the index set of cardinality Nx. Ks. This decomposition slices the cuboid into K equal-sized subcuboids by making ?  ... 
arXiv:1907.08819v1 fatcat:mh22mskkhnf7vjagfzsw2hho6y

Neighborhood Level Error Control Codes for Multi-Level Cell Flash Memories

Shohei KOTAKI, Masato KITAKAMI
2013 IEICE transactions on information and systems  
But technology scaling, increase of program/erase (P/E) cycles, and MLC storing the large number of bits can cause multiple-level shift.  ...  Evaluation results show information lengths to respective check symbol lengths are larger than nonbinary Hamming codes and other M-ary asymmetric symbol error correcting codes. key words: Integer codes  ...  The set O consists of 4 and its multiples, that is {0,4}.  ... 
doi:10.1587/transinf.e96.d.1926 fatcat:hekbj3w2fvhhnhqzd5323lwcq4

Distributed Video Coding with multiple side information

Xin Huang, Catarina Brites, Joao Ascenso, Fernando Pereira, Soren Forchhammer
2009 2009 Picture Coding Symposium  
Compared with the best available single side information solutions, the proposed DVC solution with multiple side information robustly improves the RD performance for the set of test sequences.  ...  Index Terms-Distributed Video Coding, multiple side information, soft input.  ...  WYNER-ZIV DECODER WITH MULTIPLE SIDE INFORMATION As mentioned before, the choice of the adopted side information generation scheme significantly influences the final coding efficiency.  ... 
doi:10.1109/pcs.2009.5167357 dblp:conf/pcs/HuangBAPF09 fatcat:b6vtevblt5bpvk6qythiit5z3e
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