### Citations

12423 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ... Zorba are respectively the resulting column vectors. We now define Zorba’s decoder. For an arbitrary distribution pX,Y (x, y) over finite alphabets, let the strongly ǫ-jointly typical set A n ǫ,pX,Y =-=[11]-=- (henceforth simply called the typical set) be the set of all length-n sequences (X,Y) such that the empirical distribution induced by (X,Y) differs component-wise from pX,Y (x, y) by at most ǫ/(|X ||... |

10909 | A mathematical theory of communication - Shannon - 1949 |

3611 | Compressed sensing
- Donoho
- 2006
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Citation Context ...erformance (at the cost of potentially high decoding complexity), whereas CS codes have lower decoding complexity at the cost of non-optimal rates. Some intriguing results on CS codes can be found in =-=[14]-=-, [8]. Concurrently, codes over the real field R also seem to have applications for the channel coding problem. Using significantly different techniques, Tao et al. [15] obtained channel codes that ca... |

3283 |
An introduction to probability theory and its applications, volume 2 of Wiley series in probability and mathematical statistics: Probability and mathematical statistics
- Feller
- 1971
(Show Context)
Citation Context ... |α1| 2 σ 2 . The central limit theorem states that the distribution of the normalized sum Wτ = ∑ τ j=1 Vj/(σ ′√ τ) approaches the normal N(0, 1) distribution as τ increases. The Berry-Esseen theorem =-=[17]-=- gives a uniform upper bound on the deviation of the cumulative distribution function (cdf) of Wτ from the cdf of N(0, 1). The Berry-Esseen bound is given by |Pr{Wτ < w} − Φ(w)| ≤ βγ σ ′3√ , (6) τ for... |

2621 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candes, Romberg, et al.
- 2006
(Show Context)
Citation Context ...tup, N sources each generate a single real number. The resulting length-N sequence is k-sparse, i.e., can be written with at most k ≪ N non-zero coefficients in a prespecified basis. A typical result =-=[8]-=- in this setup shows that if a receiver gets O(k log(N)) random linear combinations over R of the sources’ sequence, it can, with high probability, reconstruct the source sequence exactly in a computa... |

1398 | Decoding by linear programming
- Candes, Tao
- 2005
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Citation Context ...ts on CS codes can be found in [14], [8]. Concurrently, codes over the real field R also seem to have applications for the channel coding problem. Using significantly different techniques, Tao et al. =-=[15]-=- obtained channel codes that can be decoded solving a linear program (LP). Also, lattice codes have been shown to achieve capacity for the AWGN channel [16]. III. RSWC MODEL As is common in the SW lit... |

1262 |
Noiseless coding of correlated information sources
- Slepian, Wolf
- 1973
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Citation Context ...sed may be of independent interest for code design for a wide class of information theory problems, and for the field of compressed sensing. I. INTRODUCTION A well-known result by Slepian and Wolf in =-=[2]-=- characterizes the rate-region for near-lossless source coding of distributed sources. The result demonstrates that if two (or more) sources possess correlated data, even independent encoding of the s... |

350 | Information Theory - Ash - 1965 |

202 |
Distributed compression in a dense microsensor network
- Pradhan, Kusuma, et al.
- 2002
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Citation Context ...es’ data can still achieve essentially the same performance as when the sources encode jointly. This result has important implications for information theoretic problems as diverse as sensor networks =-=[3]-=-, secrecy [4], and low-complexity video encoding [5]. Unfortunately for the distributed source coding problem, codes that are provably both rate-optimal and computationally efficient to implement are ... |

166 |
PRISM: a new robust video coding architecture based on distributed compression principles,”
- Puri, Ramchandran
- 2002
(Show Context)
Citation Context ...ormance as when the sources encode jointly. This result has important implications for information theoretic problems as diverse as sensor networks [3], secrecy [4], and low-complexity video encoding =-=[5]-=-. Unfortunately for the distributed source coding problem, codes that are provably both rate-optimal and computationally efficient to implement are hard to come by. Section II gives a partial history ... |

149 |
Compression of correlated binary sources using turbo codes,
- Garcia-Frias, Zhao
- 2001
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Citation Context ...rs that are linear over a finite field. Some such codes use iteratively decodable channel codes to attain performance that is empirically “good”, but performance guarantees have not been proven (e.g. =-=[12]-=-). Other codes use recent theoretical advances in channel codes to produce nearlossless codes that achieve any point in the SW rate-region, but cannot give guarantees on computational complexity (e.g.... |

103 |
Linear codes for sources and source networks: Error exponents, universal coding
- Csiszár
- 1982
(Show Context)
Citation Context ...onding to Totally Unimodular matrices [6]). It is thus conceivable that suitably chosen RSWCs may be decodable with low computational complexity. Linear SW codes over finite fields were introduced in =-=[7]-=- and they were shown to achieve the SW rate-region. Decoding such codes is equivalent to finding a vertex of a hypercube satisfying some combinatorial properties. Such problems are computationally int... |

91 | Common randomness and secret key generation with a helper,”
- Csiszár, Narayan
- 2000
(Show Context)
Citation Context ...still achieve essentially the same performance as when the sources encode jointly. This result has important implications for information theoretic problems as diverse as sensor networks [3], secrecy =-=[4]-=-, and low-complexity video encoding [5]. Unfortunately for the distributed source coding problem, codes that are provably both rate-optimal and computationally efficient to implement are hard to come ... |

49 |
Towards a General Theory of Source Networks
- Csiszár, Körner
- 1980
(Show Context)
Citation Context ...ntropy decoding algorithm is shown to work for our RSWCs in Section VII. Section VIII shows that our RSWCs achieve the rate-region of more general normal source networks without helpers introduced in =-=[9]-=-. Finally Section IX concludes the paper. II. BACKGROUND AND DEFINITIONS Shannon’s seminal source coding theorem [10] demonstrates that a sequence of discrete random variables can essentially be compr... |

45 | Lattice codes can achieve capacity on the AWGN channel
- Urbanke, Rimoldi
- 1998
(Show Context)
Citation Context ...nificantly different techniques, Tao et al. [15] obtained channel codes that can be decoded solving a linear program (LP). Also, lattice codes have been shown to achieve capacity for the AWGN channel =-=[16]-=-. III. RSWC MODEL As is common in the SW literature [11], we focus on just the point (H(X), H(Y |X)) in the SW rate-region. Time-sharing between this and the symmetric point (H(X|Y ), H(Y )) enables u... |

29 | On some new approaches to practical Slepian-Wolf compression inspired by channel coding
- Coleman, Lee, et al.
- 2004
(Show Context)
Citation Context .... Other codes use recent theoretical advances in channel codes to produce nearlossless codes that achieve any point in the SW rate-region, but cannot give guarantees on computational complexity (e.g. =-=[13]-=-). C. Linear codes over real fields As mentioned in the introduction, Compressed Sensing codes operate over real (and complex) fields, and are structurally similar to the codes proposed in this work. ... |

2 |
The role of unimodularity in applying linear inequalities to combinatorial theorems
- Hoffmann
- 1979
(Show Context)
Citation Context ...nana 43107, Israel, email: mikel@openu.ac.ilDEY, JAGGI, AND LANGBERG: “REAL” SLEPIAN-WOLF CODES 2 to be computationally tractable to solve (for e.g., IPs corresponding to Totally Unimodular matrices =-=[6]-=-). It is thus conceivable that suitably chosen RSWCs may be decodable with low computational complexity. Linear SW codes over finite fields were introduced in [7] and they were shown to achieve the SW... |

1 |
Information Theory and Network Coding. Available at http://www.springerlink.com/content/978-0-387-79233-0
- Yeung
(Show Context)
Citation Context ...Y). We will briefly discuss all the terms in (32). By definition, P ′ 1 = Pr{Ac ǫ,weak }. Since the weakly ǫ-typical set is a superset of the strongly ǫ′ (ǫ, pX,Y )-typical set for some ǫ ′(ǫ, pX,Y ) =-=[19]-=-, P ′ 1 can be bounded similar to (3) as P ′ 1 ≤ 2−cn (33) where the constant c depends on pX,Y . Following similar steps as the proof of Lemma 13, we have P22 = ∑ pX,Y (x,y) ∑ N ′ ( ( x,y(t) min ˜p, ... |