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624
Good Codes based on Very Sparse Matrices
 Cryptography and Coding. 5th IMA Conference, number 1025 in Lecture Notes in Computer Science
, 1995
"... . We present a new family of errorcorrecting codes for the binary symmetric channel. These codes are designed to encode a sparse source, and are defined in terms of very sparse invertible matrices, in such a way that the decoder can treat the signal and the noise symmetrically. The decoding proble ..."
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Cited by 95 (12 self)
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. We present a new family of errorcorrecting codes for the binary symmetric channel. These codes are designed to encode a sparse source, and are defined in terms of very sparse invertible matrices, in such a way that the decoder can treat the signal and the noise symmetrically. The decoding problem involves only very sparse matrices and sparse vectors, and so is a promising candidate for practical decoding. It can be proved that these codes are `very good', in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. We give experimental results using a free energy minimization algorithm and a belief propagation algorithm for decoding, demonstrating practical performance superior to that of both BoseChaudhuryHocquenghem codes and ReedMuller codes over a wide range of noise levels. We regret that lack of space prevents presentation of all our theoretical and experimental results. The full text of this paper may be found elsewher...
Weaknesses of Margulis and RamanujanMargulis LowDensity ParityCheck Codes
 Electronic Notes in Theoretical Computer Science
, 2003
"... We report weaknesses in two algebraic constructions of lowdensity paritycheck codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sumproduct decoder; The RamanujanMargulis construction gives a code with lowweight codewords, whic ..."
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Cited by 88 (1 self)
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We report weaknesses in two algebraic constructions of lowdensity paritycheck codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sumproduct decoder; The RamanujanMargulis construction gives a code with lowweight codewords, which produce an errorfloor.
EXIT charts of irregular codes
, 2002
"... We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregula ..."
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Cited by 83 (6 self)
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We study the convergence behavior of iterative decoding of a serially concatenated code. We rederive a existing analysis technique called EXIT chart [15] and show that for certain decoders the construction of an EXIT chart simplifies tremendously. The findings are extended such that simple irregular codes can be constructed, which can be used to improve the converence of the iterative decoding algorithm significantly. An efficient and optimal optiamization algorithm is presented. Finally, some results on thresholds on the decoding convergence are outlined.
Evaluation of Gallager Codes for Short Block Length and High Rate Applications
 In Codes, Systems and Graphical Models
, 1999
"... Gallager codes with large block length and low rate (e.g., N ' 10; 00040; 000, R ' 0:250:5) have been shown to have record{breaking performance for low signal{ to{noise applications. In this paper we study Gallager codes at the other end of the spectrum. We rst explore the theoretical p ..."
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Cited by 81 (9 self)
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Gallager codes with large block length and low rate (e.g., N ' 10; 00040; 000, R ' 0:250:5) have been shown to have record{breaking performance for low signal{ to{noise applications. In this paper we study Gallager codes at the other end of the spectrum. We rst explore the theoretical properties of binary Gallager codes with very high rates and observe that Gallager codes of any rate oer runlength{limiting properties at no additional cost. We then report the empirical performance of high rate binary and non{binary Gallager codes on three channels: the binary input Gaussian channel, the binary symmetric channel, and the 16{ary symmetric channel. We nd that Gallager codes with rate R = 8=9 and block length N = 1998 bits outperform comparable BCH and Reed{Solomon codes (decoded by a hard input decoder) by more than a decibel on the Gaussian channel. Please note this is a rough draft paper, not intended for widespread circulation. Updates to this paper will appear here: http://www....
Turbo Equalization
 IEEE Signal Processing Mag
, 2004
"... Capitalizing on the tremendous performance gains of turbo codes and the turbo decoding algorithm, turbo equalization is an iterative equalization and decoding technique that can achieve equally impressive performance gains for communication systems that send digital data over channels that require e ..."
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Cited by 69 (4 self)
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Capitalizing on the tremendous performance gains of turbo codes and the turbo decoding algorithm, turbo equalization is an iterative equalization and decoding technique that can achieve equally impressive performance gains for communication systems that send digital data over channels that require equalization, i.e. those which suffer from intersymbol interference (ISI). In this paper, we discuss the turbo equalization approach to coded data transmission over ISI channels, with an emphasis on the basic ideas and some of the practical details. The original system introduced by Douillard, et al., can be viewed as an extension of the turbo decoding algorithm by considering the effect of the ISI channel as another form of error protection, i.e. as a rate1 convolutional code.
Design of serially concatenated systems depending on the blocklength
 IEEE Transactions on Communications
, 2004
"... ..."
A Class of GroupStructured LDPC Codes
, 2001
"... A class of graphs is designed using subgroups of the multiplicative group of a prime field GF(p). Instances where (p1) is divisible by 3 and 5 are used to construct quasicyclic LDPC codes with bit degree 3 and parity degree 5, among them a [155,64,20] code. While the girth of a graph in this class ..."
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Cited by 68 (1 self)
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A class of graphs is designed using subgroups of the multiplicative group of a prime field GF(p). Instances where (p1) is divisible by 3 and 5 are used to construct quasicyclic LDPC codes with bit degree 3 and parity degree 5, among them a [155,64,20] code. While the girth of a graph in this class cannot be greater than twelve, for many practical lengths the graphs have a relatively large girth and a lowdensity of short cycles. Simulation studies show that at short to moderate lengths these codes performance meets or surpasses that of randomly generated regular (3,5) LDPC codes when used with sumproduct algorithm decoders. I.
On Compressing Encrypted Data
 IN IEEE TRANS. SIGNAL PROCESSING
, 2004
"... When it is desired to transmit redundant data over an insecure and bandwidthconstrained channel, it is customary to first compress the data and then encrypt it. In this paper, we investigate the novelty of reversing the order of these steps, i.e., first encrypting and then compressing, without com ..."
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Cited by 67 (5 self)
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When it is desired to transmit redundant data over an insecure and bandwidthconstrained channel, it is customary to first compress the data and then encrypt it. In this paper, we investigate the novelty of reversing the order of these steps, i.e., first encrypting and then compressing, without compromising either the compression efficiency or the informationtheoretic security. Although counterintuitive, we show surprisingly that, through the use of coding with side information principles, this reversal of order is indeed possible in some settings of interest without loss of either optimal coding efficiency or perfect secrecy. We show that in certain scenarios our scheme requires no more randomness in the encryption key than the conventional system where compression precedes encryption. In addition to proving the theoretical feasibility of this reversal of operations, we also describe a system which implements compression of encrypted data.
Probabilistic Reasoning for Entity & Relation Recognition
, 2002
"... This paper develops a method for recognizing relations and entities in sentences, while taking mutual dependencies among them into account. E.g., the kill (Johns, Oswald) relation in: "J. V. Oswald was murdered at JFK after his assassin, K. F. Johns..." depends on identifying Oswald and J ..."
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Cited by 65 (11 self)
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This paper develops a method for recognizing relations and entities in sentences, while taking mutual dependencies among them into account. E.g., the kill (Johns, Oswald) relation in: "J. V. Oswald was murdered at JFK after his assassin, K. F. Johns..." depends on identifying Oswald and Johns as people, JFK being identified as a location, and the kill relation between Oswald and Johns; this, in turn, enforces that Oswald and Johns are people. In our
Maximum weight matching via maxproduct belief propagation
 in International Symposium of Information Theory
, 2005
"... Abstract — The maxproduct “belief propagation ” algorithm is an iterative, local, message passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many applicati ..."
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Cited by 64 (12 self)
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Abstract — The maxproduct “belief propagation ” algorithm is an iterative, local, message passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many application areas such as iterative decoding and computer vision which involve graphs with many cycles, theoretical convergence results are only known for graphs which are treelike or have a single cycle. In this paper, we consider a weighted complete bipartite graph and define a probability distribution on it whose MAP assignment corresponds to the maximum weight matching (MWM) in that graph. We analyze the fixed points of the maxproduct algorithm when run on this graph and prove the surprising result that even though the underlying graph has many short cycles, the maxproduct assignment converges to the correct MAP assignment. We also provide a bound on the number of iterations required by the algorithm. I.