| 181. |
- Lindkvist, Tina, et al.
(författare)
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A class of traceability codes
- 2002
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 48:7, s. 2094-2096
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Tidskriftsartikel (refereegranskat)abstract
- Traceability codes are identifiable parent property (IPP) codes with the additional requirement that Hamming distance can be used to trace a parent of a word. Traceability codes can be used for constructing digital fingerprints in order to deter users from illegally copying digital data. We construct a class of traceability codes and determine the exact parameters of some of the codes in this class.
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| 182. |
- Lindquist, Anders
(författare)
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Kullback-Leibler approximation of spectral density functions
- 2003
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 49:11, s. 2910-2917
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a Kullback-Leibler-type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density P by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral density is sought. In this context, we show i) that there is a unique spectral density P which minimizes this Kullback-Leibler distance, ii) that this optimal approximate is of the form psi/Q where the "correction term" Q is a rational spectral density function, and iii) that the coefficients of Q can be obtained numerically by solving a suitable convex optimization problem. In the special case where psi = 1, the convex functional becomes quadratic and the solution is then specified by linear equations.
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| 183. |
- Ljung, Lennart, 1946-
(författare)
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Analysis of Stochastic Gradient Algorithms for Linear Regression Problems
- 1984
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Ingår i: IEEE Transactions on Information Theory. - : IEEE Information Theory Society. - 0018-9448 .- 1557-9654. ; 30:2, s. 151-160
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Tidskriftsartikel (refereegranskat)abstract
- Parameter estimation problems that can be formulated as linear regressions are quite common in many applications. Recursive (on-line, sequential) estimation of such parameters can be performed using the recursive least squares (RLS) algorithm or a stochastic gradient version of this algorithm. In this paper the convergence properties of the gradient algorithm are analyzed under the assumption that the gain tends to zero. The technique is the same as the so-called ordinary differential equation approach, but the treatment here is self-contained and includes a proof of the boundedness of the estimates. A main result is that the convergence conditions for the gradient algorithm are the same as those for the recursive least squares algorithm.
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| 184. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Backwards Markovian Models for Second Order Stochastic Processes
- 1976
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Ingår i: IEEE Transactions on Information Theory. - : IEEE Information Theory Society. - 0018-9448 .- 1557-9654. ; 22:4, s. 488-491
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Tidskriftsartikel (refereegranskat)abstract
- A state-space model of a second-order random process is a representation as a linear combination of a set of state-variables which obey first-order linear differential equations driven by an input process that is both white and uncorrelated with the initial values of the state-variables. Such a representation is often called a Markovian representation. There are applications in which it is useful to consider time running backwards and to obtain corresponding backwards Markovian representations. Except in one very special circumstance, these backwards representations cannot be obtained simply by just reversing the direction of time in a forwards Markovian representation. We show how this problem can be solved, give some examples, and also illustrate how the backwards model can be used to clarify certain least squares smoothing formulas.
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| 185. |
- Loncar, Maja, et al.
(författare)
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Soft-output BEAST decoding with application to product Codes
- 2008
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 54:3, s. 1036-1049
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Tidskriftsartikel (refereegranskat)abstract
- A Bidirectional Efficient Algorithm for Searching code Trees (BEAST) is proposed for efficient soft-output decoding of block codes and concatenated block codes. BEAST operates on trees corresponding to the minimal trellis of a block code and finds a list of the most probable codewords. The complexity of the BEAST search is significantly lower than the complexity of trellis-based algorithms, such as the Viterbi algorithm and its list-generalizations. The outputs of BEAST, a list of best codewords and their metrics, are used to obtain approximate a posteriori reliabilities of the transmitted symbols, yielding a soft-input soft-output (SISO) symbol decoder referred to as the BEAST-APP decoder. This decoder is employed as a component decoder in iterative schemes for decoding of product and incomplete product codes. Its performance and convergence behavior are investigated using EXIT charts and compared to existing decoding schemes. It is shown that the BEAST-APP decoder achieves performances close to the BCJR decoder with a substantially lower computational complexity.
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| 186. |
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| 187. |
- Maarouf, Issam, et al.
(författare)
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Concatenated Codes for Multiple Reads of a DNA Sequence
- 2023
-
Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:2, s. 910-927
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Tidskriftsartikel (refereegranskat)abstract
- Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either an inner convolutional code or a time-varying block code. We propose two novel decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences and has a complexity that is linear with the number of sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence. In addition, we succeed in improving the performance of the aforementioned coding scheme by optimizing both the inner and outer codes.
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| 188. |
- Maitra, S, et al.
(författare)
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Further constructions of resilient Boolean functions with very high nonlinearity
- 2002
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 48:7, s. 1825-1834
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Tidskriftsartikel (refereegranskat)abstract
- One well-known method of generating key stream sequences for stream ciphers is to combine the outputs of several linear-feedback shift registers (LFSR) using a combining Boolean function. Here we concentrate on the design of good combining Boolean functions. We provide resilient Boolean functions with currently best known nonlinearity. These functions were not known earlier and the issues related to their existence were posed as open questions in the literature. Some of the functions we construct here achieve the provable upper bound on nonlinearity for resilient Boolean functions. Our technique interlinks mathematical results with classical computer search.
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| 189. |
- Mirmohseni, Mahtab, et al.
(författare)
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Secrecy Capacity Scaling in Large Cooperative Wireless Networks
- 2017
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Ingår i: IEEE Transactions on Information Theory. - : IEEE Press. - 0018-9448 .- 1557-9654. ; 63:3, s. 1923-1939
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate large wireless networks subject to security constraints. In contrast to point-to-point, interference-limited communications considered in prior works, we propose active cooperative relaying-based schemes. We consider a network with n(l) legitimate nodes, n(e) eavesdroppers, and path loss exponent alpha >= 2. As long as n(e)(2)(log(n(e))(gamma) = o(n(l)), for some positive gamma, we show that one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given fixed total power constraint for the entire network. We achieve this result through: 1) the source using Wyner randomized encoder and a serial ( multi-stage) block Markov scheme, to cooperate with the relays and 2) the relays acting as a virtual multi-antenna to apply beamforming against the eavesdroppers. Our simpler parallel ( two-stage) relaying scheme can achieve the same unbounded secure aggregate rate when n(e)(alpha/2+1) (log(n(e))(gamma+delta(alpha/2+1)) = o(n(l)) holds, for some positive gamma, delta. Finally, we study the improvement (to the detriment of legitimate nodes) that the eavesdroppers achieve in terms of the information leakage rate in a large cooperative network in the case of collusion. We show that again the zero-cost secure communication is possible, if n(e)((2+2/alpha)) (log n(e))(gamma) = o(n(l)) holds, for some positive gamma; that is, in the case of collusion slightly fewer eavesdroppers can be tolerated compared with the non-colluding case.
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| 190. |
- Mitchell, David G.M., et al.
(författare)
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Spatially Coupled Generalized LDPC Codes : Asymptotic Analysis and Finite Length Scaling
- 2021
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 67:6, s. 3708-3723
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Tidskriftsartikel (refereegranskat)abstract
- Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.
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