| 1. |
- Agrell, Erik, 1965
(författare)
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On the Voronoi neighbor ratio for binary linear block codes
- 1998
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 44:7, s. 3064-3072
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Tidskriftsartikel (refereegranskat)abstract
- Soft-decision decoding of block codes is regarded as the geometrical problem of identifying the Voronoi region within which a given input vector lies. A measure, called the neighbor ratio, is proposed to characterize how many facets a Voronoi region has. Theory and algorithms are presented to determine the neighbor ratio for binary linear block codes and results are given for several types of codes. An asymptotic analysis for long codes reveals that the neighbor ratio depends on whether the code rate is less than 1/2 or not. For rates below this threshold, all pairs of codewords tend to share a Voronoi facet; for higher rates, a relatively small fraction of them do.
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| 2. |
- Agrell, Erik, 1965, et al.
(författare)
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Optimization of lattices for quantization
- 1998
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 44:5, s. 1814-1828
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Tidskriftsartikel (refereegranskat)abstract
- A training algorithm for the design of lattices for vector quantization is presented. The algorithm uses a steepest descent method to adjust a generator matrix, in the search for a lattice whose Voronoi regions have minimal normalized second moment. The numerical elements of the found generator matrices are interpreted and translated into exact values. Experiments show that the algorithm is stable, in the sense that several independent runs reach equivalent lattices. The obtained lattices reach as low second moments as the best previously reported lattices, or even lower. Specifically, we report lattices in nine and ten dimensions with normalized second moments of 0.0716 and 0.0708, respectively, and nonlattice tessellations in seven and nine dimensions with 0.0727 and 0.0711, which improves on previously known values. The new nine- and ten-dimensional lattices suggest that Conway and Sloane's (1993) conjecture on the duality between the optimal lattices for packing and quantization might be false. A discussion of the application of lattices in vector quantizer design for various sources, uniform and nonuniform, is included.
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| 3. |
- Agrell, Erik, 1965
(författare)
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Voronoi regions for binary linear block codes
- 1996
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 42:1, s. 310-316
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Tidskriftsartikel (refereegranskat)abstract
- The Voronoi regions of a block code govern many aspects of the code's performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft-decision decoding. The article presents an efficient method for finding the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi regions. First, it is shown that the question of the Voronoi neighborship can be reduced into testing a simpler relation, called the Gabriel neighborship. Second, a fast method of recognising Gabriel neighbors is proposed. These results are finally employed to describe the Voronoi regions for the Golay codes and several BCH codes, including Hamming codes.
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| 4. |
- Forney, Jr., G David, et al.
(författare)
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Minimal and canonical rational generator matrices for convolutional codes
- 1996
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 42:6, Part 1, s. 1865-1880
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Tidskriftsartikel (refereegranskat)abstract
- A full-rank IC x n matrix G(D) over the rational functions F(D) generates a rate R = k/n convolutional code C. G(D) is minimal if it can be realized with as few memory elements as any encoder for C, and G(D) is canonical if it has a minimal realization in controller canonical form. We show that G(D) is minimal if and only if for all rational input sequences p1 (D), the span of U (D) G (D) covers the span of ZL (D). Alternatively, G(D) is minimal if and only if G(D) is globally zero-free, or globally invertible. We show that G(D) is canonical if and only if G(D) is minimal and also globally orthogonal, in the valuation-theoretic sense of Monna.
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| 5. |
- Gustafsson, RT, et al.
(författare)
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Adaptive detection of known signals in additive noise by means of kernel density estimators
- 1997
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Ingår i: IEEE TRANSACTIONS ON INFORMATION THEORY. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9448. ; 43:4, s. 1192-1204
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of detecting known signals contaminated by additive noise with a completely unknown probability density function f. To this end, we propose a new adaptive detection rule, It is defined by plugging a kernel density estimator (f) ove
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| 6. |
- Hössjer, Ola, et al.
(författare)
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On-line density estimators with high efficiency
- 1995
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 41:3, s. 829-833
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Tidskriftsartikel (refereegranskat)abstract
- We present on-line procedures for estimating density functions and their derivatives. At each step, M terms are updated. By increasing M the efficiency compared to the traditional off-line kernel density estimator tends to one. Already for M = 2, it exceeds 99.1% for kernel orders and derivatives of practical interest.
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| 7. |
- Höst, Stefan, et al.
(författare)
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Active distances for convolutional codes
- 1999
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 45:2, s. 658-669
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Tidskriftsartikel (refereegranskat)abstract
- A family of active distance measures for general convolutional codes is defined. These distances are generalizations of the extended distances introduced by Thommesen and Justesen (1983) for unit memory convolutional codes. It is shown that the error correcting capability of a convolutional code is determined by the active distances. The ensemble of periodically time-varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble. The active distances are very useful in the analysis of concatenated convolutional encoders
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| 8. |
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| 9. |
- Johannesson, Rolf, et al.
(författare)
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New rate 1/2, 1/3, and 1/4 binary convolutional encoders with an optimum distance profile
- 1999
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 45:5, s. 1653-1658
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Tidskriftsartikel (refereegranskat)abstract
- Tabulations of binary systematic and nonsystematic polynomial convolutional encoders with an optimum distance profile for rate 1/2, 1/3, and 1/4 are given. The reported encoders are found by computer searches that optimize over the weight spectra. The free distances for rate 1/3 and 1/4 are compared with Heller's (1968) and Griesmer's (1960) upper bounds
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| 10. |
- Johannesson, Rolf, et al.
(författare)
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Some structural properties of convolutional codes over rings
- 1998
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448. ; 44:2, s. 839-845
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Tidskriftsartikel (refereegranskat)abstract
- Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(pe) are obtained
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