An (n, d, k)-mapping f is a mapping from binary vectors of length n to permutations of length n + k such that for all x, y is an element of {0, 1}(n), d(H) (f (x), f (y)) >= d(H)(x, y) + d, if d(H) (x, y) (n + k)-...
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An (n, d, k)-mapping f is a mapping from binary vectors of length n to permutations of length n + k such that for all x, y is an element of {0, 1}(n), d(H) (f (x), f (y)) >= d(H)(x, y) + d, if d(H) (x, y) <= (n + k)-d and d(H) (f (x), f (y)) = n + k, if d(H) (x, y) > (n + k)-d. In this paper, we construct an (n, 3, 2)-mapping for any positive integer n >= 6. An (n, r)-permutation array is a permutation array of length n and any two permutations of which have Hamming distance at least r. Let P (n, r) denote the maximum size of an (n, r)-permutation array and A (n, r) denote the same setting for binary codes. Applying (n, 3, 2)-mappings to the design of permutation array, we can construct an efficient permutation array (easy to encode and decode) with better code rate than previous results [Chang (2005). IEEE Trans inf theory 51:359-365, Chang et al. (2003). IEEE Trans Inf theory 49:1054-1059;Huang et al. (submitted)]. More precisely, we obtain that, for n >= 8, P(n, r) >= A(n-2, r-3) > A(n-1, r-2) = A (n, r-1) when n is even and P(n, r) >= A(n-2, r-3) = A(n-1, r-2) > A(n, r-1) when n is odd. This improves the best bound A(n-1, r-2) so far [Huang et al. (submitted)] for n >= 8.
We present a turbo coding scheme whose constituent codes are designed using convolutional encoders with time-varying coefficients. These encoders are finite state sequence machines that operate over the Galois field G...
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We present a turbo coding scheme whose constituent codes are designed using convolutional encoders with time-varying coefficients. These encoders are finite state sequence machines that operate over the Galois field GF(q). The scheme includes an encryption polynomial whose coefficients are changed periodically by means of a user key. The trellis coding procedure thus hops from one trellis to another, following a random sequence taken over a set of subtrellises which correspond to different convolutional encoders. The proposed scheme is introduced as a turbo code with encryption properties, and is presented in two forms, the systematic and the nonsystematic schemes.
Two new binary shape-coding techniques that are based on finite automata methods are proposed. Both contour-based and bitmap-based approaches to shape coding are investigated using one-dimensional-weighted finite auto...
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Two new binary shape-coding techniques that are based on finite automata methods are proposed. Both contour-based and bitmap-based approaches to shape coding are investigated using one-dimensional-weighted finite automata (1D-WFA) and generalised finite automata (GFA) algorithms, respectively. We evaluate the fidelity of shape representation, using 1D-WFA and GFA methods in intraframe mode and compare the performance of the proposed coding techniques against each other and with the benchmark, context-based arithmetic encoding (CAE) of shapes used in MPEG-4. It is found that the GFA method is more suitable for video applications than 1D-WFA and therefore it is adapted to operate in interframe mode. More importantly, GFA is the first shape-coding technique reported to date that has the unique advantage of shape processing in the compressed domain. This is due to the fact that the shape representation in the compressed domain using GFA facilitates processing at the expense of less compression efficiency compared with MPEG-4 CAE. Moreover, shapes encoded using the GFA method can be decoded at any desirable resolution.
The authors have previously implemented a hard-decision decoder and have shown with simulation results that Hermitian codes perform well over the AWGN and Rayleigh fading channel, owing to their large code lengths. Ho...
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The authors have previously implemented a hard-decision decoder and have shown with simulation results that Hermitian codes perform well over the AWGN and Rayleigh fading channel, owing to their large code lengths. However, further increases in coding gain can be achieved by using a combined error and erasure decoding algorithm instead. In the paper a combined error and erasure decoding algorithm for Hermitian codes is implemented and simulation results over the AWGN and Rayleigh fading channel for the (64,49,10), (64,44,15) and (512,314,171) Hermitian codes are presented. The results show only a small increase in performance over the AWGN channel but more significant coding gains can be achieved over a Rayleigh fading channel.
The minimum distance of all binary cyclic codes of length 151 is determined. Almost all of these cyclic codes have the same parameters as the best linear codes given in Brouwer's database. A nested chain of linear...
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The minimum distance of all binary cyclic codes of length 151 is determined. Almost all of these cyclic codes have the same parameters as the best linear codes given in Brouwer's database. A nested chain of linear codes is derived from these cyclic codes and some new binary codes are obtained by applying Constructions X and XX to pairs of codes in this chain. Good candidates for nested codes can also be obtained by enlarging the cyclic codes of high minimum distance. In total, there are 39 new binary linear codes that have a minimum distance higher than codes previously considered to be the best linear codes.
Data Allocation on multiple I/O devices manifests itself in many computing systems, both centralized and distributed. Data is partitioned on multiple I/O devices and clients issue various types of queries to retrieve ...
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Data Allocation on multiple I/O devices manifests itself in many computing systems, both centralized and distributed. Data is partitioned on multiple I/O devices and clients issue various types of queries to retrieve relevant information. In this paper, we derive necessary and sufficient conditions for a data allocation method to be optimal for two important types of queries: partial match and bounded disagreement search queries. We formally define these query types and derive the optimality conditions based on coding-theoretic arguments. Although these conditions are fairly strict, we show how to construct good allocation methods for practical realistic situations. Not only are the response times bounded by a small value, but also the identification of the relevant answer set is efficient.
The authors present asymmetric turbo hybrid automatic-repeat-request (ATH-ARQ) schemes that employ component code selection and asymmetric rate compatible punctured turbo codes (ARCPT) for enhanced performance in fadi...
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The authors present asymmetric turbo hybrid automatic-repeat-request (ATH-ARQ) schemes that employ component code selection and asymmetric rate compatible punctured turbo codes (ARCPT) for enhanced performance in fading channels. The paper also presents a novel low-rate ARCPT encoder structure. An analysis is presented for efficient ARCPT puncture schemes for improved throughput performance at low and high SNR values. It is shown that in certain instances, the use of conventional turbo code structures results in the best performance.
A novel volume-hologram encryption system is proposed, in which the stored binary image can be restored only by the correct random binary amplitude mask. In our system the encryption is done by overlapping two hologra...
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A novel volume-hologram encryption system is proposed, in which the stored binary image can be restored only by the correct random binary amplitude mask. In our system the encryption is done by overlapping two holograms in the same volume of the crystal;one is the hologram of the original binary image and the other is that of the complementary image. The principle of the system is explained with schematic diagrams and then the experimental data is shown. (c) 2005 Elsevier B.V. All rights reserved.
Some questions related to the computation of the capacity of codes that avoid forbidden difference patterns are analysed. The maximal number of it-bit sequences whose pairwise differences do not contain some given for...
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Some questions related to the computation of the capacity of codes that avoid forbidden difference patterns are analysed. The maximal number of it-bit sequences whose pairwise differences do not contain some given forbidden difference patterns is known to increase exponentially with n;the coefficient of the exponent is the capacity of the forbidden patterns. In this paper, new inequalities for the capacity are given that allow for the approximation of the capacity with arbitrary high accuracy. The computational cost of the algorithm derived from these inequalities is fixed once the desired accuracy is given. Subsequently, a polynomial time algorithm is given for determining if the capacity of a set is positive while the same problem is shown to be NP-hard when the sets of forbidden patterns are defined over an extended set of symbols. Finally, the existence of extremal norms is proved for any set of matrices arising in the capacity computation. Based on this result, a second capacity approximating algorithm is proposed. The usefulness of this algorithm is illustrated by computing exactly the capacity of particular codes that were only known approximately.
Multimode coding is an efficient block coding technique that introduces control over sequence statistics by generating a number of alternatives to represent the source word in each encoding interval and then selecting...
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Multimode coding is an efficient block coding technique that introduces control over sequence statistics by generating a number of alternatives to represent the source word in each encoding interval and then selecting the word that best meets the system constraints. The power spectral density (PSD) of the encoded signal is of particular interest with these codes. Standard techniques for evaluation of the PSD of block coded sequences cannot be directly applied to a wide variety of multimode codes in which encoder state probabilities do not reach a stationary distribution, or in which codeword selection is random when two or more alternatives satisfy system constraints. In the paper standard spectral analysis techniques are extended to enable evaluation of the PSD of signals generated by multimode codes with these characteristics. It is demonstrated that randomness in selection can result in suppression of discrete components in the encoded signal that may otherwise arise under adverse conditions.
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