In this paper, we provide a generalization of binary quadratic residue codes to the cases of higher power prime residues over the finite field of the same order. We find generating polynomials for Such codes, define a...
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In this paper, we provide a generalization of binary quadratic residue codes to the cases of higher power prime residues over the finite field of the same order. We find generating polynomials for Such codes, define a new notion corresponding to the binary concept of an idempotent, and use this to find a lower bound for the codeword weight of the duals of such codes. This in turn leads to a lower bound on the weight of the codewords themselves. (C) 2009 Elsevier Inc. All rights reserved.
An approach to construct semi-random low-density parity-check (SR-LDPC) codes is introduced. These codes are designed with the progressive edge-growth algorithm and can be encoded with only multiple parity-check encod...
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An approach to construct semi-random low-density parity-check (SR-LDPC) codes is introduced. These codes are designed with the progressive edge-growth algorithm and can be encoded with only multiple parity-check encoders and interleavers. Therefore, the proposed codes have large girth and efficient encoding. Simulation results show that the codes perform very well over the AWGN channel with iterative decoding.
We prove that the group of permutation automorphism of a q-ary Hamming code of length n = (q (m) - 1)/(q - 1) is isomorphic to the unitriangular group UT (m) (q) if the code has a parity-check matrix composed of all c...
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We prove that the group of permutation automorphism of a q-ary Hamming code of length n = (q (m) - 1)/(q - 1) is isomorphic to the unitriangular group UT (m) (q) if the code has a parity-check matrix composed of all columns of the form (0 ...0 1 * ... *)(T). We also show that the group of permutation automorphisms of a cyclic Hamming code cannot be isomorphic to UT (m) (q). We thus show that equivalent codes can have different permutation automorphism groups.
An efficient way to reduce the dynamic power dissipation in the turbo decoder is presented. This technique is based on dynamic re-encoding of the received messages. The idea is to decrease the state transition activit...
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An efficient way to reduce the dynamic power dissipation in the turbo decoder is presented. This technique is based on dynamic re-encoding of the received messages. The idea is to decrease the state transition activity of the trellis-based algorithms by replacing the classical direct decoding of the random noisy codewords by an equivalent decoding of almost 'all zero' codewords in order to keep the survivor path on the 'zero path'.
A family of LDPC codes, called LU(3, q) codes, has been constructed from q-regular bipartite graphs. Recently, P. Sin and Q. Xiang determined the dimensions of these codes in the case that q is a power of an odd prime...
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A family of LDPC codes, called LU(3, q) codes, has been constructed from q-regular bipartite graphs. Recently, P. Sin and Q. Xiang determined the dimensions of these codes in the case that q is a power of an odd prime. They also obtained a lower bound for the dimension of an LU(3, q) code when q is a power of 2. In this paper we prove that this lower bound is the exact dimension of the LU(3,q) code. The proof involves the geometry of symplectic generalized quadrangles, the representation theory of Sp(4,q), and the ring of polynomials. (C) 2009 Elsevier Inc. All rights reserved.
We study two new concepts of combinatorial coding theory: additive stem similarity and additive stem distance between q-ary sequences. For q = 4, the additive stem similarity is applied to describe a mathematical mode...
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We study two new concepts of combinatorial coding theory: additive stem similarity and additive stem distance between q-ary sequences. For q = 4, the additive stem similarity is applied to describe a mathematical model of thermodynamic similarity, which reflects the "hybridization potential" of two DNA sequences. Codes based on the additive stem distance are called DNA codes. We develop methods to prove upper and lower bounds on the rate of DNA codes analogous to the well-known Plotkin upper bound and random coding lower bound (the Gilbert-Varshamov bound). These methods take into account both the "Markovian" character of the additive stem distance and the structure of a DNA code specified by its invariance under the Watson-Crick transformation. In particular, our lower bound is established with the help of an ensemble of random codes where distribution of independent codewords is defined by a stationary Markov chain.
In multimode conservative codes for holographic storage, an unconstrained m x n binary array S of source data is added to a set of (m + 1)(n + 1) control arrays to form the selection set, which is guaranteed to contai...
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In multimode conservative codes for holographic storage, an unconstrained m x n binary array S of source data is added to a set of (m + 1)(n + 1) control arrays to form the selection set, which is guaranteed to contain at least one conservative array of strength at least t, such that each row and each column of the output array contain at least t transitions. To be able to retrieve the original source data array S during the decoding process, at least inverted right perpendicular log(2)(m + 1)(n + 1) inverted left perpendicular redundant bits are necessary to index the (m + 1)( n + 1) control arrays. Presented is a method for embedding the index information of the control arrays into the encoded arrays in a manner which requires only inverted right perpendicular log2(m + 1) inverted left perpendicular + inverted right perpendicular log(2)(n + 1) inverted left perpendicular redundant bits, thereby attaining high coding efficiency.
A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves esse...
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A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves essentially optimal performance by applying scaling in the decoder's extrinsic information. If no such scaling is applied, then the proposed algorithm has small performance degradation, e. g. in the order of 0.1 to 0.2 dB, depending on the coded block size.
The maximum-likelihood (ML) decoder is derived for diagonal unitary space-time block code (STBC) matrices based double-differential modulation for multiple-input multiple-output systems. The ML decoder is obtained on ...
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The maximum-likelihood (ML) decoder is derived for diagonal unitary space-time block code (STBC) matrices based double-differential modulation for multiple-input multiple-output systems. The ML decoder is obtained on the basis of maximising the joint probability density function of three consecutively received data matrices.
A digital error correction technique with negligible hardware overhead is proposed for binary successive approximation ADCs. A redundant decision phase is inserted between the normal SAR operations, and the coarse dec...
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A digital error correction technique with negligible hardware overhead is proposed for binary successive approximation ADCs. A redundant decision phase is inserted between the normal SAR operations, and the coarse decision error caused by incomplete DAC settling is corrected by a digital code addition. The relaxed DAC settling requirement for coarse decision increases the conversion speed.
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