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On Maximum ContentionFree Interleavers and Permutation Polynomials over Integer Rings
 IEEE TRANS. ON INFORM. THEORY
, 2006
"... An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contentionfree interleavers have been recently shown to be suitable for p ..."
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Cited by 23 (3 self)
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An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contentionfree interleavers have been recently shown to be suitable for parallel decoding of turbo codes. In this correspondence, it is shown that quadratic permutation polynomials generate maximum contentionfree interleavers, i.e., every factor of the interleaver length becomes a possible degree of parallel processing of the decoder. Further, it is shown by computer simulations that turbo codes using these interleavers perform very well for the 3rd Generation Partnership Project (3GPP) standard.
Optical communication using subcarrier PSK intensity modulation through atmospheric turbulence channels,
 IEEE Trans. Commun.
, 2007
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Joint CodingPrecoding with LowComplexity TurboDecoding
 IEEE Transactions on Wireless Communications
, 2004
"... We combine errorcontrol coding with linear precoding (LP) for flatfading channels, as well as for wireless orthogonal frequencydivision multiplexing transmissions through frequencyselective fading channels. The performance is analyzed and compared with the corresponding errorcontrolcoded syste ..."
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Cited by 14 (5 self)
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We combine errorcontrol coding with linear precoding (LP) for flatfading channels, as well as for wireless orthogonal frequencydivision multiplexing transmissions through frequencyselective fading channels. The performance is analyzed and compared with the corresponding errorcontrolcoded system without precoding. By wedding LP with conventional errorcontrol coding, the diversity order becomes equal to the errorcontrol code's minimum Hamming distance times the precoder size. We also derive a lowcomplexity turbodecoding algorithm for joint codedprecoded transmissions. We analyze the decoding complexity and compare it with an errorcontrolcoded system without LP. Extensive simulations with convolutional and turbo codes for HiperLan/2 channels support the analysis and demonstrate superior performance of the proposed system.
Efficient hardware implementation of a highlyparallel 3GPP . . .
 INTEGRATION, THE VLSI JOURNAL 44 (2011) 305–315
, 2011
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On quadratic inverses for quadratic permutation polynomials over integer rings
 IEEE Trans. Inf. Theory
, 2006
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Permutation Polynomial Interleavers: An AlgebraicGeometric Perspective
, 2006
"... An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an interleaver is a common measure for turbo coding applications. ..."
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Cited by 8 (1 self)
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An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an interleaver is a common measure for turbo coding applications. Maximumspread interleavers are interleavers whose spread factors achieve the upper bound. An infinite sequence of quadratic permutation polynomials over integer rings that generate maximumspread interleavers is presented. New properties of permutation polynomial interleavers are investigated from an algebraicgeometric perspective resulting in a new nonlinearity metric for interleavers. A new interleaver metric that is a function of both the nonlinearity metric and the spread factor is proposed. It is numerically demonstrated that the spread factor has a diminishing importance with the block length. A table of good interleavers for a variety of interleaver lengths according to the new metric is listed. Extensive computer simulation results with impressive frame error rates confirm the efficacy of the new metric. Further, when tailbiting constituent codes are used, the resulting turbo codes are quasicyclic.
On quasicyclic interleavers for parallel turbo codes
 IEEE Trans. Inform. Theory
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Computing sparse multiples of polynomials
 In Proc. Internat. Symp. on Algorithms and Computation (ISAAC
, 2010
"... We consider the problem of finding a sparse multiple of a polynomial. Given f ∈ F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h ∈ F[x] of f such that h has at most t nonzero terms, and if so, to find such an h. When F = Q and t is con ..."
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Cited by 2 (0 self)
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We consider the problem of finding a sparse multiple of a polynomial. Given f ∈ F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h ∈ F[x] of f such that h has at most t nonzero terms, and if so, to find such an h. When F = Q and t is constant, we give a polynomialtime algorithm in d and the size of coefficients in h. When F is a finite field, we show that the problem is at least as hard as determining the multiplicative order of elements in an extension field of F (a problem thought to have complexity similar to that of factoring integers), and this lower bound is tight when t = 2. 1