Double Toeplitz(shortly DT)codes are introduced here as a generalization of double circulant codes.The authors show that such a code is isodual,hence formally self-dual(FSD).FSD codes form a far-reaching generalization of self-dual codes,the most important class of codes of rate one-half.Self-dual DT codes are characterized as double circulant or double negacirculant.Likewise,even binary DT codes are characterized as double circulant.Numerical examples obtained by exhaustive search show that the codes constructed have best-known minimum distance,up to one unit,amongst formally self-dual codes,and sometimes improve on the known values.For q=2,the authors find four improvements on the best-known values of the minimum distance of FSD codes.Over F4 an explicit construction of DT codes,based on quadratic residues in a prime field,performs equally well.The authors show that DT codes are asymptotically good over Fq.Specifically,the authors construct DT codes arbitrarily close to the asymptotic Varshamov-Gilbert bound for codes of rate one half.
In this paper,we construct three classes of Clifford subsystem maximum distance separable(MDS)codes based on Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields Fq for specific code lengths.Moreover,our Clifford subsystem MDS codes are new because their parameters differ from the previously known ones.
In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code.Accordingly,an algorithm for selecting the information bits of the short code is proposed,and a specific two-stage decoding algorithm is presented.Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10^(-6)Furthermore,the proposed design can lower the error floor of original LDPC Codes.
In this paper,we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field.It is known that iterative decoding and interleaving between concatenated parallel codes are two key elements that make turbo codes perform significantly better than the conventional error control codes.This is analytically illustrated in this paper.We show that the decoded noise mean power in the iterative decoding decreases when the number of iterations increases,as long as the interleaving decorrelates the noise after each iterative decoding step.An analytic decreasing rate and the limit of the decoded noise mean power are given.The limit of the decoded noise mean power of the iterative decoding of a turbo code with two parallel codes with their rates less than 1/2 is one third of the noise power before the decoding,which can not be achieved by any non-turbo codes with the same rate.From this study,the role of designing a good interleaver can also be clearly seen.
Saleh等在期刊Journal of Applied Mathematics and Computing的第56卷第1期上发表论文“On complementary dual qusai-twist codes”[20],证明了拟扭转码在一定条件下是线性补对偶码(LCD码)。对其中的四个关键性定理进行修正与完善,进一步给出拟扭转码是LCD的充分条件,并由此构造出许多具有优良参数的LCD码。
