基于二元二值序列构造四元低相关区序列集

该文基于长度为N=ML+r的具有理想二值自相关特性的二元序列,构造了一类四元低相关区序列集。得到的序列集参数如相关区长度和序列数目等在一定范围内可以灵活设定。当r0可以同时构造出多个具有相同参数的四元低相关区序列集。当r=0时得到的低相关区序列集中序列数目接近甚至达到理论界限。该文方法可以为准同步CDMA扩频通信系统提供更多的低相关区序列。     

二元最佳低相关区序列集构造法

基于周期为2m-1的二元伪随机序列,利用交织法构造了一类满足一定条件的周期为2m+1-1的基序列集,进而利用这些基序列集构造得到了一类参数达到Tang-Fan-Matsufuji界的二元最佳低相关区序列集。这类低相关区序列集具有更多的序列数目,应用到准同步CDMA系统可以支持更多的用户。     

基于交织法的不等价低零相关区序列集设计

本文给出两种新的移位序列集的构造方法,同时计算出不等价移位序列集数量的上界.提出移位序列起始点和初始距离的概念,CBIID方法通过设计合适的初始距离构造多个不等价移位序列集,可以利用交织技术获得多个不等价低零相关区序列集,该方法灵活选择起始点,是对现有不等价移位序列构造方法的扩展.CBVID方法以此为基础,并在一个移位序列集合中基于不同的初始距离构造移位序列,增加了移位不等价低零相关区序列集合的数量,与现有方法相比,可以构造更多的适合多小区准同步码分多址通信系统的扩频序列集,不同小区分配的低零相关区序列集移位不等价,降低不同小区间用户的干扰.     

A Note on Low-Correlation Zone Signal Sets

In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ signal sets with huge sizes over three different alphabetic sets: finite field of size, integer residue ring modulo , and the subset in the complex field which consists of powers of a primitive th root of unity. We show a connection between these sequence designs and ldquocompletely noncyclicrdquo Hadamard matrices and a construction for those sequences. We also provide some open problems along this direction.     

Stochastic iterative algorithms for signal set design for Gaussianchannels and optimality of the L2 signal set

We propose a stochastic iteration approach to signal set design. Four practical stochastic iterative algorithms are proposed with respect to equal and average energy constraints and sequential and batch modes. By simulation, a new optimal signal set, the L2 signal set (consisting of a regular simplex set of three signals and some zero signals), is found under the strong simplex conjecture (SSC) condition (equal a priori probability and average energy constraint) at low signal-to-noise ratios (SNR). The optimality of the L1 signal set, the confirmation of the weak simplex conjecture, and two of Dunbridge's (1967) theorems are some of the results obtained by simulations. The influence of SNR and a priori probabilities on the signal sets is also investigated via simulation. As an application to practical communication system design, the signal sets of eight two-dimensional (2-D) signals are studied by simulation under the SSC condition. Two signal sets better than 8-PSK are found. Optimal properties of the L2 signal set are analyzed under the SSC condition at low SNRs. The L2 signal set is proved to be uniquely optimal in 2-D space. The class of signal sets S(M, K) (consisting of a regular simplex set of K signals and M-K zero signals) is analyzed. It is shown that any of the signal sets S(M, K) for 3⩽K⩽M-1 disproves the strong simplex conjecture for M⩾4, and if M⩾7, S(M, 2) (the L1 signal set) also disproves the strong simplex conjecture. It is proved that the L2 signal set is the unique optimal signal set in the class of signal sets S(M, K) for all M⩾4. Several results obtained by Steiner (see ibid., vol.40, no.5, p.721-31, 1994) for all M⩾7 are extended to all M⩾4. Finally, we show that for M⩾7, there exists an integer K'相似文献   

交织法构造高斯整数零相关区序列集

该文提出一种新的移位序列集的构造方法,并基于这些新的移位序列,通过交织周期为N的完备高斯整数序列,得到一类具有灵活相关区长度的周期为2N的高斯整数零相关区序列集。这类新的序列集的参数能接近甚至达到Tang-Fan-Matsuji界,所以序列集的性能是最佳的或者几乎最佳的。高斯整数零相关区序列集可为高速准同步扩频系统提供更多的地址选择空间。     

Enumeration and criteria for cyclically shift-distinct GMWsequences

Gordon-Mills-Welch (GMW) sequences (also called cascaded GMW sequences) have two-level autocorrelations. This property makes them widely used in various communication and cryptographic systems. The generation of q-ary GMW sequences of period q^n-1 involves three types of parameters. To determine whether GMW sequences are cyclically shift-distinct for differing parameters has remained an open question until now. In this paper, we completely solve this problem for varying all three types of parameters. We find a criterion for cyclically shift-distinct q-ary GMW sequences of period q^n-1, and obtain the number of such sequences. For the special case of q=2, this solution facilitates counting the number of cyclic Hadamard difference sets which correspond to binary GMW sequences of period 2^n-1     

On the Distortion SNR Exponent of Some Layered Transmission Schemes

We consider the problem of joint source-channel coding for transmitting K samples of a complex Gaussian source overT bK uses of a block-fading multiple-input multiple-output (MIMO) channel with M transmit and N receive antennas. We consider the case when we are allowed to code over L blocks. The channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent. The performance measure of interest is the rate of decay of the expected mean-squared error with the signal-to-noise ratio (SNR), called the distortion SNR exponent. We first show that using a broadcast strategy similar to that of Gunduz and Erkip, but with a different power and rate allocation policy, the optimal distortion SNR exponent can be achieved for 0 les b les (|N - M| + 1)/ min(M,N) and for b > MNL₂. This is the first time the optimal exponent is characterized for 1/min(M, N) < b < (|N - M| + 1)/min(M, N). Then, we propose a digital layered transmission scheme that uses both time layering and superposition. The new scheme is at least as good as currently known schemes for the entire range of bandwidth expansion factors b, whereas at least for some M, N, and b, it is strictly better than the currently known schemes.     

交织法构造移位不等价的ZCZ/LCZ序列集

本文给出了移位不等价序列集的概念,提出一种移位序列构造方法,并基于这种移位序列,利用交织法得到了多个移位不等价的低零相关区序列集.同以前方法相比扩展了序列集的数量,可以为准同步CDMA通信系统提供更多的扩频序列.通过本文方法还可以利用任意长度的完备序列来构造相互正交的零相关区序列集,放宽了对完备序列长度的限制,从而可以...     

Stopping set distribution of LDPC code ensembles

Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a /spl radic/1-/spl lambda/'(0)/spl rho/'(1) fraction of codes with /spl lambda/'(0)/spl rho/'(1)<1, and in particular for almost all codes with smallest variable degree >2, the smallest nonempty stopping set is linear in the block length. Bounds on the average block error probability as a function of the erasure probability /spl epsi/, showing in particular that for codes with lowest variable degree 2, if /spl epsi/ is below a certain threshold, the asymptotic average block error probability is 1-/spl radic/1-/spl lambda/'(0)/spl rho/'(1)/spl epsi/.     

四元零相关区周期互补序列集构造法

该文分别基于二元零相关区周期互补序列集和二元周期互补序列集做为初始序列,利用逆Gray映射构造了四元零相关区周期互补序列集。如果选取的初始序列集参数可以达到理论界限,得到的四元零相关区周期互补序列集接近甚至达到理论界限。零相关区互补序列集相比传统互补序列集具有更多的序列数目,应用到通信系统中可以支持更多的通信用户。     

周期准互补序列集构造法

该文基于2元序列支撑集和低相关序列集,提出一种新的周期准互补序列集构造框架。在此框架基础上,分别利用最优4元序列族A、族D和Luke序列集提出了3类渐近最优和渐近几乎最优周期准互补序列集,序列集参数由2元序列和低相关序列集共同决定。与传统的完备互补序列集相比,所构造的准互补序列集具有更多的序列数目,应用到多载波扩频通信系统中可以支持更多的用户。     

Polynomial Time Low-Density Parity-Check Codes With Rates Very Close to the Capacity of the q-ary Random Deletion Channel for Large q

We demonstrate polynomial-time deletion codes based on the verification-based decoding paradigm that come arbitrarily close to capacity. The random deletion channel takes n symbols from a q-ary alphabet, and each symbol is deleted independently with probability p. Taking advantage of recent improvements on the results of Luby and Mitzenmacher for verification-based decoding by Shokrollahi and Wang, we show how to design for any epsi>0 and sufficiently large n and q deletion codes with the following properties: the rate is (1-p)(1-epsi), the failure probability is n^O(1/epsi2)/q, and the computational complexity for encoding and decoding is n^O(1/epsi2)log q. We also extend these schemes to obtain the same results even if the undeleted symbols are also transposed arbitrarily, and if a sufficiently small number of random symbols are inserted     

Commutation signaling—An antimultipath technique

Two types of commutation signaling for combating multipath are introduced: M × N signaling, in which the signal set cycles successively among N different sets of M signals each; and M + N signaling, in which the signal set at any time consists of M members of an alphabet of M + N signals, N of which are inactive at any epoch. In both cases, the objective is to remove from use any signal sent recently enough that it is still "ringing" in the multipath channel. We consider the problems of minimization of M and N, hence the total number signals used; analysis of 2 × N sets (M = 2 is almost uniformly optimal); analysis of the simplest M + N set, i.e., a 2 + 1 set; and presentation of the results of simulation of M × N and M + N signaling through realistic urban/suburban radio channels. Comparison of these simulations to simulations of other antimultipath techniques is also made. The simulation results are due to Kamil [3].     

New constructions of quaternary low correlation zone sequences

In this paper, given a composite integer n, we propose a method of constructing quaternary low correlation zone (LCZ) sequences of period 2/sup n/-1 from binary sequences of the same length with ideal autocorrelation. These new sequences are optimal with respect to the bound by Tang, Fan, and Matsufuji. The correlation distributions of these new quaternary LCZ sequences constructed from m-sequences and Gordon-Mills-Welch (GMW) sequences are derived.     

Design of sequence set with group-wise zero correlation window

Zero correlation window (ZCW) or zero correlation zone (ZCZ) sequence can be used in quasi-synchronous code division multiple access (QS-CDMA) system to eliminate multiple access and multipath interferences. However, as the length of ZCW or ZCZ increases, fewer sequences are available. Recently, a new concept, sequence set with group-wise zero correlation window is introduced, which can increase the number of available sequences for a QS-CDMA system. In this article, a new method for generating sequence set with group-wise zero correlation window is presented. This method is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M. Compared with previous methods, the proposed sequence set has a group-wise zero correlation window for both periodic and aperiodic cross-correlation functions.     

A lower bound on the undetected error probability and strictlyoptimal codes

Error detection is a simple technique used in various communication and memory systems to enhance reliability. We study the probability that a q-ary (linear or nonlinear) block code of length n and size M fails to detect an error. A lower bound on this undetected error probability is derived in terms of q, n, and M. The new bound improves upon other bounds mentioned in the literature, even those that hold only for linear codes. Block codes whose undetected error probability equals the new lower bound are investigated. We call these codes strictly optimal codes and give a combinatorial characterization of them. We also present necessary and sufficient conditions for their existence. In particular, we find all values of n and M for which strictly optimal binary codes exist, and determine the structure of all of them. For example, we construct strictly optimal binary-coded decimal codes of length four and five, and we show that these are the only possible lengths of such codes     

Generalised Sarwate bounds on periodic autocorrelations and cross-correlations of binary sequences

A general periodic correlation bound named the generalised Sarwate bound for binary zero or low correlation zone (ZCZ/LCZ) sequence sets with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum cross-correlation value and zero or low correlation zone, are derived. It is shown that all the previous periodic sequence bounds, such as the Sarwate bound, Welch bound and Tang-Fan bound, are only special cases of the generalised Sarwate bound.     

Construction of fixed-length insertion/deletion correctingrunlength-limited codes

An algorithm is presented for the construction of fixed-length insertion/deletion correcting runlength-limited (RLL) codes. In this construction binary (d,k)-constrained codewords are generated by codewords of a q-ary Lee metric based code. It is shown that this new construction always yields better codes than known constructions. The use of a q-ary Lee (1987) metric code (q odd) is based on the assumption that an error (insertion, deletion, or peak-shift) has maximal size (q-1)/2. It is shown that a decoding algorithm for the Lee metric code can be extended so that it can also be applied to insertion/deletion correcting RLL codes. Furthermore, such an extended algorithm can also correct some error patterns containing errors of size more than (q-1)/2. As a consequence, if s denotes the maximal size of an error, then in some cases the alphabet size of the generating code can be s+1 instead of 2·s+1