Constructions of Asymptotically Optimal Space–Frequency Codes for MIMO-OFDM Systems

Constructions of space-frequency (SF) codes for multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems with n_t transmit antennas and Q subcarriers are considered in this paper. Following the pairwise-error-probability analysis, it is known that in addition to the conventional rank distance criterion, the minimum column distance of (n_ttimesQ) SF codes serves as another benchmark in code design. SF codes with larger minimum column distance are expected to have better performance. Following this principle, the rate-diversity tradeoff for the MIMO-OFDM channels as well as two SF code constructions are presented. The first construction is obtained by right-multiplying the code matrices in a maximal rank-distance (MRD) code by a fixed (QtimesQ) nonsingular matrix. Codes obtained from this construction are called linearly transformed MRD (LT-MRD) codes. Minimum column distance of the LT-MRD codes, when averaged over all code ensembles, is shown to meet the Gilbert-Varshamov bound. For the case of constructing the (2times256) quadrature phase-shift keying (QPSK)-modulated SF codes, it is shown that the LT-MRD codes can provide a much larger minimum column distance at the value of ges50, compared to the values of 3,5, or 6 obtained by other available constructions. The second code construction, termed cyclotomic construction, is reminiscent of the construction of the Reed-Solomon codes except that the code polynomials are now selected according to the cyclotomic cosets of the underlying field. Exact minimum rank distances of the resultant codes are presented. It is shown that this newly constructed code is asymptotically optimal in terms of rate-diversity tradeoff. Bounds on the minimum column distance of these codes are also given     

Enhanced Public Key Security for the McEliece Cryptosystem

This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutation equivalent to the secret code. This increases the security level of the public key, thus opening the way for reconsidering the adoption of classical families of codes, like Reed–Solomon codes, that have been longly excluded from the McEliece cryptosystem for security reasons. It is well known that codes of these classes are able to yield a reduction in the key size or, equivalently, an increased level of security against information set decoding; so, these are the main advantages of the proposed solution. We also describe possible vulnerabilities and attacks related to the considered system and show what design choices are best suited to avoid them.     

Generalized concatenation of encoded tamed frequency modulation

A novel construction for encoded tamed frequency modulation (TFM) is introduced which is based on the principles of generalized concatenation. The inner TFM is partitioned into nested subsystems which increases the free Euclidean distances. In order to obtain a large distance among the nested TFM subsystems, the scrambler matrices have to be computed which transfer the original TFM into the equivalent TFM with better partitioning properties. Then outer convolutional codes with different error-correcting capabilities are used to protect the partitioning. The new concatenated and generalized concatenated constructions were simulated in an additive white Gaussian noise channel. A multistep decoding algorithm based on soft-output demodulation was used. We present various simulation results which show a significant coding gain in comparison with the best known trellis codes having the same trellis state complexity     

Simulation and Spectral Analysis of the Scrambler for 56Kbps Modem

Scrambler is a device that performs one-to-one mapping between input data bits and channel codes. It is used in synchronous data communication systems to retrieve timing information from the received data i.e. to aid synchronization between two modems. Present paper deals with the computer-aided simulation and spectral analysis of the scrambler to be used in 56Kbps voice-band modem. Matlab has been used for simulation and pre-spectral analysis including power spectral density, cross-correlation and auto-correlation. Implementation of scrambler has been done on Texas Instrument’s TMS320C50 digital signal processor (DSP) and post- spectral analysis has been performed using Signalogic DSP software. Simulated and practical results have been found identical, which ensures the successful implementation of scrambler.     

Shift-full-rank matrices and applications in space-time trellis codes for relay networks with asynchronous cooperative diversity

To achieve full cooperative diversity in a relay network, most of the existing space-time coding schemes require the synchronization between terminals. A family of space-time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed. The family is based on the stack construction by Hammons and El Gamal and its generalizations by Lu and Kumar. It has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted, where a row corresponds to a terminal (or transmit antenna) and its length corresponds to the memory size of the trellis code on that terminal. We call such matrices as shift-full-rank (SFR) matrices. A family of SFR matrices has been also constructed, but the memory sizes of the corresponding space-time trellis codes (the number of columns of SFR matrices) grow exponentially in terms of the number of terminals (the number of rows of SFR matrices), which may cause a high decoding complexity when the number of terminals is not small. In this paper, we systematically study and construct SFR matrices of any sizes for any number of terminals. Furthermore, we construct shortest (square) SFR (SSFR) matrices that correspond to space-time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity. We also present some simulation results to illustrate the performances of the space-time trellis codes associated with SFR matrices in asynchronous cooperative communications.     

Theoretical analysis of a correlation attack based on convolutional codes

One general class of attacks on stream ciphers is correlation attacks. Most of previous results regarding performance of correlation attacks have been based entirely on simulations. We use random coding bounds for convolutional codes to give a theoretical analysis of a previously proposed correlation attack based on convolutional codes. The results from the theoretical derivation are verified by simulations.     

公共广播工程部分声学特性测量报告——《公共广播系统工程技术规范(草案)》验证报告之一

公共广播系统声学特性指标测量是一项新的尝试,到目前为止还没有相应的国家标准可循。笔者根据《公共广播系统工程技术规范(草案)》的规定,选取了几个公共广播系统的若干个广播服务区进行了实地测量,并结合《公共广播系统工程技术规范(草案)》的规定对几种主要的指标进行了讨论。     

Limited-Shift-Full-Rank Matrices With Applications in Asynchronous Cooperative Communications

Shift-full-rank (SFR) matrices are matrices that have full row rank no matter how their rows are shifted. SFR matrices have been used lately as generator matrices for a family of space-time trellis codes to achieve full diversity in asynchronous cooperative communications, where the numbers of columns of the SFR matrices correspond to the memory sizes of the trellis codes. A systematic construction of SFR matrices, including the shortest (square) SFR (SSFR) matrices, has been also previously proposed. In this paper, we study a variation of SFR matrices with a relaxed condition: limited-shift-full-rank (LT-SFR) matrices, i.e., the matrices that have full row rank no matter how their rows are shifted as long as the shifts are within some range called delay tolerance. As the generator matrices for the previously proposed space-time trellis codes, LT-SFR matrices can guarantee asynchronous full diversity of the corresponding codes when the timing errors are within the delay tolerance. Therefore, due to the relaxed condition imposed on LT-SFR matrices, more eligible generator matrices than SFR matrices become available.     

基于GF(qN)上秩距离码的校验矩阵的验证方案

J.Stern(1996)在“公钥验证的一个新范例”中基于GF（2）上纠错码的校验矩阵提出了一验证方案。该文基于GF（q^N)(q为素数）上秩距离码的校验矩阵提出了一新的验证方案,将J.Stern的方案中对秘密数据s的重量限制改为对s秩的限制;证明了在随机预方模型中给出的协议是零知识交互证明,并显示出通过参数的适当选取,此方案比J.Stern的方案更安全。     

Reduction of polarization-dependent gain due to signal-to-signal Raman interaction in fiber Raman amplifier

An excellent polarization-dependent gain (PDG) suppression technique using a polarization scrambler is proposed in this letter. Investigations on PDG due to signal-to-signal Raman interaction among 40 wavelength-division-multiplexer signal channels were carried out experimentally to evaluate the system performance after incorporating a polarization scrambler in the system. It was confirmed by experiment that the use of polarization scrambler is an effective way to reduce PDG caused by signal-to-signal Raman interaction.     

An Overlay Photonic Layer Security Approach Scalable to 100 Gb/s [Topics in Optical Communications]

As data rates outpace the capabilities of electronic encryption schemes, photonic layer security may fill the gap in providing a communication security solution at high data rates. In this article we review and highlight the advantages of our proposed optical code-division multiplexed (OCDM)-based photonic layer security (PLS) system based on high-resolution control of the optical phase of tightly spaced phase locked laser lines. Such a PLS system is scaleable to 100 Gb/s and provides a protocol independent security solution. We review the use of high-resolution control of the optical phase of mode-locked laser frequency combs as an enabling technology for a new class of OCDM systems. A network based on such systems is compatible with and can have comparable spectral efficiency to existing DWDM networks. Through inverse multiplexing of 10 Gb/s tributaries, we have already demonstrated optical transmission of a 40 Gb/s aggregate OCDM signal over 400 km. Such a PLS solution is achieved through shared phase scrambling of the individual OCDM codes assigned to each of the tributaries using an integrated micro-ring resonator-based phase coder/ scrambler. The confidentiality of OCDM-based PLS is robust against exhaustive, known plain text, and archival/forensic attacks, and can complement digital encryption operating at higher layers. Moreover, the integrity of the PLS solution is ensured through the inherent coupling to confidentiality, since knowledge of the key is needed in order to easily alter the transmitted data stream without introducing observable errors. This system can leverage advances in optical integration to support new applications where electronic encryption is impractical because of space, weight, power, availability, and cost requirements. Such applications range from timely security support for the emerging 100 GbE standards to all-optical multilevel security offered through the compatibility of PLS with transparent DWDM networks.     

T-Code: 3-Erasure Longest Lowest-Density MDS Codes

In this paper, we study longest lowest-density MDS codes, a simple kind of multi-erasure array code with optimal redundancy and minimum update penalty. We prove some basic structure properties for longest lowest-density MDS codes. We define a "perfect" property for near-resolvable block designs (NRBs) and establish a bijection between 3-erasure longest lowest-density MDS codes (T-Codes) and perfect NRB(3κ + 1, 3, 2)s. We present a class of NRB(3κ+1, 3, 2)s, and prove that it produces a family of T-Codes. This family is infinite assuming Artin?s Conjecture. We also test some other NRBs and find some T-Code instances outside of this family.     

On the theory of space-time codes for PSK modulation

The design of space-time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas. The lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords, which is difficult to relate to traditional code designs over finite fields and rings. We present general binary design criteria for PSK-modulated space-time codes. For linear BPSK/QPSK codes, the rank of (binary projections of) the unmodulated codewords, as binary matrices over the binary field, is a sufficient design criterion: full binary rank guarantees full spatial diversity. This criterion accounts for much of what is currently known about PSK-modulated space-time codes. We develop new fundamental code constructions for both quasi-static and time-varying channels. These are perhaps the first general constructions-other than delay diversity schemes-that guarantee full spatial diversity for an arbitrary number of transmit antennas     

Full-diversity, high-rate space-time block codes from division algebras

We present some general techniques for constructing full-rank, minimal-delay, rate at least one space-time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field /spl Qopf/ embedded in matrix rings. The first half of the paper deals with constructions using field extensions of /spl Qopf/. Working with cyclotomic field extensions, we construct several families of STBCs over a wide range of signal sets that are of full rank, minimal delay, and rate at least one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field extensions. In the later half of the paper, we discuss two ways of embedding noncommutative division algebras into matrices: left regular representation, and representation over maximal cyclic subfields. The 4/spl times/4 real orthogonal design is obtained by the left regular representation of quaternions. Alamouti's (1998) code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it. Also, we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the STBCs obtained from this construction. Another family of cyclic division algebras discovered by Brauer (1933) is discussed and several examples of STBCs derived from each of these constructions are presented.     

Matrix partitioning code family for spectral amplitude coding OCDMA

This paper presents a family of newly constructed codes to mitigate the multiple access interference (MAI) and phase-induced intensity noise (PIIN) in spectral amplitude-coding optical code division multiple access systems. The family of newly constructed codes, named matrix portioning (MP) code, is derived from arithmetic sequence, and their cross-correlation is not larger than one. In addition, the weight code can be any number which makes an MP promising code for future optical communication systems. We have also described detailed examples on how to construct this code family. The results reveal that the MP code is effective in reducing the MAI and PIIN, while maintaining a good signal-to-noise ratio and low bit error probability. Simulation results taken from a commercial optical system simulator, Virtual Instrument Photonic \((\hbox {VPI}^{\mathrm{TM}})\) , are also demonstrated. The results obtained for MP code have shown significant improvement compared to other schemes that employ flexible cross-correlation, multi diagonal, dynamic cyclic shift, and random diagonal codes. It is shown that, when the effective power is large, the intensity noise specifies as the main factor that deteriorates the system performance. When the effective power is not sufficiently large, thermal and shot noise sources become the main limiting factors and the effect of thermal noise is more influential than that of shot noise.     

New optical orthogonal codes by using diophantine equations

Two families of optical orthogonal codes (OOC's) are algebraically designed by using the parametric binary quartic and quadratic forms. The first family of codes has ideal auto and cross-correlation properties and the second family has nonideal cross-correlation properties. The performance of these codes is presented as function of the number of simultaneous OCDMA system users. We present examples of the constructed codes for illustration purposes. The algebraic OOC's being proposed in this paper find applications in asynchronous optical code division multiple access (OCDMA) systems.     

Golomb Costas序列的结构及其在OFDM系统中的应用

研究了用循环移位法获得的Golomb Costas序列族的特性,建立了含有一个间隙行和一个间隙列的Golomb Costas序列的结构理论,深入研究了含有一个间隙行和一个间隙列的Golomb Costas序列的代数结构、构造方法和自（互）相关特性,并证明了相关的定理。探索了用含有一个间隙行和一个间隙列的Golomb Costas序列设计OFDM 系统中跳频图样的方法,举例说明了如何设计跳频码和怎样将跳频码分配给 OFDM 系统中的用户。用含有一个间隙行和一个间隙列的Golomb Costas序列设计跳频码能获得理想的自相关特性,并且当无线通信系统中多普勒频移受限时能获得极佳的互相关性能。     

Bounds on covering codes with the rank metric

In this paper, we investigate geometrical properties of the rank metric space and covering properties of rank metric codes. We first establish an analytical expression for the intersection of two balls with rank radii, and then derive an upper bound on the volume of the union of multiple balls with rank radii. Using these geometrical properties, we derive both upper and lower bounds on the minimum cardinality of a code with a given rank covering radius. The geometrical properties and bounds proposed in this paper are significant to the design, decoding, and performance analysis of rank metric codes.     

Bounds on the error probability ofml decoding for block and turbo-block codes

The performance of either structured or random turbo-block codes and binary, systematic block codes operating over the additive white Gaussian noise (Awgn) channel, is assessed by upper bounds on the error probalities of maximum likelihood (Ml) decoding. These bounds on the block and bit error probability which depend respectively on the distance spectrum and the input-output weight enumeration function (Iowef) of these codes, are compared, for a variety of cases, to simulated performance of iterative decoding and also to some reported simulated lower bounds on the performance ofMl decoders. The comparisons facilitate to assess the efficiency of iterative decoding (as compared to the optimalMl decoding rule) on one hand and the tightness of the examined upper bounds on the other. We focus here on uniformly interleaved and parallel concatenated turbo-Hamming codes, and to that end theIowefs of Hamming and turbo-Hamming codes are calculated by an efficient algorithm. The usefulness of the bounds is demonstrated for uniformly interleaved turbo-Hamming codes at rates exceeding the cut-off rate, where the results are compared to the simulated performance of iteratively decoded turbo-Hamming codes with structured and statistical interleavers. We consider also the ensemble performance of ‘repeat and accumulate’ (Ka) codes, a family of serially concatenated turbo-block codes, introduced by Divsalar, Jin and McEliece. Although, the outer and inner codes possess a very simple structure: a repetitive and a differential encoder respectively, our upper bounds indicate impressive performance at rates considerably beyond the cut-off rate. This is also evidenced in literature by computer simulations of the performance of iteratively decodedRa codes with a particular structured interleaver.     

低秩循环矩阵的构造方法及其关联的多元LDPC码

在图像处理中,低秩矩阵的冗余信息可用于图像恢复和图像特征提取,而在迭代译码中,校验矩阵的冗余行可以加快译码收敛速度。该文研究一类易于硬件实现的低秩循环矩阵。首先将循环矩阵转换为位置集合,并基于同构理论简化了位置集合的搜索空间,从而基于比特移位方法提出了循环矩阵的构造方法。考虑非零域元素的列赋值与矩阵秩之间的关系,选取Tanner图中没有长度为4的环的循环矩阵,基于非零域元素的列赋值思想提出了不同阶数、不同码率的多元LDPC码构造方法。数值仿真结果表明,与基于PEG算法构造的二元LDPC码比较,所构造的多元LDPC码在BPSK调制方式下在误码字率10–5附近有0.9 dB的增益;在与高阶调制相结合时,有更大的性能提升。此外,所构造的多元LDPC码在迭代5次与50次下的性能几乎一致,这为低时延高可靠通信提供了一种有效的候选编码方案。