The power amplifier (PA) is an indispensable component in wireless communication systems, while the nonlinearity induced by PA can lead to significant performance degradation. The conventional nonlinearity equalization (NLE) method can effectively mitigate the nonlinear effects and provide superior BER performance but requires intensive computational complexity. To this end, we propose a novel NLE method in the time domain, which can significantly reduce the computational complexity without sacrificing the BER performance. Specifically, we first propose a novel PA representation of the sum of products (SPs), which is a unified time-domain representation for several typical memory and memoryless PA models. On this basis, the SPs-iterative least square equalizer (SPs-ILSE) method is proposed to mitigate the impact of both the memory and memoryless PA’s nonlinear distortions at the receiver side. The computational complexity of complex multiplication (CCCM) in the proposed method isO(NlogN) for the memoryless PA models andO(KN2) for the memory PA models. Moreover, considering the commonly utilized PA models, we also derive the closed-form expression for the achievable SINR of the SPs-ILSE method in the ideal conditions. Numerical results show that (i) the closed-form SINR expression is valid for both the memory and memoryless scenarios (ii) the proposed method exhibits the superior bit error rate (BER) performance in comparison to several relevant nonlinear signal processing methods such as digital pre-distortion (DPD), and power amplifier nonlinearity cancellation (PANC) (iii) the proposed NLE method achieves the same BER performance as the previous NLE method, i.e., reconstruction of distorted signals (RODS), while the CCCM of the proposed method is much lower.

The emergence of Industrial Internet of Things along with fog computing (FC) has brought great benefits in the industry field through real-time monitoring, resource optimization configuration, and intelligent cloud control. The deployment of fog nodes in industrial plants is the essential precondition for FC implementation. Existing works are mainly based on pregiven sensor traffic in the deployment of fog nodes, which largely ignores the stochastic uncertainty imposed by the dynamic industrial environment. In this article, without requiringa prioriknowledge of the sensor traffic pattern, we establish a mathematical model based on uncertain programming to formulate the fog node location determination and the sensor association problem. Owing to the complexity of the model, we introduce a learning-based algorithm to effectively solve the problem with an acceleration mechanism. Finally, intensive simulations are implemented to verify the performance of the algorithm. The results indicate that our approach outperforms other benchmarks in terms of transmission energy on planning fog nodes in industrial plants with stochastic sensor traffic.

Radio frequency fingerprint identification (RFFI) is a promising physical layer security technique that employs the hardware-introduced features extracted from the received signals for device identification. In this paper, we consider an RFFI problem in the presence of hybrid time-varying distortions (HTVDs) induced by multipath fading channel, carrier frequency offset (CFO), and phase offset. To solve this problem, an HTVDs-robust RFFI framework is proposed. Firstly, we derive that the residual HTVDs after CFO correction can be approximated as multiplicative interference in the frequency domain. Secondly, we define a novel signal analysis dimension named spectral quotient (SQ) representation and then present the spectral circular shift division (SCSD) method to generate the HTVDs-robust SQ signals, where the multiplicative interference can be suppressed. Thereafter, the statistics including root mean square (RMS), variance (VAR), skewness (SKE), and kurtosis (KUR) are extracted from the real and imaginary components of the SQ signals, respectively. Finally, the statistical features are used for the training and testing of the support vector machine (SVM) classifiers. To further enhance the performance of the proposed RFFI scheme, we also present the spectral circular multi-shift division (SCMSD) method, which increases the flexibility in the generation of the HTVDs-robust SQ signals. Given what we knew, this is the first time attempting to mitigate the HTVDs by leveraging the strong frequency correlation at the neighboring subcarriers in the multivariate hypothesis tasks. Compared to several handcraft feature-based RFFI methods, the proposed method exhibits superior identification accuracy and strong robustness. Experimental results show that the proposed RFFI scheme can achieve the accuracy of 91.3%with five devices and 86.4% with sixteen devices when the classifiers are trained with the additive white Gaussian noise but are tested with the Rayleigh channel.

Almost regular permutation (ARP) and quadratic permutation polynomials (QPP) are two common types of interleavers for parallel turbo decoding. However, for a turbo decoder using such an interleaver, previous memory-mapping schemes are applicable only if, P, the number of processors used, divides L, the interleaver length, and P satisfies various other constraints. In this paper, we introduce a novel memory-mapping scheme that removes these restrictions and allows the user more flexibility in determining the numbers of processors to be used, at the expense of some overhead.

This paper introduces a multiple signal mapped LDPC-BICM that enhances performance by combining coding and modulation similar to trellis coded modulations. Furthermore, a symbol decoding of LDPC-BICM is introduced, which directly uses the symbol metric. With the symbol decoding, an LDPC-BICM system can take the advantage of non-Gray constellation mappings. Simulation results are presented to show that the mixed non-Gray and Gray mapped LDPC-BICM with symbol decoding outperforms the conventional single Gray mapped LDPC-BICM with bit decoding by at least 0.2 dB.

Burst error detection codes and cyclic redundancy check (CRC) codes are generalized to event-error detection codes, which are useful in various noisy channels. A systematic linear block code is constructed that detects any event error from an arbitrary list of event errors. The result is generalized to detection and correction of multiple event errors. Bounds are found on the minimum number of redundant bits needed to construct such codes. It is shown that, under certain conditions, the linear code construction is optimal. Various applications are discussed, where there is a Markov source or a Markov channel. It is argued that the codes described herein can be employed either as error detection codes, or as distance-enhancing codes when complete decoders are applied. Specific examples covered in this correspondence include hybrid automatic repeat request (ARQ) systems, intersymbol interference (ISI) channels, and Gilbert (1958) channels.

Puncturing is the predominant strategy to construct high code rate convolutional encoders, and infinite impulse response (IIR) convolutional encoders are an essential building block in turbo codes. In this paper, various properties of convolutional encoders with these characteristics are developed. In particular the closed-form representation of a punctured convolutional encoder and its generator matrix is constructed, necessary and sufficient conditions are given such that the punctured encoders retain the IIR property, and various lower bounds on distance properties, such as effective free distance, are developed. Finally, necessary and sufficient conditions are given on the inverse puncturing problem: representing a known convolutional encoder as a punctured encoder.

A new bounded-distance (BD) decoding algorithm is presented for binary linear (n, k, d) block codes on additive white Gaussian noise channels. The algorithm is based on the generalized minimum distance (GMD) decoding algorithm of Forney (1989) using the acceptance criterion of Taipale and Pursley (GMD/TP) proposed in 1991. It is shown that the GMD/TP decoding algorithm is a BD decoding algorithm with effective error coefficient (/sup n//sub d/). It is also shown that the decision regions of GMD/TP are good inner approximations of those of full GMD decoding, and therefore full GMD decoding is BD and has an effective error coefficient that is well approximated by (/sup n//sub d/). Moreover, by adding a d-erasure-correction step to GMD decoding, the effective error coefficient can be reduced to A/sub d/, the number of minimum-weight codewords, which is the same as the effective error coefficient of maximum-likelihood decoding. The decoding algorithm is mainly based on algebraic errors-and-erasures decoding and therefore has polynomial rather than exponential complexity.

A simple method based on Newton's identities and their extensions is presented for determining the actual minimum distance of cyclic codes. More significantly, it is shown that this method also provides a mechanism for generating the type of syndrome matrices needed by Feng and Tzeng's (see ibid., vol.40, p.1364-1374, Sept. 1994) new procedure for decoding cyclic and BCH codes up to their actual minimum distance. Two procedures for generating such matrices are given. With these procedures, we have generated syndrome matrices having only one class of conjugate syndromes on the minor diagonal for all binary cyclic codes of length n<63 and many codes of length 63/spl les/n/spl les/99. A listing of such syndrome matrices for selected codes of length n<63 is included. An interesting connection of the method presented to the shifting technique of van Lint (1986) and Wilson is also noted.

A new algorithm is developed for decoding geometric Goppa codes (algebraic-geometric codes) up to their designed minimum distance. This algorithm is constructed on the basis of the one introduced by Porter, Shen, and Pellikaan (1992), but has improved it considerably in decoding capability by incorporating a majority voting scheme conceptually analogous to that employed by the algorithms of Feng and Rao (1993), and Duursma (1993). The algorithm is distinct from others in that its major steps are accomplished by solving a key equation in an affine ring. The result is a new algorithm with decoding capability on a par with that of Feng and Rao's and Duursma's algorithms. The new algorithm is applicable to a large class of geometric Goppa codes and thus provides a viable alternative to the algorithms of Feng and Rao, as well as Duursma for decoding geometric Goppa codes up to designed minimum distance.

Newton's identities have played a significant role in decoding and minimum distance determination of cyclic and BCH codes. The present paper carries the notion over from cyclic codes to algebraic-geometric (AG) codes and introduces Newton's identities for AG codes, also for the purpose of minimum distance determination and decoding.

An approach based on code decomposition and partial transform for constructing algorithms for decoding cyclic codes and algebraic-geometric (AG) codes is introduced. A general decoding procedure applicable to arbitrary linear codes and their subfield subcodes is then developed. In particular, we have developed algorithms for error-and-erasure decoding of cyclic codes up to their actual minimum distance, error-and-erasure decoding of AG codes up to their designed minimum distance, and decoding of subfield subcodes of AG codes (geometric BCH codes). Moreover, a generalization of geometric BCH codes is introduced. It is shown by an example that for a simple class of AG codes, the so-called one-point codes, this generalization brings a better estimate of their minimum distance. It is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minimum distance.

An explicit construction of a sequence of binary codes that asymptotically meet the Zyablov bound for rates lower than 0.30 is given by using Justesen's construction of concatenation. The outer codes are constructed from generalized Hermitian curves. These outer codes can be described without any algebraic geometry terminology, while the proofs of some properties deeply rely on algebraic geometry.>

Decoding geometric Goppa codes can be reduced to solving the key congruence of a received word in an affine ring. If the codelength is smaller than the number of rational points on the curve, then this method can correct up to 1.2 (d*-L)/2-s errors, where d* is the designed minimum distance of the code and s is the Clifford defect. The affine ring with respect to a place P is the set of all rational functions which have no poles except at P, and it is somehow similar to a polynomial ring. For a special kind of geometric Goppa code, namely C/sub Omega /(D,mP), the decoding algorithm is reduced to solving the key equation in the affine ring, which can be carried out by the subresultant sequence in the affine ring with complexity O(n/sup 3/), where n is the length of codewords.>

An infinite series of curves is constructed in order to show that all linear codes can be obtained from curves using Goppa's construction. If conditions are imposed on the degree of the divisor use, then criteria are derived for linear codes to be algebraic-geometric. In particular. the family of q-ary Hamming codes is investigated, and it is proven that only those with redundancy one or two and the binary (7,4,3) code are algebraic-geometric in this sense. For these codes. the authors explicitly give a curve, rational points, and a divisor. It is proven that this triple is in a certain sense unique in the case of the (7,4,3) code.>