In this paper, we analyze the existing results to derive the cross-correlation distributions of p-ary m-sequences and their decimated sequences for an odd prime p and various decimations d. Based on the previously known results, a methodology to obtain the distribution of their cross-correlation values is also formulated.

In this paper, for an odd prime p and i=0,1, we investigate the cross-correlation between two decimated sequences, s(2t+i) and s(dt), where s(t) is a p-ary m-sequence of period pn-1. Here we consider two cases of ${d}$, ${d=rac{(p^m +1)^2}{2} }$ with ${n=2m}$, ${p^m equiv 1 pmod{4}}$ and ${d=rac{(p^m +1)^2}{p^e + 1}}$ with n=2m and odd m/e. The value distribution of the cross-correlation function for each case is completely determined. Also, by using these decimated sequences, two new p-ary sequence families of period ${rac{p^n -1}{2}}$ with good correlation property are constructed.

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn-1, pe-1, (pn -1)/(pe -1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. This generalization becomes possible due to a completely new proof comprising any prime p. Under this proof, the quaternary case can be considered as a specific example for p = 2.

In this letter, we propose a multi-stage decoding scheme with post-processing for low-density parity-check (LDPC) codes, which remedies the rapid performance degradation in the high signal-to-noise ratio (SNR) range known as error floor. In the proposed scheme, the unsuccessfully decoded words of the previous decoding stage are re-decoded by manipulating the received log-likelihood ratios (LLRs) of the properly selected variable nodes. Two effective criteria for selecting the probably erroneous variable nodes are also presented. Numerical results show that the proposed scheme can correct most of the unsuccessfully decoded words of the first stage having oscillatory behavior, which are regarded as a main cause of the error floor.

Many selected mapping (SLM) schemes have been proposed to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signal sequences. In this paper, an efficient selection (ES) method of the OFDM signal sequence with minimum PAPR among many alternative OFDM signal sequences is proposed; it supports various SLM schemes. Utilizing the fact that OFDM signal components can be sequentially generated in many SLM schemes, the generation and PAPR observation of the OFDM signal sequence are processed concurrently. While the u-th alternative OFDM signal components are being generated, by applying the proposed ES method, the generation of that alternative OFDM signal components can be interrupted (or stopped) according to the selection criteria of the best OFDM signal sequence in the considered SLM scheme. Such interruption substantially reduces the average computational complexity of SLM schemes without degradation of PAPR reduction performance, which is confirmed by analytical and numerical results. Note that the proposed method is not an isolated SLM scheme but a subsidiary method which can be easily adopted in many SLM schemes in order to further reduce the computational complexity of considered SLM schemes.

Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg {rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.

Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pn+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.

In this paper, for an odd prime p such that p≡3 mod 4, odd n, and d=(pn+1)/(pk+1)+(pn-1)/2 with k|n, the value distribution of the exponential sum S(a,b) is calculated as a and b run through $mathbb{F}_{p^n}$. The sequence family $mathcal{G}$ in which each sequence has the period of N=pn-1 is also constructed. The family size of $mathcal{G}$ is pn and the correlation magnitude is roughly upper bounded by $(p^k+1)sqrt{N}/2$. The weight distribution of the relevant cyclic code C over $mathbb{F}_p$ with the length N and the dimension ${ m dim}_{mathbb{F}_p}mathcal{C}=2n$ is also derived.

In this paper, for an odd prime p, two positive integers n, m with n=2m, and pm≡1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm+1), and the upper bound is derived as $rac{3}{2}p^m + rac{1}{2}$. In fact, those two sequences correspond to the p-ary sequences used for the construction of Kasami sequences decimated by 2. This result is also used to obtain an upper bound on the cross-correlation magnitude between a p-ary m-sequence and its decimated sequence with the decimation factor $d=rac{(p^m +1)^2}{2}$.

In this paper, using the exact expression for the pairwise error probability derived in terms of the message symbol distance between two message vectors rather than the codeword symbol distance between two transmitted codeword matrices, the exact closed form expressions for the symbol error probability of any linear orthogonal space-time block codes in slow Rayleigh fading channel are derived for QPSK, 16-QAM, 64-QAM, and 2 56-QAM.

In this paper, a new class of bent functions is constructed by combining class M and class C bent functions. Using the construction method of the class D bent functions defined on the binary vector space, new p-ary generalized bent functions are also introduced for odd prime p.

It is known that in the selected mapping (SLM) scheme for orthogonal frequency division multiplexing (OFDM), correlation (CORR) metric outperforms the peak-to-average power ratio (PAPR) metric in terms of bit error rate (BER) performance. It is also well known that four times oversampling is used for estimating the PAPR performance of continuous OFDM signal. In this paper, the oversampling effect of OFDM signal is analyzed when CORR metric is used for the SLM scheme in the presence of nonlinear high power amplifier. An analysis based on the correlation coefficients of the oversampled OFDM signals shows that CORR metric of two times oversampling in the SLM scheme is good enough to achieve the same BER performance as four times and 16 times oversampling cases. Simulation results confirm that for the SLM scheme using CORR metric, the BER performance for two times oversampling case is almost the same as that for four and 16 times oversampling cases.

In this paper, using p-ary bent functions defined on vector space over the finite field Fpk, we generalized the construction method of the families of p-ary bent sequences with balanced and optimal correlation properties introduced by Kumar and Moreno for an odd prime p, called generalized p-ary bent sequences. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuchi and Imamura is a special case of the newly constructed generalized p-ary bent sequences.

In this letter, we enumerate the number of cyclically inequivalent M-ary Sidel'nikov sequences of given length as well as the number of distinct autocorrelation distributions that they can have, while we change the primitive element for generating the sequence.

In this letter, we analyze the convergence speed of layered decoding of block-type low-density parity-check codes and verify that the layered decoding gives faster convergence speed than the sequential decoding with randomly selected check node subsets. Also, it is shown that using more subsets than the maximum variable node degree does not improve the convergence speed.

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = pk +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pn -1 because gcd(d, pn - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pn -1 is constructed, whose family size is pn and Cmax is 1 + p.

In this paper, a new construction method of quaternary sequences of even period 2N having the ideal autocorrelation and balance properties is proposed. These quaternary sequences are constructed by applying the inverse Gray mapping to binary sequences of odd period N with the ideal autocorrelation. Autocorrelation distribution of the proposed quaternary sequences is derived. These sequences can be used to construct quaternary sequence families of even period 2N. Family size and the maximum absolute value of correlation spectrum of the proposed quaternary sequence families are also derived.

There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem, called compressed sensing (CS). In the MPAs, the correlation step makes a dominant computational complexity. In this paper, we propose a new fast correlation method for the MPA when we use partial Fourier sensing matrices and partial Hadamard sensing matrices which are widely used as the sensing matrix in CS. The proposed correlation method can be applied to almost all MPAs without causing any degradation of their recovery performance. Also, the proposed correlation method can reduce the computational complexity of the MPAs well even though there are restrictions depending on a used MPA and parameters.

In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field Fq which is the splitting field of x2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.

The probability of making mistakes on the decoded signals at the relay has been used for the maximum-likelihood (ML) decision at the receiver in the decode-and-forward (DF) relay network. It is well known that deriving the probability is relatively easy for the uncoded single-antenna transmission with M-pulse amplitude modulation (PAM). However, in the multiplexing multiple-input multiple-output (MIMO) transmission, the multi-dimensional decision region is getting too complicated to derive the probability. In this paper, a high-performance near-ML decoder is devised by applying a well-known pairwise error probability (PEP) of two paired-signals at the relay in the MIMO DF relay network. It also proves that the near-ML decoder can achieve the maximum diversity of MSMD+MR min (MS,MD), where MS, MR, and MD are the number of antennas at the source, relay, and destination, respectively. The simulation results show that 1) the near-ML decoder achieves the diversity we derived and 2) the bit error probability of the near-ML decoder is almost the same as that of the ML decoder.