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 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.

In this paper, we analyze the best relay selection scheme for the soft-decision-and-forward (SDF) cooperative networks with multiple relays. The term `best relay selection' implies that the relay having the largest end-to-end signal-to-noise ratio is selected to transmit in the second phase transmission. The approximate performances in terms of pairwise error probability (PEP) and bit error rate (BER) are analyzed and compared with the conventional multiple-relay transmission scheme where all the relays participate in the second phase transmission. Using the asymptotics of the Fox's H-function, the diversity orders of the best relay selection and conventional relay scheme for the SDF cooperative networks are derived. It is shown that both have the same full diversity order. The numerical results show that the best relay selection scheme outperforms the conventional one in terms of bit error rate.

In this paper, the performance of the soft-decision-and-forward (SDF) protocol in the cooperative communication network with one source, one relay, and one destination, where each node has two transmit and receive antennas, is analyzed in terms of the bit error rate (BER) obtained from the pairwise error probability (PEP). Using the moment generating function and Q-function approximation, the PEP of SDF protocol is calculated and we confirm that the SDF with two antennas achieves the full diversity order. For the slow-varying Rayleigh fading channel, the optimal power allocation ratio can be determined so as to minimize the average PEP (or BER). Due to the difficulty of deriving the optimal value analytically, an alternative strategy of maximizing the product signal-to-noise ratio (SNR) of direct and relay links, which we call the suboptimal power allocation, is considered. Through a numerical analysis, we show that the performance gap between the suboptimal and optimal power allocation strategies is negligible in the high SNR region.

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.