In the realm of mobile communications, the receiver often encounters undesired situations where it receives only noise, interference, or unintended signals. In such cases, it may incorrectly infer that the decoding result is valid, particularly when the error detection capability, mainly provided by a cyclic redundancy check (CR C) code, falls short. While bounded distance decoding techniques based on the employed error-correcting code have been introduced to address this issue, there is still room for improvement especially when dealing with unintended signals. In this paper, we present a formula to identify the situation of unintended signals and find it expressed in terms of a metric called discrepancy. Utilizing this discrepancy, we interpret the problem of determining the validity of decoding results as a binary classification task. Then, we propose suitable machine learning techniques to improve the accuracy of the binary classification process. Our experimental results, conducted for the 5G New Radio (NR) system, demonstrate significant performance improvement resulting from the application of the proposed methods.

We address the suboptimality of successive cancellation (SC) decoding for polar codes, which is caused by treating as random variables all the future bits to be estimated later. For a target information bit, we define the frozen and parity bits located behind it as its future constraints (FCs). To incorporate FCs into the sequential decoding of the target bit, we propose two elementary techniques: an SC check (SCC) algorithm and an FC conversion rule enabling belief propagation (BP). Focusing on the binary erasure channel (BEC), we also present a tree search technique based on stack-based backjumping (SBJ) to efficiently solve dynamic constraint satisfaction problems (CSP) formulated by FCs. Numerical results show that the combination of BP and SCC decoding algorithms accompanied with the SBJ technique achieves excellent erasure recovery performance over the BEC, which is close to the dependence testing (DT) achievability bound.

Concatenated polar codes under successive cancellation list (SCL) decoding have excellent error-correction performance. However, their expected error-detection capability becomes degraded, when we increase the list size of the SCL decoder in order to improve their error-correction performance. In this paper, we propose a configuration design scheme for the SCL decoder and a post-decoding validation check scheme in order to provide a better tradeoff between error-detection and error-correction performance. Firstly, a configuration of the SCL decoder is designed to improve its own error detection capability. Specifically, a part of dynamic frozen bits (also called parity-check bits) is used for path checking during SCL decoding rather than their original purpose of use, path pruning. Furthermore, the number of paths to be checked by the applied cyclic redundancy check (CRC) code is limited. Secondly, a new metric corresponding to the correlation between the received signal vector and the decoded one is presented to check the validity of the decoding result. These proposed schemes are analyzed to provide a proper configuration of the SCL decoder and determine a threshold for post-decoding validation check. Numerical results show that a better tradeoff between error correction and detection is achieved, compared with conventional schemes.

Shaped polar codes were recently proposed to improve the spectral efficiency of polar coded modulation, based on probabilistic shaping. The key principle for them is to adjust the probability of occurrence of 1's in each codeword by introducing the shaping bits, which makes the distribution of modulated symbols close to the Gaussian distribution. But, they have a serious problem from a practical viewpoint, since additional polar decoding is required to determine the shaping bits. In this paper, we investigate an algebraic approach to the design of structurally shaped polar codes. We first select a shaping set in an algebraic and systematic way and determine the shaping bits by using simple binary and integer operations without any additional polar decoding. We then propose a method to construct structurally shaped polar codes, and analyze their shaped probability in an approximate way. Finally, we present the encoding and decoding procedures for the proposed shaped polar codes. Numerical results show that the proposed shaping scheme has similar performance than the conventional shaping scheme regardless of whether cyclic redundancy check is employed, while the former can be implemented in an extremely simpler way than the latter.

Integer-forcing (IF) receivers are a class of linear multiple-input multiple-output (MIMO) receivers to achieve near-optimal performance under quasi-static channels, with almost the same complexity as that of conventional linear receivers. Instead of trying to recover the transmitted messages directly, an IF receiver recovers their integer-linear combinations corresponding to a chosen integer-valued effective channel matrix, and then obtains them. Recently, the IF strategy has been extended to a block fading scenario. In this paper, we propose a novel IF receiver for block fading channels, called a multimode IF (M-IF) receiver. Unlike conventional IF receivers, the proposed M-IF receiver employs several integer-valued effective channel matrices for IF decoding. We also propose an efficient search algorithm for selecting such matrices with the aid of Gaussian elimination. We then show that for any channel realizations, the proposed M-IF receiver has better performance in terms of the effective noise variance than conventional IF receivers. Simulation results demonstrate that it works really well in various environments.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made incapable (by puncturing) or to be shortened are governed by binary domination. In particular, we show that binary domination completely determines incapable or shortened bit patterns for polar codes, and that all the possible incapable or shortened bit patterns can be identified. We then present the patterns of the corresponding encoder output bits to be punctured or fixed, when the incapable or shortened bits are given.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination. For punctured and shortened polar codes, we prove that the partial order by binary domination completely determines both incapable bit patterns (by puncturing) and fixed bit patterns (by shortening). In particular, we give a necessary and sufficient condition for an encoder output bit to be fixed by additionally shortening a single encoder input bit, as well as a necessary and sufficient condition for an encoder input bit to be made incapable by additionally puncturing a single encoder output bit. We also identify all the puncturing bit patterns yielding a given incapable bit pattern. These results provide a guidance to design a practical rate-matching scheme for polar codes. As an example, we present a rate-matching scheme based on our analytical observations. Numerical results show that it performs well over a wide range of code lengths and rates, compared with conventional rate-matching schemes.

Trapping sets with short cycles are known to give a detrimental effect on the error floor performance of a low-density parity-check (LDPC) code. Unlike in binary LDPC codes., short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is crucial to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles.

Short cycles in a nonbinary low-density parity-check (NB-LDPC) code may be even more harmful to its performance if they do not satisfy the so-called full rank condition (FRC). This is because they may induce low-weight codewords or absorbing sets in that case. Thus, it is important to count the number of short cycles not satisfying the FRC as well as the number of short cycles for analyzing the performance of an NB-LDPC code. In this paper, we first develop a novel message-passing algorithm and identify how it is related to the FRC. We then propose a low-complexity algorithm for counting the number of short cycles not satisfying the FRC in an NB-LDPC code, as well as the number of short cycles. Finally, we propose a low-complexity algorithm for designing an NB-LDPC code with low error floor. Depending on the modulation scheme, the codes constructed by the proposed design algorithm have similar or slightly worse performance, compared with those constructed via the method by Poulliat et al. However, the proposed design algorithm does not require a cycle enumeration algorithm with high complexity, and therefore is feasible even in the case of large code length, say ≥5000.

The extended min-sum (EMS) algorithm for decoding low-density parity-check codes over the finite field with q elements significantly reduces decoding complexity by truncating each message of length q into a message of effective length nm. The number of effectively dominant components in each truncated message may gradually decrease with the number of decoding iterations. Based on this observation, we propose a novel adaptive EMS algorithm, called a two-length EMS (TL-EMS) algorithm. It chooses one of two candidate values as the effective message length nmfor each message by reflecting the concept called message separation. Numerical results show that it can significantly reduce the computational complexity with little performance degradation.

In this study, the coverage of downlink cellular orthogonal frequency‐division multiple‐access networks transmitting one quadrature‐amplitude modulation symbol per hop is analysed. The coverage probability is first defined by using an upper bound on the bit error rate (BER) of a bit‐interleaved coded modulation system. Moreover then, the moment generating functions of the legacy Gaussian and Laplacian metrics (LMs) for soft‐decision decoding of an employed error‐correcting code are derived for computing the upper bound on the BER and the corresponding coverage probability of the networks. Numerical results demonstrate that due to the impulsive nature of the inter‐cell interference for moderate‐to‐small cell loads, the networks using the LM for soft‐decision decoding significantly outperform those employing the legacy Gaussian metric in terms of the achievable cell radius and the amount of the average transmit power reduction.

In optical communication systems supporting multiple quality-of-services, variable-weight optical orthogonal codes (VW-OOCs) are employed as spreading codes. In this paper, we present three new families of optimal VW-OOCs with length (q - 1)N and maximum correlation value 1, where q is a prime power and N is a positive integer with gcd(q - 1, N) = 1. These new optimal VW-OOCs can be obtained from optimal constant-weight optical orthogonal codesof length N. Compared with the previously known optimal VW-OOCs, these families can have codewords of higher weights.

The extended min‐sum (EMS) and improved EMS (I‐EMS) algorithms for non‐binary low‐density parity‐check codes over GF( q ) significantly reduce the decoding complexity with an acceptable performance degradation, but they suffer from high latency because of many serial computations, including a sorting process. On the other hand, the trellis‐based EMS algorithm can greatly reduce the latency, but it does not solve the complexity problem in high‐order fields ( q ≥ 64). To improve the latency problem with low‐complexity advantages, the authors propose heap‐based EMS (H‐EMS) and heap‐based I‐EMS (HI‐EMS) algorithms that are modifications of the EMS and I‐EMS algorithms, respectively. The authors also propose double H‐EMS and double HI‐EMS algorithms trading off the latency against the performance by heaping messages twice. Numerical results show that the H‐EMS algorithm has 2.74–9.52 times lower latency than the EMS algorithm with a negligible performance degradation over a wide range of code rates, whereas the HI‐EMS algorithm has 1.20–1.62 times lower latency than the I‐EMS algorithm. Furthermore, the proposed algorithms may be employed regardless of the decoding schedules.

Multitone‐frequency and quadrature‐amplitude modulation (MFQAM) is a combination of multitone frequency‐shift keying and quadrature‐amplitude modulation (QAM). In this study, the authors consider MFQAM with active subcarriers grouped in balance, where the active subcarriers are divided into a specified number of groups and the same QAM symbol is conveyed by every subcarrier in each group. This grouping may make MFQAM have frequency diversity in itself. They first derive the joint probability density function of the correlator outputs of an MFQAM receiver. They then compute the channel capacity of a coded modulation (CM) system employing MFQAM over Rayleigh fading channels. As a result, they demonstrate that for a moderate code rate between 1/3 and 2/3, its normalised throughput is close to the channel capacity limit in the low signal‐to‐noise ratio region, contrary to a CM system employing the conventional modulation. They also evaluate the frame error rate (FER) performance of a CM system employing MFQAM when a non‐binary error‐correcting code is employed. Numerical results demonstrate that the normalised throughput of the CM system computed via the FER shows a similar trend to that obtained via the channel capacity.

The optical orthogonal codes (OOCs) have been widely used as spreading codes in communication systems employing the unipolar transmission. They are classified into constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs) according to the number of distinct Hamming weights which their codewords have. In this paper, we present a new generic construction of VW-OOCs of length (q - 1)N from a CW-OOC of length N, where q is a prime power and gcd(q - 1, N) = 1. As a result, three new families of optimal VW-OOCs with a maximum correlation value 1 are obtained. In particular, these families can have the codewords of high weights, while most of the previously known optimal VW-OOCs have only codewords of weight less than 8.

The induced correlations of a pair of sequences are defined as the full-period correlations between the linear phase-shifting sequences of one of the given pair and the other one. This concept was introduced in the analysis of their partial-period correlations which are an important performance measurement of the employed communication system. In this paper, we investigate the induced correlations of Zadoff-Chu sequences in a transform approach. For a pair of Zadoff-Chu sequences, we first compute the spectrums of their induced correlations. By taking the inverse discrete Fourier transform (IDFT) on these spectrums, we then derive their induced correlations in a closed form. As a result, we show that their induced correlations can be viewed as expanded and scaled Zadoff-Chu sequences of a smaller period. Not only does our approach give the magnitudes of the induced correlations of Zadoff-Chu sequences, but it also gives the phase information which is applicable to computation of their partial-period correlations.

The distribution of the intercell interference (ICI) in conventional cellular networks employing orthogonal frequency-division multiple-access (OFDMA) with quadrature-amplitude modulation (QAM) tends to approach a Gaussian distribution when all available subcarriers in each cell are fully loaded. Recently, it has been also shown that the worst-case distribution of the ICI as additive noise in wireless networks with respect to the channel capacity is Gaussian. Thus, the channel capacity in cellular networks is expected to be further enhanced when the ICI could be designed properly so that it has a non-Gaussian distribution. This observation motivates us to propose, in this paper, a downlink cellular OFDMA network employing a modulation scheme called frequency and QAM (FQAM). We also derive maximum-likelihood metrics for the binary or non-binary error-correcting codes employed in the proposed network and propose their practical sub-optimal versions. Numerical results demonstrate that the distribution of the ICI in the proposed network deviates far from the Gaussian distribution. As a result, the transmission rates for the cell-edge users in the proposed network are significantly improved. In addition, the measurement results using practically implemented FQAM-based OFDMA systems verify that the transmission rates for the cell-edge users can dramatically increase, compared with the conventional QAM-based OFDMA network.

Frequency-hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency-hopping spread spectrum systems. In this paper, we present two new constructions for FHS sets. We first give a new construction for FHS sets of length nN for two positive integers n and N with gcd(n, N) = 1. We then present another construction for FHS sets of length (q - 1)N, where q is a prime power satisfying gcd(q - 1, N) = 1. By these two constructions, we obtain infinitely many new optimal FHS sets with respect to the Peng-Fan bound as well as new optimal FHSs with respect to the Lempel-Greenberger bound, which have length nN or n(q -1)N. As a result, a great deal of flexibility may be provided in the choice of FHS sets for a given frequency-hopping spread spectrum system.

Partial-period correlations of sequences are an important performance measure of communication systems employing them, but are known to be notoriously difficult to analyze. In this paper, we present a systematic approach to partial-period correlations as a generalization of the Paterson-Lothian approach. For a pair of sequences (not necessarily distinct), we introduce the linear phase-shifting sequences of one of them and analyze their full-period correlations, called the induced correlations, with the other one. By exploiting the induced correlations, we obtain the partial-period correlation properties of the given pair. We then investigate Zadoff-Chu sequences, and give some theoretical results on their partial-period autocorrelations, including closed-form expressions, and the first and second moments. We also derive an upper bound on the magnitudes of the partial-period cross-correlations of Zadoff-Chu sequences. Finally, we explore generalized chirp-like discrete Fourier transform sequences and show that their partial-period cross-correlations have the same magnitudes as the partial-period autocorrelations of the employed Zadoff-Chu sequence up to permutation.

Short cycles in the Tanner graph of a low-density parity-check (LDPC) code may cause a severe performance degradation. In this paper, we investigate the cycle properties of quasi-cyclic LDPC (QC-LDPC) codes. We first analyze a necessary and sufficient condition for a cycle of a given length to exist, by using the sequence representation of a parity-check matrix for a QC-LDPC code. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. Our necessary conditions are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds for many classes of regular QC-LDPC codes.

In this paper, we investigate the partial-period correlation of Zadoff-Chu sequences. For a pair of Zadoff-Chu sequences, we define the linear phase-shifting sequences of one of them and analyze their full-period correlation properties with the other one. By linking them to the partial-period correlation of the given pair, we derive an upper bound on the magnitude of the partial-period correlation of Zadoff-Chu sequences.

In this paper we propose a novel importance sampling (IS) scheme to estimate the low error-rate performance of low-density parity-check (LDPC) codes over Rayleigh fading channels. The proposed scheme exploits the structural weakness of LDPC codes due to trapping sets (TSs). The Rayleigh fading distribution on the bits belonging to a TS is biased by parameter scaling (PS), while the noise distribution on them is biased via mean translation (MT) according to their fading coefficients. The biases in PS and MT are determined so that the variance of the proposed IS estimator is minimized. The proposed IS scheme is compared with the Monte Carlo (MC) simulator and other IS schemes modified from the conventional IS scheme employed for performance estimation of LDPC codes over an AWGN channel. Numerical results show that it provides much more accurate performance than other IS schemes. Furthermore, the proposed IS estimator is even more efficient than the MC estimator and other IS estimators from the viewpoint of the number of required simulation runs.

Length-compatible polar codes are a class of polar codes which can support a wide range of lengths with a single pair of encoder and decoder. In this paper we propose a method to construct length-compatible polar codes by employing the reduction of the 2n× 2npolarizing matrix proposed by Arikan. The conditions under which a reduced matrix becomes a polarizing matrix supporting a polar code of a given length are first analyzed. Based on these conditions, length-compatible polar codes are constructed in a suboptimal way by codeword-puncturing and information-refreezing processes. They have low encoding and decoding complexity since they can be encoded and decoded in a similar way as a polar code of length 2n. Numerical results show that length-compatible polar codes designed by the proposed method provide a performance gain of about 1.0 - 5.0 dB over those obtained by random puncturing when successive cancellation decoding is employed.

In quasi-synchronous frequency-hopping multiple-access systems where relative delays between different users are restricted within a zone around the origin, low-hit-zone frequency-hopping sequences (LHZ-FHSs) are employed as spreading sequences. In this paper, we study LHZ-FHS sets obtained from the Cartesian product of some FHS sets. We first derive an upper bound on the Hamming correlation of FHSs constructed by the Cartesian product. We also give a general method to construct LHZ-FHS sets by the Cartesian product. We then present four new classes of optimal LHZ-FHS sets. The first three classes of sets are obtained from the product of Solomon's FHS sets and Kumar's FHS sets. The last one is constructed by the product of FHS sets based on interleaving techniques. These LHZ-FHS sets have new parameters not covered in the literature.

A mapping from ZNto ZMcan be directly applied for the design of a sequence of period N with alphabet size M, where ZNdenotes the ring of integers modulo N. The nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence. When M is a divisor of N, the sequence corresponding to a perfect nonlinear mapping has perfect autocorrelation, but it is not balanced. In this paper, we study balanced near-perfect nonlinear (NPN) mappings applicable for the design of sequence sets with low correlation. We first construct a new class of balanced NPN mappings from Z(p2-p) to Zpfor an odd prime p. We then present a general method to construct a frequency-hopping sequence (FHS) set from a nonlinear mapping. By applying it to the new class, we obtain a new optimal FHS set of period p2-p with respect to the Peng-Fan bound, whose FHSs are balanced and optimal with respect to the Lempel-Greenberger bound. Moreover, we construct a low-correlation sequence set with size p, period p2-p, and maximum correlation magnitude p from the new class of balanced NPN mappings, which is asymptotically optimal with respect to the Welch bound.

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. An (N, w, λa, λc)-OOC with size L is a family of L {0,1}-sequences with length N, weight w, maximum autocorrelation λa, and maximum cross correlation λc. In this paper, we present two new constructions for OOCs with λa=λc=1 which are asymptotically optimal with respect to the Johnson bound. We first construct an asymptotically optimal (Mpn, M, 1,1)-OOC with size (pn-1)/M by using the structure of Zpn, the ring of integers modulo pn, where p is an odd prime with M|p-1, and n is a positive integer. We then present another asymptotically optimal (Mp1...pk, M, 1,1)-OOC with size (p1...pk-1)/M from a product of k finite fields, where piis an odd prime and M is a positive integer such that M| pi-1 for 1 ≤ i ≤ k. In particular, it is optimal in the case that k=1 and (M-1)2> p1-1.

In this paper, we investigate the cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation of a parity-check matrix for a QC-LDPC code, we analyze a necessary and sufficient condition for a cycle of a given length to exist. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. We also give a bound which is a sufficient condition for a QC-LDPC code of a given girth to be constructed by a greedy algorithm. The bounds derived here are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds in many classes of regular LDPC codes.

Selected mapping (SLM) based schemes effectively reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) systems. However, they require side information (SI) transmission, which incurs a loss in the data throughput in addition to the increased system complexity. This paper presents a blind SLM scheme based on a decision metric obtained from pilot sub-channel responses. A novel SI detection method enabling low complexity data decoding is proposed. The SI is detected by exploiting the high autocorrelation between adjacent pilot sub-channel responses. The SI detection error rate is analytically derived and compared with that obtained by simulations. Simulation results of the data decoding scheme based on the proposed SI detection method show the bit error rate performance comparable to that of the simplified maximum likelihood (ML) data decoding scheme, while the computational complexity is close to that of the embedded SI based decoding scheme.

In this paper we investigate the cycle properties of regular quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation, we analyze the conditions for short cycles to exist in regular QC-LDPC codes and then give necessary conditions for avoiding short cycles in terms of their parameters. Numerical results show that our bounds on the number of rows in the parity-check matrices for regular QC-LDPC codes without cycles of length 4 or 6 are tighter than any other known bounds.

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. For reliable and efficient data transmission in these systems, it is required to design OOCs with low correlation and large size. In this paper, we present two new constructions for asymptotically optimal OOCs with respect to the Johnson bound, whose maximum nontrivial correlation value is 1. We first construct an asymptotically optimal OOC of length (p - 1)p2for an odd prime p by using the structure of the ring of integers modulo p2. We then present an asymptotically optimal OOC of length Mp1p2from a product of two finite fields, where p1and p2are odd primes, and M is an integer such that M|pi- 1 for i = 1, 2.

In frequency-hopping multiple-access systems, the average Hamming correlation (AHC) among frequency-hopping sequences (FHSs) as well as the maximum Hamming correlation (MHC) is an important performance measure. Moreover, each FHS is required to be balanced for its robustness against jamming or fading environments. In this study, the authors investigate FHS sets with optimal AHC and (near-)optimal MHC, whose FHSs are balanced. The authors first show that any uniformly distributed FHS set has optimal AHC with respect to the Peng–Niu–Tang bound. The authors also present two classes of FHS sets with optimal AHC and (near-)optimal MHC, whose FHSs are (perfectly) balanced. The authors then analyse the AHC of FHS sets constructed by interleaving techniques, and present some new FHS sets with optimal AHC and MHC, whose FHSs are perfectly balanced.

A blind algorithm is proposed in order to compensate for the phase noise resulting from imperfect oscillators in orthogonal frequency-division multiplexing (OFDM) systems over constant modulus modulation. In the proposed algorithm, one received OFDM symbol is partitioned into subblocks in the time domain and the phase noise over each subblock is approximated as its time-average. Under the approximation, the squared magnitude of the channel gain multiplied by the data symbol at each subcarrier is shown to be expressed in terms of these time-averages and the discrete Fourier transform (DFT) coefficients of the received samples at each subblock with zero padding. Based on the relation, the proposed algorithm compensates for the phase noise without pilot symbols. Numerical results show that the proposed algorithm outperforms conventional algorithms as well as it requires lower computational complexity.

The diversity-multiplexing tradeoff (DMT) of a multiple-input multiple-output (MIMO) multiple-access system is analyzed, where a successive cancellation (SC) receiver is employed. In order to analyze the asymptotic performance of each user in a practical MIMO multiple-access system, we derive the per-user DMT considering error propagation due to imperfect cancellation of the SC process. The diversity gain of each user is shown to be expressed as a simple function of the multiplexing gains of the previously detected users as well as its own multiplexing gain. Also, we show that the diversity gain of each user who suffers from error propagation is strictly smaller than that under the assumption of perfect cancellation in a range of multiplexing gains of the users. Numerical results show that our DMT analysis matches well with the performance of practical multiple-access systems.

A very simple design rule for parallel concatenated Turbo codes over GF(q) with q-ary orthogonal modulation is proposed. Unlike previously proposed exhaustive search methods, the proposed design rule allows straightforward and systematic code designs for any value of q ≥ 2 and any constraint length greater than 2.

An iterative algorithm employing decision feedback provided by either an equalizer or a channel decoder is proposed in order to compensate for the phase noise resulting from imperfect oscillators in orthogonal frequency-division multiplexing (OFDM) systems. In the proposed algorithm, the received OFDM symbol is partitioned into subblocks in the time domain and the estimate of the time-average of the phase noise at each subblock is used to compensate for the phase noise. A formula for the signal-to-interference-plus-noise ratio (SINR) after phase noise compensation is derived and its values are evaluated under a variety of conditions in order to demonstrate the efficiency of the proposed algorithm. Numerical results show that the proposed algorithm achieves performance close to that of an OFDM system without phase noise over a wide range of conditions, while requiring only one-half the complexity of the partial intercarrier interference reduction algorithm.

For an integer k ≥ 1, let , 1≤ qi ≤ k,be prime powers such that qi - Mif + 1 for some integers Miand f. In this paper, the k-fold cyclotomy of Fqk× ⋯ × Fqkas a nontrivial generalization of the conventional cyclotomy (k = 1 case) and its application to frequency-hopping sequences (FHSs) are presented, where Fqis the finite field with q elements. First, the definitions of k-fold cyclotomic classes and k-fold cyclotomic numbers are given. And then, their basic properties including k-fold diagonal sums are derived. Based on them, new optimal FHS sets of length N and frequency set size M or M + 1 with respect to the Peng-Fan bound are constructed for a product N of distinct odd primes and a di visor M of N - 1. Furthermore, new optimal FHSs of length N and frequency set size M with respect to the Lempel-Greenberger bound are constructed when N has at least one prime factor which is 3 modulo 4 and (N - 1)/M is an even integer. Our constructions give several new optimal parameters not covered in the literature, which are summarized in Table I.

For an integer k ≥ 1, k-fold cyclotomic numbers of Fq1× ... × Fqkare introduced, where Fqis the finite field with q elements and qi's are powers of distinct primes. They are a generalization of the conventional cyclotomic numbers (k = 1 case). Some of their basic properties including k-fold diagonal sums are derived. As an application of the k-fold cyclotomy, frequency-hopping sequences (FHSs) of length p1... pkare constructed for distinct odd primes p1, ..., pk, which are optimal with respect to the Lempel-Greenberger bound and the Peng-Fan bound.

Bounds on the diversity-multiplexing tradeoff (DMT) curves of the Bell labs layered space-time (BLAST) architecture are analyzed, where zero-forcing successive interference cancellation (ZF-SIC) receivers are employed. The DMT curve in the presence of error propagation caused by SIC process is derived under the assumption that each transmit antenna employs Gaussian random coding and the interference caused by detection errors has Gaussian distribution. This result can provide a lower bound on that of the ZF-SIC receiver with error propagation.

In this paper we propose an adaptive modulation and coding (AMC) scheme which uses only a single low-density parity-check (LDPC) encoder/decoder with irregular modulation. Two Gray-mapped quadrature-amplitude modulations are employed within a codeword so that the transmission rates of the proposed AMC can be controlled even though the rate of the employed LDPC code is fixed. The rate and degree distribution of the employed LDPC code are selected properly for the proposed scheme. We also optimize the bit-to-symbol mapping for the LDPC code over irregular modulation at each transmission rate. The performance of the proposed scheme is compared with that of the AMC scheme with a dedicated LDPC code at each transmission rate. Numerical results show that the proposed scheme has a performance comparable to that of the AMC scheme with dedicated LDPC codes.

In this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in Bell labs layered space-time (BLAST) architectures employing successive decoding and interference cancellation. We then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of BLAST architectures. Since the methods are developed by using ergodic capacity and outage capacity functions of the layers, the allocated rates and powers depend only on a given channel statistic. Finally, we prove that the rate allocation yields a better asymptotic performance than the power allocation. Numerical results show that BLAST architectures with the rate and power allocation perform better by 4 dB and 3 dB, respectively, than a BLAST architecture with the same rate and power in all layers.

A new scheduling to reduce the complexity of a turbo equalizer (TE) combined with a low-density parity-check (LDPC) decoder is proposed. Simple metrics and criteria for the proposed scheduling are derived from its convergence behavior. The TE with the proposed scheduling monitors the status of its iterative process and determines whether additional equalization is needed or not. Based on the decision, it adjusts performing equalization and reduces the execution number of equalization. Consequently, this leads to lowering the overall complexity of the TE. Numerical results show that the proposed scheduling has lower complexity than conventional schedulings, while they have almost the same performance.

A frequency-hopping sequence (FHS) of lengthvand frequency set sizeMis called a(v,M,¿)-FHS if its maximum out-of-phase Hamming autocorrelation is¿. Three new classes of optimal FHSs with respect to the Lempel-Greenberger bound are presented in this paper. First, new optimal (p,M,f)-FHSs are constructed when p = Mf +1 is an odd prime such thatfis even and p ¿ 3 mod 4 . And then, a construction for optimal (kp,p,k)-FHSs is given for any odd prime p and a positive integer K1,p1(p1+ 2 ),2m-1,or p1m-1, where p1and p1+2 are odd primes. Finally, several new optimal FHSs with maximum out-of-phase Hamming autocorrelation 1 or 2 are also presented. In particular, the existence of optimal (v,N,1)-FHSs is proven for any integer N ¿ 3 and any integer v with N +1 ¿ v ¿ 2 N-1, as well as the existence of optimal (2N +1,N,2)-FHSs is shown for any integer N ¿ 3. These classes of optimal FHSs have new parameters which are not covered in the literature.

In this paper we present a method to construct low correlation zone (LCZ) sequence sets of period kN for some integers k and N which are relatively prime. We construct kN-periodic LCZ sequences by combining an N-periodic sequence having good autocorrelation with a k times k Hadamard matrix. We also give some examples of our construction, which are optimal or nearly optimal with respect to the Tang-Fan-Matsufuji bound. Our construction gives flexible parameters in the sense of period and LCZ size.

In this paper we propose a stopping rule for adaptive turbo equalizers based on low-density parity-check (LDPC) codes. Using an extrinsic information transfer (EXIT) chart, we analyze the convergence behavior of a turbo equalizer and devise an adaptive turbo equalizer with stopping rule. It monitors the status of iterative decoding and stops performing equalization when the decoding messages are reliable enough to converge successfully only by LDPC decoding. Simulation results show that the proposed scheme has lower complexity than the conventional schemes, while it has a similar performance.

Group layered multi-antenna architectures (GLAs) employing orthogonal space-time block codes and spatial multiplexing techniques may simultaneously exploit diversity and multiplexing gains with simple decoding algorithms based on successive interference cancellation (SIC). In this paper we first describe a decoding method of a SIC receiver based on QR decomposition in a GLA using LDPC codes, and then find a combination of code rate and modulation order which optimizes the asymptotic performance of the GLA. Simulation results show that the performance of the GLA using code rates and modulation orders found by our method is better by 2 dB than that of a GLA using the same code rate and modulation order in all layers. Our optimization method can be applied to adaptive modulation and coding schemes for GLAs.

In this paper we derive the symbol error rate (SER) of the vertical Bell laboratories layered space-time (V-BLAST) detection algorithm based on zero-forcing successive interference cancellation (ZF-SIC) over an independent and identically distributed Rayleigh flat fading channel. By introducing the concepts of "event" and "state" related to error propagation, we evaluate the effect of error propagation and calculate the exact SER of each layer in a simple way. Compared with the pre-existing results, our approach can offer the closed-form expression of the SER of arbitrary quadrature-amplitude modulation (QAM) for an arbitrary number of transmit and receiver antennas. Furthermore, our analysis matches very well with Monte Carlo simulation results.

In this paper we construct new classes of optimal frequency-hopping sequences (FHSs) with respect to the Lempel-Greenberger bound and the Peng-Fan bound by interleaving techniques which are used to construct a sequence of length kN from k sequences of length N. We first give two generic constructions for optimal FHS sets from some known optimal FHS sets by interleaving techniques and present some examples of new optimal FHS sets. We then design new optimal FHSs whose parameters include those of the known optimal constructions with length kN and frequency set size n for some positive integers k and N. We also construct optimal FHS sets of length kp from power-residue sequences for any odd prime p and 2 les k < p. In particular, our constructions give several new parameters not covered in the literature, which are summarized in I and II.

It is well known that the magnitude of the cross correlation between any distinct constant multiple sequences of anM-ary power residue sequence of periodpis upper bounded byradicp+2 and that of anM-ary Sidel'nikov sequence of periodpm-1 is upper bounded byradic{pm} +3, wherepis a prime andmis a positive integer. In this paper, we first show that their cross-correlation functions are closely related to Jacobi sums and cyclotomic numbers. We then derive the cross-correlation distribution of constant multiple sequences of anM-ary power residue sequence. In the case of constant multiple sequences of anM-ary Sidel'nikov sequence, we get the possible cross-correlation values whose occurrence numbers are expressed in terms of the cyclotomic numbers of orderMand are possibly zero.

A(v,l, lambda)-FHS denotes a frequency-hopping sequence of lengthvover a frequency set of sizelwith maximum out-of-phase Hamming autocorrelationlambda. Recently, Ding and Yin constructed two FHS families for a prime powerqsatisfyingq=ef+1 with positive integerseandf. Theorems 4 and 5 in their paper claim that these two FHS families include optimal(q-1,e,f)-FHSs and(q-1,e+1,f-1)-FHSs with respect to the Lempel-Greenberger bound, respectively. In this paper, we give counterexamples and make corrections to them. Furthermore, we observe that these FHSs are closely related to Sidel'nikov sequences. Based on our results on the spectrum of their Hamming autocorrelation values, we also correct the theorem on the spectrum of Hamming distances of nearly equidistant codes derived by Sidel'nikov.

In this paper we construct near-optimal frequency-hopping sequences whose maximum Hamming autocorrelation is given by λopt+ 1 where λoptis the optimal Hamming autocorrelation value with respect to the Lempel-Greenberger bound. Their period, frequency set size, and maximum Hamming autocorrelation are given as pq, m and pq−1/m + 1, respectively, where p and q are distinct odd primes, and m is an even common divisor of p − 1 and q − 1.

In this paper we first perform the density evolution of LDPC codes in layered multi-antenna architectures using bit- interleaved coded modulation and detection based on successive decoding and interference cancellation. The noise thresholds of LDPC codes are shown to be achieved within 1.2 dB of the capacity for these architectures. We then present a rate allocation method which optimizes the performance of a layered architecture and find good degree distributions for LDPC codes with the rates allocated by our method. Simulation results show that the performance for an optimized layered architecture is better by 4 dB than that for the layered architecture using LDPC codes with the same rate in all layers.

In this correspondence, we present new construction methods for quaternary low-correlation zone (LCZ) sequence sets from a binary sequence with good autocorrelation. We show that the sets obtained by our methods are optimal or nearly optimal with respect to the Tang–Fan–Matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period, family size, and zone size. We also give a construction method for a quaternary LCZ sequence set from a binary LCZ sequence set. Finally, we give a new construction method for quaternary Hadamard matrices by the inverse of the Gray map.

In this paper we construct M-ary sequence families from power residue sequences of odd prime period p and their constant multiple sequences using the shift-and-add method, when M is a divisor of p - 1. We show that the maximum correlation values of the proposed sequence families of size p + M - 2 and (M - 1)2(p - 1)/2 + M - 1 are upper bounded by 2radic(p) + 5 and 3radic(p) + 4, respectively.

In this paper we present a class of structured LDPC codes over GF(q) which are suitable for efficient encoding. We derive the conditions under which the Phi matrix defined by Richardson & Urbanke in (2001) is an identity matrix over GF(q). If the parity-check matrix satisfies the derived conditions, the inversion of the Phi matrix can be removed in encoding process so that the computational complexity grows linearly with the code length. Simulation results show that efficiently encodable structured LDPC codes have no performance degradation due to the constraint on their design structure, compared with randomly constructed LDPC codes.

In this correspondence, we study the statistical stability properties of pm-periodic binary sequences in terms of their linear complexity and k-error linear complexity, where p is n prime number and 2 is a primitive root modulo p2. We show that their linear complexity and k-error linear complexity take a value only from some specific ranges. We then present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity in a new viewpoint different from the approach by Meidl. We also derive the distribution of pm-periodic binary sequences with specific k-error linear complexity. Finally, we get an explicit formula for the expectation value of the k-error linear complexity and give its lower and upper bounds, when k les [p/2].

In this paper we present a class of structured low-density parity-check (LDPC) codes from affine permutation matrices, called the APM-LDPC codes, which are a generalization of quasi-cyclic LDPC codes. We give a necessary and sufficient condition under which an APM-LDPC code has a cycle and introduce a simple method to construct APM-LDPC codes of large length by combining those of small length based on the Chinese remainder theorem. In particular, we show that the girth of APM-LDPC codes obtained in this method is always larger than or equal to those of given APM-LDPC codes

In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.

Repeat-accumulate (RA) codes are random-like codes having remarkably good performance over an additive white Gaussian noise (AWGN) channel, like turbo and low-density parity-check (LDPC) codes. In this correspondence, we introduce an ensemble of random codes called "weighted nonbinary repeat-accumulate (WNRA) codes" whose encoder consists of a nonbinary repeater, a weighter, a pseudorandom symbol interleaver, and an accumulator over a finite field GF(q). They can be decoded in a simple way by applying the sum-product algorithm to their factor graphs over GF(q). Simulation results show that WNRA codes with proper weighting values over GF(4) or GF(8) are superior to binary RA codes on AWGN channels.

In this paper, we introduce an ensemble of random codes called weighted nonbinary repeat accumulate (WNRA) codes. The encoder consists of a nonbinary repeater, a weighter, a pseudorandom symbol interleaver and an accumulator over the finite field GF(q). These codes can be decoded in a simple way by applying the sum-product algorithm to their factor graphs over GF(q). The degree distributions and noise thresholds for the codes are also derived. Simulation results show that WNRA codes with proper weighting are superior to binary RA codes on AWGN channels. Furthermore, WNRA codes over GF(2/sup m/) can be used as full-rate space-time codes with full diversity in a multiantenna system where m is the number of transmit antennas.

Like turbo codes, repeat-accumulate codes have remarkably good performance when r/spl ges/3, where r is the number of repetition times. We present space-time codes with full antenna diversity using "weighted" nonbinary repeat-accumulate codes. Compared with the space-time turbo codes of Y. Liu et al. (see IEEE J. Select. Areas Commun., vol.19, p.969-80, 2001) and of H. Su and E. Geraniotis (see ibid., vol.49, p.47-57, 2001), the main advantage of this new scheme is to construct space-time codes with full diversity for any m/spl les/r and any length of frame without searching for interleavers, where m is the number of transmit antennas. These space-time codes have rate m/r and, so, have full rate when m=r. Furthermore, they have an efficient decoding based on the message passing algorithm.

For a prime q and an integer j/spl les/q, the code C(q,j) is a class of low-density parity-check (LDPC) codes from array codes which has a nice algebraic structure. In this correspondence, we investigate the minimum distance d(q,j) of the code in an algebraic way. We first prove that the code is invariant under a doubly transitive group of "affine" permutations. Then, we show that d(5,4)=8, d(7,4)=8, and d(q,4)/spl ges/10 for any prime q>7. In addition, we also analyze the codewords of weight 6 in the case of j=3 and the codewords of weight 8 in C(5,4) and C(7,4).

We present a construction for binary sequences {s(t)} of period N=p/sup m/-1 for an odd prime p based on the polynomial (z+1)/sup d/+az/sup d/+b, and discuss them in some cases of parameters p, m, d, a, and b. We show that new sequences from our construction are balanced or almost balanced and have optimal three-level autocorrelation for the case when the polynomial (z+1)/sup d/+z/sup d/+a can be transformed into the form z/sup 2/-c. We also derive the distribution of autocorrelation values they take on. The sequences satisfy constant-on-the-coset property, and we show that there are more than one characteristic phases with constant-on-the-coset property. Some other interesting properties of those sequences are presented. For the cases when the polynomial (z+1)/sup d/+z/sup d/+a cannot be transformed into the form z/sup 2/-c, we performed extensive computer search, and results are summarized. Based on these results, some open problems are formulated.

The notion of quasi-orthogonal sequence (QOS) as a means of increasing the number of channels in synchronous code-division multiple-access (CDMA) systems that employ Walsh sequences for spreading information signals and separating channels is introduced. It is shown that a QOS sequence may be regarded as a class of Bent (almost Bent) functions possessing, in addition, a certain window property. Such sequences while increasing the system capacity, minimize interference to the existing set of Walsh sequences. The window property gives the system the ability to handle variable data rates. A general procedure of constructing QOSs from well-known families of binary sequences with good correlation, including the Kasami and Gold (1967) sequence families, as well as from the binary Kerdock code is provided. Examples of QOSs are presented for small lengths. Some examples of quaternary QOSs drawn from Family A are also included.

This article contains results on the generalized Hamming weights (GHW) for the Goethals and Preparata codes over Z/sub 4/. We give an upper bound on the rth generalized Hamming weights d/sub r/(m,j) for the Goethals code G/sub m/(j) of length 2/sup m/ over Z/sub 4/, when m is odd. We also determine d/sub 3.5/(m,j) exactly. The upper bound is shown to be tight up to r=3.5. Furthermore, we determine the rth generalized Hamming weight d/sub r/(m) for the Preparata code of length 2/sup m/ over Z/sub 4/ when r=3.5 and r=4.

The rth generalized Hamming weight d/sub r/(m,j) of the Goethals code /spl Gscr//sub m/(j) of length 2/sup m/ over Z/sub 4/ is considered in this correspondence. In the case that m/spl ges/3 is an odd integer, d/sub r/(m,j) is exactly determined for r=0.5, 1, 1.5, 2, 2.5, and 3.0. For a composite m, we give an upper bound d/sub r/(m,j) using the lifting technique.

We present a construction, in a closed form, for an optimal family of 2/sup m/ binary sequences of period 2/sup 2m/-1 with respect to Welch's (1974) bound, whenever there exists a balanced binary sequence of period 2/sup m/-1 with ideal autocorrelation property using the trace function. This construction enables us to reinterpret a small set of Kasami and No (1988) sequences as a family constructed from m-sequences. New optimal families of binary sequences are constructed from the Legendre sequences of Mersenne prime period, Hall's sextic residue sequences, and miscellaneous sequences of unknown type. In addition, we enumerate the number of distinct families of binary sequences, which are constructed from a given binary sequence by this method.

Hammons et al. (see ibid., vol.40, p.301-19, 1994) showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z/sub 4/, the so called Preparata code over Z/sub 4/. We consider the rth generalized Hamming weight d/sub r/(m) of the Preparata code of length 2/sup m/ over Z/sub 4/. For any m/spl ges/3, d/sub r/(m) is exactly determined for r=0.5, 1, 1.5, 2, 2.5 and 3.0. For a composite m, we give an upper bound on d/sub r/(m) using the lifting technique. For m=3, 4, 5, 6 and 8, the weight hierarchy is completely determined. In the case of m=7, the weight hierarchy is completely determined except for d/sub 4/(7).

In this correspondence, it is shown that Legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2/sup n/ elements, whenever p=2/sup n/-1 is prime for some n/spl ges/3.

The rth generalized Hamming weight d/sub r/ of the Kerdock code of length 2/sup m/ over Z/sub 4/ is considered. A lower bound on d/sub r/ is derived for any r, and d/sub r/ is exactly determined for r=0.5, 1, 1.5, 2, 2.5. In the case of length 2/sup 2m/, d/sub r/ is determined for any r, where 0/spl les/r/spl les/m and 2r is an integer. In addition, it is shown that it is sometimes possible to determine the generalized Hamming weights of the Kerdock codes of larger length using the results of d/sub r/ for a given length. The authors also provide a closed-form expression for the Lee weight of a Kerdock codeword in terms of the coefficients in its trace expansion.

The weight hierarchy of a linear code is the set of generalized Hamming weights of the code. In the paper, the authors consider geometric Goppa codes and provide a lower bound on their generalized Hamming weights similar to Goppa's lower bound on their minimum distance. In the particular case of Hermitian codes, exact results on the second and third generalized Hamming weights are given for any m except a few cases, where m is a parameter that governs the dimension of these codes. In many instances, the authors are able to provide considerably more information on their generalized Hamming weights. An upper bound relating the generalized Hamming weights of Hermitian codes to the pole numbers at a special point on the curve is also provided. Similar results are given in the case of codes from some subfields of the Hermitian function fields, which are also maximal. Finally, a nontrivial family of codes is also presented whose weight hierarchy is completely determined.>

The rth generalized Hamming weight of a linear code is the minimum support size of any r-dimensional subcode. It has been found useful in the studies of cryptography and trellis coding. The authors derive several results on expressing the generalized Hamming weights of a product code in terms of those of its component codes. They also formulate a general conjecture.>