The primary computational complexity of the lattice-based post-quantum cryptosystems (PQCs), aside from hashing, comes from the polynomial multiplication. Especially, the multiplication efficiency of large-degree polynomials becomes increasingly important for current applications. Therefore, in this article, we propose efficient polynomial multiplication methods, termed as the extended number theoretic transform (NTT), eventually aimed at developing efficient lightweight PQCs suitable for the Internet of Things. The proposed methods utilize the extension of finite fields and an early termination technique to enable efficient NTT implementation using better parameter values. The adoption of arithmetic in the extension field$\mathbb {F}_{q^{m}}$provides more efficient NTT computation, even when a primitive$2n$th root of unity, required for NTT, does not exist in the base field$\mathbb {Z}_{q}$. More importantly, the proposed methods allow for more flexible selection of PQC parameters. Moreover, by using early termination of NTT over the extension field, we further enhance the efficiency of polynomial multiplication. As a result, the proposed methods flexibly select suitable (or smaller) modulus q by optimizing the extension degree m and the incomplete degree l. Finally, we validate the effectiveness of our methods by demonstrating their capability to offer a wide range of parameter values and significantly reduce the size of modulus q. It is confirmed through simulation that the communication efficiency and security are improved by up to 21.43% and 9.09%, respectively. Finally, it is shown that lightweight Crystals-Kyber can be easily constructed by using the proposed methods.

Despite significant progress in federated learning (FL), persistent challenges, such as stragglers, adversaries, and communication costs remain. To address these issues, we propose FedLSC, a novel FL framework that leverages layer-selected correlation (LSC) to enhance both robustness and efficiency. In contrast to the existing methods, FedLSC does not rely on public data during model training, making it more practical and resilient in real-world scenarios. FedLSC introduces three key innovations: 1) preprocessing of layer selection (LS), which identifies significant layers to reduce communication costs and performance degradation; 2) local updates using LS-based scaled sign-stochastic gradient descent (SSS), introducing a layer-specific scaling mechanism to mitigate performance loss from quantization and significantly reduce communication costs; and 3) model aggregation via LSC-based schemes, which enhances robustness by processing only the significant layers and mitigating the impact of stragglers and adversaries. Furthermore, integrating the SSS scheme into FedLSC reduces communication costs to as little as 0.01% of those in state-of-the-art (SOTA) method while maintaining performance. Evaluations conducted across various FL scenarios show that FedLSC effectively supports robust performance and efficiency, even in bandwidth-constrained environments, thereby confirming its practicality in modern FL applications.

Irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes with the block dual-diagonal (BDD) parity structure are widely adopted in many communication standards because the BDD structure supports an efficient encoding and many degree-2 variable nodes inside are adequate for the construction of mid- to high-rate codes. However, we observe that low-rate irregular QC LDPC codes with the BDD parity structure inherently contain too many degree-2 variable nodes and suffer from error floors in high signal-to-noise ratio (SNR) region. In this paper, a generalized BDD structure including double-weight circulants as well as circulant permutation matrices is proposed for low-rate irregular QC LDPC codes with low error floors which is achieved with a little bit giving up error performance in the waterfall region. When constructing the parity part of a code with the generalized BDD structure, the portion of double-weight circulants is variable so that the resulting LDPC code can achieve a desired degree distribution including degrees 2 and 3 while supporting the efficient encoding. We show that low-rate QC LDPC codes constructed with the proposed BDD structure have better theoretical properties and lower error floor than those with the conventional BDD structure.

Partial transmit sequence (PTS), a well‐known peak‐to‐average power ratio (PAPR) reduction scheme for orthogonal frequency division multiplexing (OFDM) systems, has been actively investigated to reduce its high computational complexity. Ku et al . proposed a selection method of dominant time‐domain samples and by only using the selected samples, the PAPR of each alternative OFDM signal vector is calculated. This method clearly reduces the computational complexity but it is crucial to select proper time‐domain samples to achieve acceptable PAPR reduction performance. In this study, a new selection method of dominant time‐domain samples is proposed based on rotating samples of inverse fast Fourier transformed (IFFTed) subblocks to the local area on which the corresponding sample of the IFFTed first subblock is located. Moreover, pre‐exclusion of phase rotating vectors based on the above time‐domain sample rotation is proposed to further reduce the computational complexity. Numerical results confirm that the proposed PTS schemes substantially reduce the computational complexity with negligible degradation of PAPR reduction performance.

As a metric for amplitude fluctuation of orthogonal frequency division multiplexing (OFDM) signal, cubic metric (CM) has received an increasing attention because it is more closely related to the distortion induced by nonlinear devices than the well-known peak-to-average power ratio (PAPR). In this letter, the properties of CM of OFDM signal is investigated. First, asymptotic distribution of CM is derived. Second, it is verified that 1.7 times oversampling rate is good enough to capture the CM of continuous OFDM signals in terms of mean square error, which is also practically meaningful because the fast Fourier transform size is typically 1.7 times larger than the nominal bandwidth in the long-term evolution (LTE) cellular communication systems.

An interference alignment (IA) scheme for interference channels was recently proposed to achieve the maximum degrees of freedom (DoF). Although most studies of IA focus on network throughput, that is, DoF, reliability in terms of diversity order is also an important performance measure. In this study, interference cancellation (IC) scheme based on Alamouti code in the multi‐access scenario is applied to the K ‐user, multi‐input–multi‐output (MIMO) interference channel. This IC scheme gives the benefit of diversity order and requires no channel‐state‐information at the transmitters (CSIT). However, it requires more receive antennas than the IA scheme to achieve the same DoF. In order to reduce the number of receive antennas, especially for the three‐user MIMO interference channel, an IA‐and‐cancellation (IAC) scheme based on Alamouti code is proposed. It keeps the same DoF as the IC scheme, but requires partial CSIT. It is analytically shown that the IC and IAC schemes enable symbol‐by‐symbol decoding and achieve diversity order of two, while the conventional IA scheme achieves diversity order of one.

In this study, two relay‐aided interference alignment (IA) schemes are proposed for the quasi‐static M × 2 X channel where M is the number of transmitters and two is the number of receivers, respectively. The first scheme utilises one full‐duplex relay and the second one utilises two half‐duplex relays. In the proposed schemes, the transmitters transmit signals in every time slot and the relays operate in the amplify‐and‐forward (AF) mode. By verifying the linear independence between the desired signals and the interference, it is shown that the proposed schemes can achieve 2 M /( M + 1) degrees of freedom (DoF) which is the maximum DoF for the M × 2 X channel. It is also shown by using the concept of reciprocity that the proposed IA schemes are applicable to the 2 × M X channel. Finally, through the numerical analysis, it is confirmed that the proposed IA schemes provide good alternatives to the previously known relay‐aided IA scheme.

In this study, a new peak‐to‐average power ratio (PAPR) reduction scheme for orthogonal frequency division multiplexing (OFDM) is proposed based on the selected mapping (SLM) scheme. The proposed SLM scheme generates alternative OFDM signal sequences by cyclically shifting the connections in each subblock at an intermediate stage of inverse fast Fourier transform (IFFT). Compared with the conventional SLM scheme, the proposed SLM scheme achieves similar PAPR reduction performance with much lower computational complexity and no bit error rate degradation. The performance of the proposed SLM scheme is analysed mathematically and verified through numerical analysis. Also, it is shown that the proposed SLM scheme has the lowest computational complexity among the existing low‐complexity SLM schemes exploiting the signals at an intermediate stage of IFFT.

For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.

There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them focus on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple (i.e., parallel) edges. Compared to single-edge protographs, multiple-edge protographs have benefits such that QC LDPC codes lifted from them can potentially have larger minimum Hamming distance. In this paper, all subgraph patterns of multiple-edge protographs, which prevent QC LDPC codes from having large girth by inducing inevitable cycles, are fully investigated based on a graph-theoretic approach. By using combinatorial designs, a systematic construction method of multiple-edge protographs is proposed for regular QC LDPC codes with girth at least 12 and another method is proposed for regular QC LDPC codes with girth at least 14. Moreover, a construction algorithm of QC LDPC codes based on certain liftings of multiple-edge protographs is proposed and it is shown that the resulting QC LDPC codes have larger upper bounds on the minimum Hamming distance than those lifted from single-edge protographs. Simulation results are provided to compare the performance of the proposed QC LDPC codes with progressive edge-growth (PEG) LDPC codes and with PEG QC LDPC codes.

The block dual-diagonal (BDD) parity structure is widely adopted in many practical irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes. These QC LDPC codes have good error-correcting performance in waterfall region but usually show relatively high error floors in low error rate region. In this paper, by using multi-weight circulants, a new BDD structure is proposed for the parity part of irregular QC LDPC codes to lower error floors and support efficient encoding. Since the parity part of parity-check matrices has flexible degree distribution with the aid of multi-weight circulants, QC LDPC codes with the proposed BDD structure can have large minimum Hamming distance compared to those with the conventional BDD structure, especially, in the low-rate case. Simulation results show that QC LDPC codes with the proposed BDD structure have lower error floor than those with the conventional BDD structure.

In this paper, two relay-aided interference alignment (IA) schemes are proposed for the quasi-static M×2 X channel. The first scheme utilizes one full-duplex relay and the second scheme utilizes two half-duplex relays. In the proposed schemes, transmitters transmit in every time slot and relays operate in amplify-and-forward (AF) mode. By confirming the linear independence between the desired signals and interference and also among the desired signals, it is shown that the proposed schemes can achieve 2M/(M + 1) degrees of freedom (DoF) which is the maximum DoF of M × 2 X channel.

In this paper, all subgraph patterns of protographs which prevent quasi-cyclic (QC) low-density parity-check (LDPC) codes from having large girth are searched in allowance with multiple edges based on graph theoretic approach. A systematic construction of protographs with multiple edges using combinatorial design is proposed for designing QC LDPC codes with girth greater than or equal to 14.

In this paper, a new relay selection scheme for decode-and-forward (DF) relay cooperative network with multiple antennas is proposed based on both channel state information (CSI) and transmission scheme by deriving the upper bound on the pairwise error probability (PEP) of the near-maximum-likelihood (near-ML) decoder. It is also proved that the proposed relay selection which selects m (1≤ m≤ N) relays from N relays achieves full diversity MSMD+N MRmin[MS, MD] regardless of the value of m in the DF relay network consisting of one source, one destination, and N relays with MS, MD, and MRantennas, respectively. Through Monte Carlo simulation, the error correction performance of the proposed relay selection for various m is shown for the uncoded single-antenna, Alamouti coded, and multiple-input multiple-output (MIMO) DF relay networks.

In this paper, a new SLM scheme for peak to average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems is proposed. This scheme is special case of selected mapping (SLM) scheme. The proposed SLM scheme generates alternative OFDM signal sequences by exploiting the intermediate OFDM signal sequence in inverse fast Fourier transform (IFFT). By using this technique, the proposed SLM scheme achieves similar PAPR reduction performance with much lower computational complexity and no bit error rate (BER) degradation. the performance of the proposed SLM scheme is verified through the simulations.

The peak to average power ratio (PAPR) reduction performance depends on the phase vectors of selected mapping (SLM) scheme where the alternative input symbol vectors are generated by multiplying an input symbol vector by phase vectors. Thus, the symbol powers of alternative orthogonal frequency division multiplexing (OFDM) signals obtained by inverse Fourier transforming the alternative input symbol vectors become correlated. In this paper, the relationship between the correlations of component powers of alternative OFDM signal vector and the correlations of phase vectors are evaluated. Then, the complementary cumulative distribution function (CCDF) of PAPR in SLM scheme is derived using multivariate gamma distribution. The derived CCDF coincides exactly with the simulation result for peak reduced OFDM system with SLM.

In this paper, a near maximum-likelihood (ML) decoder for orthogonal decode-and-forward (ODF) protocol with multiple antennas is proposed and the upper bound on the average pairwise error probability (PEP) for large signal to noise ratio is also derived, regardless of the modulation scheme. From the upper bound on the average PEP, we show that the ODF protocol with near ML decoder can achieve full diversity MSMD+MRmin(MS, MD) for a cooperative network consisting of one source, one relay, and one destination with MS, MR, and MDantennas, respectively.

A cooperative protocol called soft-decision-and-forward (SDF) is introduced. SDF protocol exploits the soft decision values of the received signal at the relay node. Alamouti code is used for orthogonal transmission and distributed space-time codes are designed for non-orthogonal transmission. The maximum likelihood decoders with low decoding complexity are proposed. From simulations, it can be seen that SDF protocol outperforms AF protocol.

In this paper, a new criterion for reordering of low-density parity-check (LDPC) coded orthogonal frequency division multiplexing (OFDM) subframes is proposed for type I hybrid automatic repeat request (H-ARQ) systems. It is verified from numerical analysis that a subframe reordering pattern having larger channel capacity shows better bit error rate (BER). Also, it is shown that the subframe reordering pattern achieving equal combined power allocation for each subframe maximizes the channel capacity and outperforms other subframe reordering patterns in terms of BER performance. Simulation results are provided to confirm that for a very slow varying fading channel, the proposed subframe reordering scheme for achieving equal combined power allocation gives better BER performance than the conventional Chase combining scheme without increasing the decoding complexity.

In this paper, we propose a new selected mapping (SLM) scheme for reducing peak to average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals modulated with quadrature amplitude modulation (QAM), called partial bit inverted SLM (PBISLM). The proposed scheme changes the magnitudes as well as the phases of QAM symbols by applying binary phase sequences to the binary data sequence before mapped to QAM symbols. Simulation results show that the proposed scheme has better PAPR reduction performance than the conventional SLM scheme for the QAM modulated OFDM signals, especially for the small number of subcarriers.

In this paper, we propose a new blind SLM scheme with low complexity using m-sequence as a phase sequence in OFDM. The proposed scheme significantly reduces the computational complexity for searching the side information of the phase sequence and decoding the alternative symbol sequence at the receiver. After generating alternative symbol sequences using a set of phase sequences, the side information for each alternative symbol sequence is embedded in it through block partitioning and phase rotation. The proposed method does not need additional inverse fast Fourier transform (IFFT) and has the same PAPR reduction performance compared to the conventional SLM scheme. In order to find the side information, a maximum likelihood (ML) decoder with lower complexity is derived, which guarantees lower detection failure probability of side information compared to the conventional blind SLM scheme.

In this letter, a new rate-control scheme, called splitting, is proposed to construct low-rate codes from highrate codes, which splits rows of parity-check matrices of repeat accumulate-type (RA-Type) LDPC codes by adding new parity bits. When a high-degree check node is split into two low-degree check nodes, by making the check node degree distribution in a concentrated form, the performance of low-rate codes can be improved. We also explicitly construct rate-compatible repeat RA-Type LDPC (RC RA-Type LDPC) codes using splitting for code rates from 1/3 to 4/5 and compare this with other RC RA-Type LDPC codes.

In this paper, we derive the relationship between the bit error probability (BEP) of maximum a posteriori (MAP) bit detection and the bit minimum mean square error (BMMSE). By using this result, the relationship between the mutual information and the BEP is derived for multiple-input multiple-output (MIMO) communication systems with the bit-linear linear-dispersion (BLLD) codes for the Gaussian channel. From the relationship, the lower and upper bounds on the mutual information can be derived.

It is critical to adapt clear and representative real world traffic properties as groundwork for the contemporary and emergent future Internet workload generation. Byte count process and packet count process have been regarded as two prominent manifestations of the underlying characteristics of the network traffic. The long-range dependent property of these processes is already widely known. However, inter-relationship between the two processes remains to be discovered. The objective of this work is to investigate packet size aspects of network traffic that are yet to be discovered. This paper introduces bandwidth frequency distribution as an approach to analyze the traffic. It first focuses on Hurst parameter as a means to assess self-similarity. Then, it introduces bandwidth frequency histogram and analyzes the distribution. As a result of analyzing the bandwidth frequency histogram, the observed bandwidth frequency distribution is decided by aggregation of the bandwidth behavior of five packet size distributions. It is found that packet interval distribution is well fitted with Gaussian distribution.

In this paper, we analyze the sequential message- passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This decoding algorithm shows better bit error rate (BER) performance than the conventional message-passing decoding algorithm, especially for the small number of iterations. Analytical results indicate that as the number of partitioned subsets of check nodes increases, the BER performance is improved. We also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a Gaussian approximation. From these equations, the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding BER values are calculated. They show that the sequential decoding algorithm converges faster than the conventional one. Finally, the analytical results are confirmed by the simulation results.

For an odd prime p, n=4k, and d=((p2k+1)/2)2, there are (p2k+1)/2 distinct decimated sequences s(dt+l), 0lesl2k+)/2,of a p-ary m-sequence s(t) of period pn-1 because gcd(d,pn-1)=(p2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l),0lesl2k+1)/2, takes the values in {-1, -1 -radic(pn),-1+radic(pn),-1+2radic(pn)} and their cross-correlation distribution is also derived.

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices. In this paper, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i,i= 6,7,8,9,10, i.e., the cycles existing regardless of the shift values of circulants. It is also derived that if the girth of the protograph is 2g,gges 2, its protograph code cannot have the inevitable cycles of length smaller than 6g. Based on these subgraph patterns, we propose new combinatorial construction methods of the protographs, whose protograph codes can have girth larger than or equal to 14.

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 les In- 1 since gcd(d, pn-1) = p + 1. 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. The maximum magnitude of their cross-correlation values is l+p radic pnif I = 0 mod p + 1 for n = 0 mod 4 or I = (p + l)/2 mod p + 1 for n = 2 mod 4 and otherwise, 1 + radicpn. Also by using s(t) and s(dt + I), a new family of p-ary sequences of period pn-1 is constructed, whose family size is pnmiddot and Cmaxis 1+ pradicpn.

For an odd prime p, n=4k, and d=((p2k+1)/2)2, there are (p2k+1)/2distinct decimated sequences s(dt+l), 0lesl2k+1)/2, of a p-ary m-sequence s(t) of period pn-1 because gcd(d,pn-1)=(p2k+1)/2. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+I), 0lesl2k+1)/2, takes the values in {-1, -1 - radicpn, -1+radicpn-1+2radicpn} and their cross-correlation distribution is also derived.

In this paper, we propose a new peak-to-average power ratio (PAPR) reduction scheme of orthogonal frequency division multiplexing (OFDM) system, called a modified selected mapping (SLM) scheme, which considerably reduces the computational complexity with keeping the similar PAPR reduction performance compared with the conventional SLM scheme. The proposed scheme is analytically and numerically evaluated for the OFDM system specified in the IEEE 802.16 standard. For the OFDM system with 2048 subcarriers, the proposed scheme with 4 binary phase sequences can reduce the complex multiplications by 63.5% with the similar PAPR reduction compared with the SLM scheme with 16 binary phase sequences.

In this paper, we derive the relationship between the bit error probability (BEP) of maximum a posteriori (MAP) bit detection and the bit minimum mean square error (MMSE), that is, the BEP is greater than a quarter of the bit MMSE and less than a half of the bit MMSE. By using this result, the lower and upper bounds of the derivative of the mutual information are derived from the BEP in the multiple-input multiple-output (MIMO) communication systems with the bit-linear linear- dispersion (BLLD) codes in the Gaussian channel.

In the tone reservation (TR) scheme, it is known that the set of randomly selected peak reduction tones (PRT's) performs better than the contiguous PRT set and the interleaved PRT set in the PAPR reduction of orthogonal frequency division multiplexing (OFDM) signals. It is also known that finding the optimal PRT set is equivalent to solving the secondary peak minimization problem in the TR scheme. However, this problem cannot be solved for the practical number of tones because choosing k tones out of N subcarriers requires O(k) computational complexity. In this paper, the near optimal PRT set of the TR scheme is proposed, which is constructed from the cyclic difference set.

In this paper, we propose multicode multiple-input multiple- output (MIMO) systems with quaternary low correlation zone (LCZ) and zero correlation zone (ZCZ) sequences as spreading codes. Quaternary LCZ and ZCZ sequences have very low correlation values when the time shifts of correlation function are within the predetermined correlation zone and thus the multi-user or multipath interference can be substantially reduced when the delay is within a few chips. The bit error probability of the proposed systems is theoretically analyzed, which is numerically confirmed. It is also numerically shown that the performance of multicode MIMO systems with quaternary LCZ and ZCZ sequences is better than that of the conventional multicode MIMO systems with quaternary spreading codes constructed from a pair of binary Hadamard codes.

In this paper, we propose a construction method of rate-compatible block-type low-density parity-check (RC B-LDPC) codes using extending and puncturing, which works well over a wide range of code rates by decreasing the amount of puncturing nodes to mitigate the performance degradation at high rate range. RC B-LDPC code constructed by the proposed scheme to achieve the target code rates from 1/3 to 4/5 results in good frame error rate (FER) performance, even better than the well- designed rate-1/3 code in the small number of iterations (say, < 20).

In this paper, we show that irregular concatenated zigzag (ICZZ) codes are suitable as mother codes to support a wide range of code rates. We introduce the degree distribution matching method to derive the optimal puncturing and pruning patterns in order to achieve the rate-compatible target code rates of ICZZ code. By combining ICZZ code with the optimal puncturing and pruning patterns, new rate-compatible ICZZ (RC-ICZZ) codes are constructed. In an example, n RC-ICZZ code to achieve the code rates 1/3, 1/2, 2/3, 4/5, and 8/9 is constructed and shown to outperform RCTC adopted in 3GPP. Therefore, RC-ICZZ codes are suitable for hybrid automatic repeat request to increase the system throughput.

In this paper, an adaptive bit-reliability mapping is proposed for the bit-level Chase combining in LDPC-coded high-order modulation systems. Contrary to the previously known bit-reliability mapping that assigns the information (or parity) bits to more (or less) reliable bit positions, the proposed mapping flexibly assigns codeword bits to the bit positions of various reliabilities by considering the characteristics of code and protection levels. Compared with the symbol-level Chase combining and the constellation rearrangement bit mapping, the proposed mapping gives 0.7 - 1.3 dB and 0.1 - 1.0 dB performance gain at FER = 10-3with no additional complexity, respectively. The adaptive bit-reliability mappings are derived for various environments and the validity of them is confirmed through simulation.

In this paper, the authors propose new decoding scheme of punctured LDPC codes with dual-diagonal parity structure by merging check nodes connected to the punctured parity nodes. This check-node merging decoding not only needs smaller number of operations at each iteration but also shows faster decoding convergence speed than the conventional erasure decoding. For the binary erasure channel (BEC) and AWGN channel, the authors analyze and compare the check-node merging and the conventional erasure decoding schemes of the punctured LDPC codes with dual-diagonal parity structure using density evolution. Analytical results show that the check-node merging decoding gives faster convergence speed for both BEC and AWGN channel. Also, simulation results are provided to confirm the analytical results.

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices (or circulants). In this correspondence, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9,10, i.e., the cycles that always exist regardless of the shift values of circulants. It is also derived that if the girth of the protograph is 2g, g > 2, its protograph code cannot have the inevitable cycles of length smaller than 6g. Based on these subgraph patterns, we propose new combinatorial construction methods of the protographs, whose protograph codes can have girth larger than or equal to 14 or 18. We also propose a couple of shift value assigning rules for circulants of a QC LDPC code guaranteeing the girth 14.

In this paper, we construct rate-compatible block-type low-density parity-check (B-LDPC) codes using splitting that cover a wide range of code rates from 1/3 to 4/5. They outperform other rate-compatible B-LDPC codes for all rates and can be decoded conveniently and efficiently. A strong motivation for proposing splitting scheme comes from the observation that the quality of the initial transmission is the most important factor to achieve high throughput of type-II HARQ. Proposed scheme builds low-rate codes from high-rate codes by splitting rows of the given LDPC parity-check matrix. Thus, rate-compatible LDPC codes obtained by splitting have good FER (Frame Error Rate) performance in the first transmission. Contrary to other rate-control methods such as puncturing, shortening, and extending, the splitting algorithm not only needs smaller number of operations but also shows faster decoding convergence speed since more efficient Tanner graph is used for the decoding.

In this correspondence, the cycles of Tanner (3,5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4,6,8, and 10 in Tanner (3,5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15th root of unity of the prime field F/sub p/. By checking the existence of solutions for these equations over F/sub p/, the girths of Tanner (3,5) QC LDPC codes are derived.

In the next-generation mobile communication systems for various high-speed data services, the error correcting codes are required to have rate-compatibility, low decoding complexity and good performance for various frame lengths. In this paper, new rate-compatible punctured concatenated zigzag (RCPCZ) codes are proposed and analyzed by using the density evolution. As their application, type-II HARQ using RCPCZ code is shown to have better throughput at short frame lengths than yype-II HARQ using turbo code.

In this paper, new rate-compatible punctured concatenated zigzag (RCPCZ) codes are proposed and analyzed by using the density evolution technique. This analysis gives the design criteria for the rate-compatible puncturing patterns and accordingly good puncturing patterns for constructing RCPCZ codes are obtained. Since RCPCZ codes are linear-time encodable and show capacity-approaching performance, they can be a good candidate technology for the next-generation communication systems. As their applications, Type-II hybrid automatic repeat request (HARQ) using RCPCZ code is constructed, which gives higher throughput than Type-II HARQ using RCMCZ code

Capacity-approaching codes using iterative decoding have been the main research subject of coding area during past decade. In this paper, a new channel coding scheme called irregular concatenated zigzag (ICZZ) code is proposed. ICZZ codes can be viewed as a special case of irregular low-density parity-check (LDPC) codes with linear-time encodable structure. They are different from concatenated zigzag (CZZ) codes in the sense that the number of information bits entering into each zigzag encoder can be different and different zigzag codes can be used as component codes. A simple method to design ICZZ codes is proposed and by using an example, it is shown that ICZZ code of rate 1/3 has better performance than the optimal CZZ code and turbo code adopted in 3GPP

In this paper, the cycles of Tanner's (3,5) quasicyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner's (3,5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15-th root of unity of the prime field Fp. By checking the existence of solutions for these equations over Fp, the girths of Tanner's (3,5) QC LDPC codes are derived

The block coding scheme for OFDM, which is combining Golay complementary sequence with Reed-Muller code (GCRM) that limits PAPR up to 3 dB with error-correcting capability, has been introduced recently [J. A. Davis et al. (1999)]. However, the coding gain of GCRM cannot overcome ICI caused by frequency error in OFDM. In this paper, a new combined scheme of ICI self-cancellation [Y. Zhao et al. (2001)] [Y. Fu et al. (2002)] and GCRM code is proposed. This scheme is analyzed to show that it limits PAPR up to 6 dB and can compensate the nonlinear distortion by TWTA. It is also verified that for the low back-off value of TWTA, our scheme shows better performance than GCRM.

We generalize the construction method of the family of binary bent sequences introduced by Olsen, Scholtz, and Welch (1982) to obtain a family of generalized binary bent sequences with optimal correlation and balance property by using the modified trace transform. Then, the conventional binary bent sequence becomes a special case of our construction method. Several families of the generalized binary bent sequences are constructed by using the bent functions on the intermediate field. Using some of the generalized binary bent sequences, new families of binary sequences with optimal correlation and balance property can be constructed by the lifting idea similar to No (1988) sequences, which are referred to as binary bent-lifted sequences.