Non-volatile memories are paid attention to as a promising alternative to memory design. Data stored in them still may be destructed due to crosstalk and radiation. We can restore the data by using error-correcting codes which require extra bits to correct bit errors. Further, non-volatile memories consume ten to hundred times more energy than normal memories in bit-writing. When we configure them using error-correcting codes, it is quite necessary to reduce writing bits. In this paper, we propose a method to generate a bit-write-reducing code with error-correcting ability. We first pick up an error-correcting code which can correct t-bit errors. We cluster its codeswords and generate a cluster graph satisfying the S-bit flip conditions. We assign a data to be written to each cluster. In other words, we generate one-to-many mapping from each data to the codewords in the cluster. We prove that, if the cluster graph is a complete graph, every data in a memory cell can be re-written into another data by flipping at most S bits keeping error-correcting ability to t bits. We further propose an efficient method to cluster error-correcting codewords. Experimental results show that the bit-write-reducing and error-correcting codes generated by our proposed method efficiently reduce energy consumption. This paper proposes the world-first theoretically near-optimal bit-write-reducing code with error-correcting ability based on the efficient coding theories.

Many studies have applied the three-dimensional discrete wavelet transform (3D DWT) to video coding. It is known that corruptions of the lowest frequency sub-band (LL) coefficients of 3D DWT severely affect the visual quality of video. Recently, we proposed an error resilient 3D DWT video coding method (the conventional method) that employs dispersive grouping and an error concealment (EC). The EC scheme of our conventional method adopts a replacement technique of the lost LL coefficients. In this paper, we propose a new 3D DWT video transmission method in order to enhance error resilience. The proposed method adopts an error correction scheme using invertible codes to protect LL coefficients. We use half-rate Reed-Solomon (RS) codes as invertible codes. Additionally, to improve performance by using the effect of interleave, we adopt a new configuration scheme at the RS encoding stage. The evaluation by computer simulation compares the performance of the proposed method with that of other EC methods, and indicates the advantage of the proposed method.

This paper proposes an effective signal processing scheme using a modulation code with two-dimensional (2D) run-length limited (RLL) constraints for bit-patterned media magnetic recording (BPMR). This 2D signal processing scheme is applied to be one of two-dimensional magnetic recording (TDMR) schemes for shingled magnetic recording on bit patterned media (BPM). A TDMR scheme has been pointed out an important key technology for increasing areal density toward 10Tb/in2. From the viewpoint of 2D signal processing for TDMR, multi-track joint decoding scheme is desirable to increase an effective transfer rate because this scheme gets readback signals from several adjacent parallel tracks and detect recorded data written in these tracks simultaneously. Actually, the proposed signal processing scheme for BPMR gets mixed readback signal sequences from the parallel tracks using a single reading head and these readback signal sequences are equalized to a frequency response given by a desired 2D generalized partial response system. In the decoding process, it leads to an increase in the effective transfer rate by using a single maximum likelihood (ML) sequence detector because the recorded data on the parallel tracks are decoded for each time slot. Furthermore, a new joint pattern-dependent noise-predictive (PDNP) sequence detection scheme is investigated for multi-track recording with media noise. This joint PDNP detection is embed in a ML detector and can be useful to eliminate media noise. Using computer simulation, it is shown that the joint PDNP detection scheme is able to compensate media noise in the equalizer output which is correlated and data-dependent.

In this study, we develop a new algorithm for decoding binary linear codes for symbol-pair read channels. The symbol-pair read channel was recently introduced by Cassuto and Blaum to model channels with higher write resolutions than read resolutions. The proposed decoding algorithm is based on linear programming (LP). For LDPC codes, the proposed algorithm runs in time polynomial in the codeword length. It is proved that the proposed LP decoder has the maximum-likelihood (ML) certificate property, i.e., the output of the decoder is guaranteed to be the ML codeword when it is integral. We also introduce the fractional pair distance dfp of the code, which is a lower bound on the minimum pair distance. It is proved that the proposed LP decoder corrects up to ⌈dfp/2⌉-1 errors.

Measurement matrix construction is critically important to signal sampling and reconstruction for compressed sensing. From a practical point of view, deterministic construction of the measurement matrix is better than random construction. In this paper, we propose a novel deterministic method to construct a measurement matrix for compressed sensing, CS-FF (compressed sensing-finite field) algorithm. For this proposed algorithm, the constructed measurement matrix is from the finite field Quasi-cyclic Low Density Parity Check (QC-LDPC) code and thus it has quasi-cyclic structure. Furthermore, we construct three groups of measurement matrices. The first group matrices are the proposed matrix and other matrices including deterministic construction matrices and random construction matrices. The other two group matrices are both constructed by our method. We compare the recovery performance of these matrices. Simulation results demonstrate that the recovery performance of our matrix is superior to that of the other matrices. In addition, simulation results show that the compression ratio is an important parameter to analyse and predict the recovery performance of the proposed measurement matrix. Moreover, these matrices have less storage requirement than that of a random one, and they achieve a better trade-off between complexity and performance. Therefore, from practical perspective, the proposed scheme is hardware friendly and easily implemented, and it is suitable to compressed sensing for its quasi-cyclic structure and good recovery performance.

In this paper, we propose a compressed sensing scheme using sparse-graph codes and peeling decoder (SGPD). By using a mix method for construction of sensing matrices proposed by Pawar and Ramchandran, it generates local sensing matrices and implements sensing and signal recovery in an adaptive manner. Then, we show how to optimize the construction of local sensing matrices using the theory of sparse-graph codes. Like the existing compressed sensing schemes based on sparse-graph codes with “good” degree profile, SGPD requires only O(k) measurements to recover a k-sparse signal of dimension n in the noiseless setting. In the presence of noise, SGPD performs better than the existing compressed sensing schemes based on sparse-graph codes, still with a similar implementation cost. Furthermore, the average variable node degree for sensing matrices is empirically minimized for SGPD among various existing CS schemes, which can reduce the sensing computational complexity.

Let R=Z4 be the integer ring mod 4 and C be a linear code over R. The code C is called a triple cyclic code of length (r, s, t) over R if the set of its coordinates can be partitioned into three parts so that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as R[x]-submodules of R[x]/×R[x]/×R[x]/. In this paper, we determine the generator polynomials and the minimum generating sets of this kind of codes.

Coordinate interleaved orthogonal design (CIOD) using four transmit antennas provides full diversity, full rate (FDFR) properties with low decoding complexity. However, the constellation expansion due to the coordinate interleaving of the rotated constellation results in peak to average power ratio (PAPR) increase. In this paper, we propose two signal constellation design methods which have low PAPR. In the first method we propose a signal constellation by properly selecting the signal points among the expanded square QAM constellation points, based on the co-prime interleaving of the first coordinate signal. We design a regular interleaving pattern so that the coordinate distance product (CPD) after the interleaving becomes large to get the additional coding gain. In the other method we propose a novel constellation with low PAPR based on the clipping of the rotated square QAM constellation. Our proposed signal constellations show much lower PAPR than the ordinary rotated QAM constellations for CIOD.

Secret sharing is a method of information protection for security. The information is divided into n shares and reconstructed from any k shares, but no knowledge of the information is revealed from k-1 shares. Physical layer security is a method of achieving favorable reception conditions at the destination terminal in wireless communications. In this study, we propose a security enhancement technique for wireless packet communications. The technique uses secret sharing and physical layer security to exchange a secret encryption key. The encryption key for packet information is set as the secret information in secret sharing, and the secret information is divided into n shares. Each share is located in the packet header. The base station transmits the packets to the destination terminal by using physical layer security based on precoded multi-antenna transmission. With this transmission scheme, the destination terminal can receive more than k shares without error and perfectly recover the secret information. In addition, an eavesdropper terminal can receive less than k-1 shares without error and recover no secret information. In this paper, we propose a protection technique using secret sharing based on systematic Reed-Solomon codes. The technique establishes an advantageous condition for the destination terminal to recover the secret information. The evaluation results by numerical analysis and computer simulation show the validity of the proposed technique.

A projective Reed-Muller (PRM) code, obtained by modifying a Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and the dual code of a PRM code are known, and some decoding examples have been presented for low-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of correctable errors of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of the minimum distance decoding.

In this letter, a new method is presented to suppress fractional pseudocodewords by eliminating small instantons of irregular low-density parity-check (LDPC) codes under the linear programming (LP) decoding over the binary symmetric channel (BSC). By appending several new rows found by the integer linear programming formulation to the original parity-check matrix, the optimal distribution spectrum of BSC-instantons in the modified code is obtained. Simulation results show that the proposed method can improve the fractional distance of parity-check matrices and considerably enhance the error-correcting performance of irregular LDPC codes under the LP decoding at the cost of a slightly loss of the original code rate.

We present numerical results on the rate-distortion performance of convolutional coding for the binary symmetric source, and show how convolutional codes approach the rate-distortion bound by increasing the trellis states.

Cassuto and Blaum proposed new error correcting codes which are called symbol-pair codes. They presented a coding framework for channels whose outputs are overlapping pairs of symbols in storage applications. Such channels are called symbol-pair read channels. The pair distance and pair error are used in symbol-pair read channels. Cassuto et al. and Yaakobi et al. presented decoding algorithms for symbol-pair codes. However, their decoding algorithms cannot always correct errors whose number is not more than half the minimum pair distance. In this paper, we propose a new decoding algorithm using syndromes of symbol-pair codes. In addition, we show that the proposed algorithm can correct all pair errors within the pair error correcting capability.

Data stored in non-volatile memories may be destructed due to crosstalk and radiation but we can restore their data by using error-correcting codes. However, non-volatile memories consume a large amount of energy in writing. How to reduce maximum writing bits even using error-correcting codes is one of the challenges in non-volatile memory design. In this paper, we first propose Doughnut code which is based on state encoding limiting maximum and minimum Hamming distances. After that, we propose a code expansion method, which improves maximum and minimum Hamming distances. When we apply our code expansion method to Doughnut code, we can obtain a code which reduces maximum-flipped bits and has error-correcting ability equal to Hamming code. Experimental results show that the proposed code efficiently reduces the number of maximum-writing bits.

Let v=p1m1p2m2…ptmt be the canonical prime factorization of v. In this paper, we give a construction of optimal ((s+1)×v,s+1,1) two-dimensional optical orthogonal codes with both at most one-pulse per wavelength and at most one-pulse per time slot, where s | gcd(p1-1,p2-1,...,pt-1). The method is much simpler than that in [1]. Optimal (m×v,k,1) two-dimensional optical orthogonal codes are also constructed based on the Steiner system S[2,k,m].

To improve the BER performance of the conventional cooperative communication, this letter proposes an efficient method for the reliability, and it uses hierarchical modulation that has both the high priority (HP) layer and the low priority (LP) layer. To compensate more reliable transmission, the proposed method uses the error correction capability of Reed-Solomon (RS) codes additionally. The simulation results show that the proposed method can transmit data more reliably than the basic RS coded decode-and-forward (DF) method.

In the log-likelihood ratio (LLR) domain, the belief propagation (BP) decoding algorithm for polar codes incurs high computation complexity due to the computation of the hyperbolic functions in the node update rules. In this paper, we propose a linear approximation method based on the principle of equal spacing to simplify the hyperbolic functions in the BP decoding algorithm. Our method replaces the computation of hyperbolic functions with addition and multiplication operations in the node update rules. Simulation results show that the performance of the modified BP decoding algorithm is almost the same as the original BP decoding algorithm in the low Signal to Noise Ratio (SNR) region, and in the high SNR region the performance of our method is slightly worse. The modified BP decoding algorithm is only implemented with addition and multiplication operations, which greatly reduces computation complexity, and simplifies hardware implementation.

Recent studies on switching fabrics mainly focus on the switching schedule algorithms, which aim at improving the throughput (a key performance metric). However, the delay (another key performance metric) of switching fabrics cannot be well guaranteed. A good switching fabric should be endowed with the properties of high throughput, delay guarantee, low component complexity and high-speed multicast, which are difficult for conventional switching fabrics to achieve. This has fueled great interest in designing a new switching fabric that can support large-scale extension and high-speed multicast. Motivated by this, we reuse the self-routing Boolean concentrator network and embed a model of multicast packet copy separation in front to construct a load-balanced multicast switching fabric (LB-MSF) with delay guarantee. The first phase of LB-MSF is responsible for balancing the incoming traffic into uniform cells while the second phase is in charge of self-routing the cells to their final destinations. In order to improve the throughput, LB-MSF is combined with the merits of erasure codes against packet loss. Experiments and analyses verify that the proposed fabric is able to achieve high-speed multicast switching and suitable for building super large-scale switching fabric in Next Generation Network(NGN) with all the advantages mentioned above. Furthermore, a prototype of the proposed switch is developed on FPGA, and presents excellent performance.

In this article, we study skew cyclic codes over $R=mathbb{F}_{q}+vmathbb{F}_{q}+v^{2}mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v3=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomial of the dual of a skew cyclic code over R. Moreover, the idempotent generators of skew cyclic codes over $mathbb{F}_{q}$ and R are considered.

Nonprimitive non-narrow-sense BCH codes have been studied by many scholars. In this paper, we utilize nonprimitive non-narrow-sense BCH codes to construct a family of asymmetric quantum codes and two families of quantum convolutional codes. Most quantum codes constructed in this paper are different from the ones in the literature. Moreover, some quantum codes constructed in this paper have good parameters compared with the ones in the literature.