This paper introduces open-wire fault-resilient multiple-valued codes for reliable asynchronous point-to-point global communication links. In the proposed encoding, two communication modules assign complementary codewords that change between two valid states without an open-wire fault. Under an open-wire fault, at each module, the codewords don't reach to one of the two valid states and remains as “invalid” states. The detection of the invalid states makes it possible to stop sending wrong codewords caused by an open-wire fault. The detectability of the open-wire fault based on the proposed encoding is proven for m-of-n codes. The proposed code used in the multiple-valued asynchronous global communication link is capable of detecting a single open-wire fault with 3.08-times higher coding efficiency compared with a conventional multiple-valued code used in a triple-modular redundancy (TMR) link that detects an open-wire fault under the same dynamic range of logical values.

NAND multi-level cell (MLC) flash memories are widely used due to low cost and high capacity. However, the increased number of levels in MLC results in larger interference and errors. The errors in MLC flash memories tend to be directional and limited-magnitude. Many related works focus on asymmetric errors, but bidirectional errors also occur because of the bidirectional interference and the adjustment of the hard-decision reference voltages. To take advantage of the characteristics, we propose t bidirectional (lu,ld) limited-magnitude error correction codes, which can reduce errors more effectively. The proposed code is systematic, and can correct t bidirectional errors with upward and downward magnitude of lu and ld, respectively. The proposed method is advantageous in that the parity size is reduced, and it has lower bit error rate than conventional error correction codes with the same code rate.

In this paper, an area-efficient decoder architecture is proposed for the quasi-cyclic low-density parity check (QC-LDPC) codes specified in the IEEE 802.16e WiMAX standard. The decoder supports all the code rates and codeword lengths defined in the standard. In order to achieve low area and maximize hardware utilization, the decoder utilizes 4 decoding function units, which is the greatest common divisor of the expansion factors. In addition, the decoder adopts a novel scheduling scheme named stride scheduling, which stores the extrinsic messages in non-sequential order to replace the conventional complex flexible permutation network with simple small-sized cyclic shifters and also minimize the number of memory accesses. To further minimize the complexity, the number of extrinsic memory instances for 24 block columns is reduced to 5 banks by identifying independent sets. All the memory instances used in the decoder are single-port memories which cost less area and price compared to dual-port ones. Finally, the decoding function units have partially parallel structure to make the decoding throughput sufficiently over the requirement of the WiMAX standard. The proposed decoder is synthesized with 49 K equivalent gates and 54,144 bits of memory, and the implementation occupies 0.40 mm2 in a 65 nm CMOS technology.

This paper introduces the concept of order complexity, which represents the minimum number of partial ordering operations to make a string of perfectly ordered symbols. A novel variable-length code expressing such order complexity using binary digits is proposed herein. The proposed code is general, uniquely decipherable, and useful for coding a string of random permuted symbols having unknown statistics or which are preferred to have a uniform distribution.

Nowadays, error control codes have become an essential technique to improve the reliability of various digital systems. A new type error control codes called m-spotty byte error control codes are applied to computer memory systems. These codes are essential to make the memory systems reliable. Here, we introduce the m-spotty Rosenbloom-Tsfasman weights and m-spotty Rosenbloom-Tsfasman weight enumerator of linear codes over Fq[u]/(uk) with uk=0. We also derive a MacWilliams type identity for m-spotty Rosenbloom-Tsfasman weight enumerator.

In this paper, we present a novel class of long quasi-cyclic low-density parity-check (QC-LDPC) codes. Each of the codes in this class has a structure formed by concatenating single-parity-check codes and QC-LDPC codes of shorter lengths, which allows for efficient, high throughput encoder/decoder implementations. Using a code in this class, we design a forward error correction (FEC) scheme for optical transmission systems and present its high throughput encoder/decoder architecture. In order to demonstrate its feasibility, we implement the architecture on a field programmable gate array (FPGA) platform. We show by both FPGA-based simulations and measurements of an optical transmission system that the FEC scheme can achieve excellent error performance and that there is no significant performance degradation due to the constraint on its structure while getting an efficient, high throughput implementation is feasible.

Turbo equalization is an iterative equalization and decoding technique that can achieve impressive performance gains for communication systems. In this letter, we investigate the turbo equalization method for the decoding of the Davey-MacKay (DM) construction over the IDS-AWGN channels, which indicates a cascaded insertion, deletion, substitution (IDS) channel and an additive white Gaussian noise (AWGN) channel. The inner decoder for the DM construction can be seen as an maximum a-posteriori (MAP) detector. It receives the beliefs generated by the outer LDPC decoder when turbo equalization is used. Two decoding schemes with different kinds of inner decoders, namely hard-input inner decoder and soft-input inner decoder, are investigated. Simulation results show that significant performance gains are obtained for both decoders with respect to the insertion/deletion probability at different SNR values.

In this paper, through extrinsic information transfer (EXIT) band chart analysis, an adaptive iterative decoding approach (AIDA) is proposed to reduce the iterative decoding complexity and delay for finite-length differentially encoded Low-density parity-check (DE-LDPC) coded systems with multiple-symbol differential detection (MSDD). The proposed AIDA can adaptively adjust the observation window size (OWS) of the MSDD soft-input soft-output demodulator (SISOD) and the outer iteration number of the iterative decoder (consisting of the MSDD SISOD and the LDPC decoder) instead of setting fixed values for the two parameters of the considered systems. The performance of AIDA depends on its stopping criterion (SC) which is used to terminate the iterative decoding before reaching the maximum outer iteration number. Many SCs have been proposed; however, these approaches focus on turbo coded systems, and it has been proven that they do not well suit for LDPC coded systems. To solve this problem, a new SC called differential mutual information (DMI) criterion, which can track the convergence status of the iterative decoding, is proposed; it is based on tracking the difference of the output mutual information of the LDPC decoder between two consecutive outer iterations of the considered systems. AIDA using the DMI criterion can adaptively adjust the out iteration number and OWS according to the convergence situation of the iterative decoding. Simulation results show that compared with using the existing SCs, AIDA using the DMI criterion can further reduce the decoding complexity and delay, and its performance is not affected by a change in the LDPC code and transmission channel parameters.

In this letter, the tradeoff between symbol rate and diversity gain of Space-Time Block Codes (STBCs) with linear receivers is considered. It is known that Group Orthogonal-Toeplitz Codes (GOTCs) can achieve a good tradeoff with linear receivers. However, the symbol rate of GOTCs is limited to that of the base Orthogonal Space-Time Block Codes (OSTBCs). We propose to simply change the GOTC base codes from OSTBCs to Quasi-Orthogonal Space-Time Block Codes (Q-OSTBCs). Q-OSTBCs can improve the symbol rate of GOTCs at the expense of diversity gain. Simulation results show that Q-OSTBC based GOTCs can improve the tradeoff between symbol rate and diversity gain over that of the original GOTCs.

Granular gain of low-dimensional lattices based on binary linear codes is estimated using a quantization algorithm which is equivalently a soft-decision decoding of the underlying code. It is shown that substantial portion of the ultimate granular gain is achieved even in limited dimensions.

Variable-weight optical orthogonal codes (OOCs) have application in multimedia optical code division multiple access (OCDMA) systems supporting multiple quality of services (QoS). In this paper, several combinatorial constructions for optimal variable-weight OOCs are presented explicitly. A useful recursive construction for optimal variable-weight OOCs is proposed as well. Based on these results, two new infinite classes of optimal variable-weight OOCs with Hamming weights 3 and 4 are obtained.

In this paper, a method is proposed for reconstruction of the parameters of a non-binary block encoder using an intercepted sequence of noisy coded data. The proposed method is a generalization of the Barbier's method for the reconstruction of binary block codes to the more problematic case of non-binary codes. It has been shown mathematically that considering some revisions in definitions, such a generalization is possible. The proposed method is able to estimate the code parameters such as the code length, the code dimension, number of bits per symbol, and the dual-code subspace, and also to synchronize the sequence. Since the Reed-Solomon code is the most important type of non-binary block codes, an additional method is proposed to reconstruct the generator polynomial in the case of Reed-Solomon codes. The proposed method is evaluated via computer simulations which verify its strength and effectiveness.

This letter presents a novel weighted reliability-based (WRB) algorithm for decoding low-density parity-check (LDPC) codes. Viewing the well-known normalized min sum (NMS) algorithm as reliability-based, the WRB algorithm can be seen as a simplified version of the NMS algorithm. Unlike the NMS algorithm, the WRB algorithm does not update the soft information sent between the variable nodes and check nodes, which greatly reduces the decoding complexity. For finite geometry LDPC codes with larger row redundancy and column weights, simulation results show that the WRB algorithm almost matches the error performance of the NMS algorithm.

In time-varying frequency selective channels, to obtain high-rate joint time-frequency diversity, linear dispersion coded orthogonal frequency division multiplexing (LDC-OFDM), has recently been proposed. Compared with OFDM systems, single-carrier systems may retain the advantages of lower PAPR and lower sensitivity to carrier frequency offset (CFO) effects, which motivates this paper to investigate how to achieve joint frequency and time diversity for high-rate single-carrier block transmission systems. Two systems are proposed: linear dispersion coded cyclic-prefix single-carrier modulation (LDC-CP-SCM) and linear dispersion coded zero-padded single-carrier modulation (LDC-ZP-SCM) across either multiple CP-SCM or ZP-SCM blocks, respectively. LDC-SCM may use a layered two-stage LDC decoding with lower complexity. This paper analyzes the diversity properties of LDC-CP-SCM, and provides a sufficient condition for LDC-CP-SCM to maximize all available joint frequency and time diversity gain and coding gain. This paper shows that LDC-ZP-SCM may be effectively equipped with low-complexity minimum mean-squared error (MMSE) equalizers. A lower complexity scheme, linear transformation coded SCM (LTC-SCM), is also proposed with good diversity performance.

A low complexity log-likelihood ratio (LLR) calculation for high-order amplitude phase shift keying (APSK) signals is proposed. Using proper constellation partitioning together with a look-up table, the number of terms for the comparison of Euclidean distances can be significantly reduced. Compared with the log-sum LLR approximation, the proposed method reduces the computational complexity by more than 65% and 75% for 16-APSK and 32-APSK signals, respectively, with very small bit error rate performance degradation.

Entangled states play crucial roles in quantum information theory and its applied technologies. In various protocols such as quantum teleportation and quantum key distribution, a good entangled state shared by a pair of distant players is indispensable. In this paper, we numerically examine entanglement sharing protocols using quantum LDPC CSS codes. The sum-product decoding method enables us to detect uncorrectable errors, and thus, two protocols, Detection and Resending (DR) protocol and Non-Detection (ND) protocol are considered. In DR protocol, the players abort the protocol and repeat it if they detect the uncorrectable errors, whereas in ND protocol they do not abort the protocol. We show that DR protocol yields smaller error rate than ND protocol. In addition, it is shown that rather high reliability can be achieved by DR protocol with quantum LDPC CSS codes.

In this letter, we provide an asymptotic error rate performance evaluation of space-time block codes from coordinate interleaved orthogonal designs (STBCs-CIODs), especially in shadowed Rayleigh fading channels. By evaluating a simplified probability density function (PDF) of Rayleigh and Rayleigh-lognormal channels affecting the STBC-CIOD system, we derive an accurate closed-form approximation for the tight upper and lower bounds on the symbol error rate (SER). We show that shadowing asymptotically affects coding gain only, and conclude that an increase in diversity order under shadowing causes slower convergence to asymptotic bound due to the relatively larger loss of coding gain. By comparing the derived formulas and Monte-Carlo simulations, we validate the accuracy of the theoretical results.

An important concept in secret sharing scheme is the access structure. However, determining the access structure of the secret sharing scheme based on a linear code is a very difficult problem. In this work, we provide a method to construct a class of two-weight linear codes over finite rings. Based on the two-weight codes, we present an access structure of a secret sharing scheme.

We propose a 2Nr MIMO ARQ scheme that uses multi-strata space-time codes composed of two layers. The phase and transmit power of each layer are assigned adaptively at each transmission round to mitigate the inter-layer interference and improve the block error rate by retransmission. Simulation results show that the proposed scheme achieves better performance than the conventional schemes in terms of the throughput and the block error rate.

In this paper, we derive a simple formula to generate a wide-sense systematic generator matrix(we call it quasi-systematic) B for a Reed-Solomon code. This formula can be utilized to construct an efficient interpolation based erasure-only decoder with time complexity O(n2) and space complexity O(n). Specifically, the decoding algorithm requires 3kr + r2 - 2r field additions, kr + r2 + r field negations, 2kr + r2 - r + k field multiplications and kr + r field inversions. Compared to another interpolation based erasure-only decoding algorithm derived by D.J.J. Versfeld et al., our algorithm is much more efficient for high-rate Reed-Solomon codes.