Outer Code Research Articles

Concatenated LDPC/2-D-Marker Codes and Non-Iterative Detection/Decoding for Recovering Position Errors in Racetrack Memories

Racetrack memories (RMs) are prone to alignment faults called position errors (PEs), which manifest as insertions and deletions of stored data bits. Conventional coding schemes for PEs demonstrate the promising results by employing low-density parity-check (LDPC) codes with an iterative detection and decoding algorithm. However, the computational complexity of detection is relatively high. In this article, for channels with PEs, we present a new coding scheme that can effectively decode corrupted data, even if the detection is executed only once (i.e., a non-iterative detection and decoding scenario). The proposed code consists of a concatenation of an inner 2-D marker code, which is specialized for PEs to mitigate the effect of insertion and deletion (ID) errors, and an outer irregular LDPC code. We also provide tractable design methodologies for these constituent codes. First, we identify the 2-D-marker code structures that offer higher achievable information rates in a non-iterative scenario and then optimize irregular LDPC codes to ensure good decoding properties. Through asymptotic-performance analysis and finite-length simulation, we confirm the effectiveness of the proposed coding scheme. Ultimately, the proposed coding scheme has the capability to reduce code rate loss and to provide excellent decoding performance under a non-iterative scenario, which also helps in understanding the reliability of RM when a low-complexity decoding algorithm is used to correct ID errors caused by PEs.

Efficient Compression of Long Arbitrary Sequences With No Reference at the Encoder

In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect reconstruction is required, we present two contributions to the solution of this problem. One result shows that when a set of potential reference vectors is available to the encoder, lower compression rates can be achieved when the set satisfies a certain clustering property. Another result reduces the best known decoding complexity from exponential in the vector length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{1.5})$ </tex-math></inline-formula> by generalized concatenation of inner coset codes and outer error-correcting codes. One potential application of the results is the compression of DNA sequences, where similar (but not identical) reference vectors are shared among senders and receivers.

Spatially coupled turbo-coded continuous phase modulation: asymptotic analysis and optimization

For serially or parallel concatenated communication systems, spatial coupling techniques enable to improve the threshold of these systems under iterative decoding using belief propagation (BP). For the case of low-density parity-check (LDPC) codes, it has been shown that, under some asymptotic assumptions, spatially coupled ensembles have BP thresholds that approach the bitwise maximum a posteriori (MAP) threshold of the related uncoupled ensemble. This phenomenon is often referred to as threshold saturation, and it has sometimes very important consequences. For example, in the case of regular LDPC code ensembles, spatial coupling enables to achieve asymptotically the capacity for any class of binary memoryless symmetric channels. Since then, this threshold saturation has been conjectured or proved for several other types of concatenations. In this work, we consider a serially concatenated scheme which is the serial concatenation of a simple outer convolutional code and a continuous phase modulator (CPM) separated by an interleaver. Then, we propose a method to do the spatial coupling of several replicas of this serially concatenated scheme, aiming to improve the asymptotic convergence threshold. First, exploiting the specific structure of the proposed system, an original procedure is proposed in order to terminate the spatially coupled turbo-coded CPM scheme. In particular, the proposed procedure aims to ensure the continuity of the transmitted signal among spatially coupled replicas, enabling to keep one of the core characteristics and advantages of coded CPM schemes. Then, based on an asymptotic analysis, we show that the proposed scheme has very competitive thresholds when compared to carefully designed spatially coupled LDPC codes. Furthermore, it is shown how we can accelerate the convergence rate of the designed systems by optimizing the connection distributions in the coupling matrices. Finally, by investigating on different continuous phase modulation schemes, we corroborate the conjecture stating that spatially coupled turbo-coded CPM schemes saturate to a lower bound very close to the threshold given by the extrinsic information transfer (EXIT) area theorem.

HEDGES error-correcting code for DNA storage corrects indels and allows sequence constraints

Synthetic DNA is rapidly emerging as a durable, high-density information storage platform. A major challenge for DNA-based information encoding strategies is the high rate of errors that arise during DNA synthesis and sequencing. Here, we describe the HEDGES (Hash Encoded, Decoded by Greedy Exhaustive Search) error-correcting code that repairs all three basic types of DNA errors: insertions, deletions, and substitutions. HEDGES also converts unresolved or compound errors into substitutions, restoring synchronization for correction via a standard Reed-Solomon outer code that is interleaved across strands. Moreover, HEDGES can incorporate a broad class of user-defined sequence constraints, such as avoiding excess repeats, or too high or too low windowed guanine-cytosine (GC) content. We test our code both via in silico simulations and with synthesized DNA. From its measured performance, we develop a statistical model applicable to much larger datasets. Predicted performance indicates the possibility of error-free recovery of petabyte- and exabyte-scale data from DNA degraded with as much as 10% errors. As the cost of DNA synthesis and sequencing continues to drop, we anticipate that HEDGES will find applications in large-scale error-free information encoding.

PSTGF: Time-independent R-matrix atomic electron-impact code

stgf is a community code employed for outer-region R-matrix calculations, describing electron-impact collisional processes. It is widely recognised that the original version of stgf was written by M.J. Seaton in 1983, but through constant refinement over the next decades by worldwide contributors has evolved into its current form that more reflects modern coding practice and current computer architectures. Despite its current wide acceptance, it was never formally published.Therefore, we present an updated high-performance parallel version of pstgf, that balances the requirements of small university clusters, yet can exploit the computational power of cutting edge supercomputers. There are many improvements over the original stgf, but most noticeably, the full introduction of MQDT options that provide subsequent integration with ICFT (Intermediate Coupling Frame Transformation) codes, and for either Breit–Pauli/DARC (Dirac Atomic R-matrix Codes), better load balancing, high levels of vectorisation and simplified output. Semantically, the program is full Fortran 90 in conjunction with MPI (Message Passing Interface) though has CUDA Fortran options for the most numerically intensive code sections. Program summaryProgram Title: RMATRX-PSTGFCPC Library link to program files:http://dx.doi.org/10.17632/3j55fmr86g.1Licensing provisions: GNU Lesser General Public License v2.1Programming language: Fortran 90Nature of problem: The R-matrix outer region code, pstgf directly calculates various electron-impact driven processes such as excitation and ionisation, or provides K-matrices for input for subsequent ICFT, differential or magnetic sub-level codes. As the problem size increases, there is an associated increase in the input/output, the numerical computation and unbalanced workload, especially for electron-impact energies where the number of open-channels is of a similar size to the number of closed. The code has been significantly modified to address these issues.pstgf interfaces the R-matrix inner region with the outer region, with the R-matrix acting as intermediary between the two regions. The outer region expresses an electron moving in the multi-pole expansion of the target and predominantly employs Coulomb functions, perturbed or otherwise to achieve this. This is a computationally expensive task, as the R-matrix must be formed for every energy point of every partial wave.Solution method: An approach that permutes both the partial wave and energy of the incident electron has been implemented. In this version, each processor does not calculate the same incident energy point for each partial wave, but rather distributes all energy points across all processors. This achieves better load-balancing of the work between cores and avoids the case where an overloaded single processor has to always calculate in the energy range where there are approximately the same number of half-open or half-closed channels, which is numerically intensive.Additional comments including restrictions and unusual features: Dimension parameters used to define arrays and matrices within pstgf (PARAM file) have been removed, all array dimensions are dynamically allocatable based upon the H.DAT file and set to the exact dimension. A CUDA subroutine for matrix multiplications using GPUs has been included, it can be activated or deactivated commenting this module in the source. Users of serial version stgf or older parallel versions of pstgf can move to current version without any modification in the input files.[1] M.J. Seaton, Coulomb functions for attractive and repulsive potentials and for positive and negative energies, Comp. Phys. Comm. 146 (2) (2002) 225–249. doi:https://doi.org/10.1016/S0010-4655(02)00275-8.[2] M.J. Seaton, Quantum defect theory, Rep. Prog. Phys. 46 (2) (1983) 167.doi:https://doi.org/10.1088/0034-4885/46/2/002.

Error control scheme for malicious and natural faults in cryptographic modules

Today’s electronic systems must simultaneously fulfill strict requirements on security and reliability. In particular, their cryptographic modules are exposed to faults, which can be due to natural failures (e.g., radiation or electromagnetic noise) or malicious fault-injection attacks. We present an architecture based on a new class of error-detecting codes that combine robustness properties with a minimal distance. The new architecture guarantees (with some probability) the detection of faults injected by an intelligent and strategic adversary who can precisely control the disturbance. At the same time it supports automatic correction of low-multiplicity faults. To this end, we discuss an efficient technique to correct single nibble/byte errors while avoiding full syndrome analysis. We also examine a Compact Protection Code (CPC)-based system level fault manager that considers this code an inner code (and the CPC as its outer code). We report experimental results obtained by physical fault injection on the SAKURA-G FPGA board. The experimental results reconfirm the assumption that faults may cause an arbitrary number of bit flips. They indicate that a combined inner–outer coding scheme can significantly reduce the number of fault events that go undetected due to erroneous corrections of the inner code.

Improvement the Performance of MIMO Channel Employing Concatenation (BCH –STBC) Codes.

Wireless communication system has been matured as a key technique to realize high data rates, more handling power, and optimizing 5G applications to increase users rapidly. Due to the issues of fading, it is difficult to obtain high data rates and maximum capacity. Different coding schemes have been implemented to contend the effect of fading. Multiple – input multiple-output (MIMO) technology remains robust technology besides channel coding. Here in this research paper, concentrate on employing the available resources in the wireless communication system to enhance the performance of the MIMO system when concatenated STBC code with forward error correction (FEC) code, such as (BCH) code without additional power or further bandwidth. The outcomes show the coding technique gives better improvement in the BER and obtain good coding gain when using BCH(31,16)-STBC, BCH(127,106)-STBC the coding gain is about 5.8 dB,3.7 dB consecutively under AWGN channel and improved by 13.25 dB, 9 dB successively under Rayleigh fading channel at BER about 10−3, when compared with uncoded system. Additionally, this research manifests that the proposed model gives the improvement in BER performance about (5% to 86%)over AWGN channel and (6% to 100%) over Rayleigh fading channel when compared with the uncoded system.

Low Complexity Rate Compatible Puncturing For Future Communication network

An efficient low complexity puncturing method has studied to achieve rate compatible. The parallel concatenation codes are use mixing of one component of Quasi-Cyclic (QC) low-density parity check codes LDPC codes with two components of (LDPC) in linear coding. The proposed QC-PCGC have lower computation complexity when compared with traditional punctured PCGC. The decreasing in the complexity analysis yields to the reducing in the memory requirement for the encoding/decoding system. It is possible to use the suggested coding system structure in the future communication applications like fifth generation (5G), where it is needed to have coding flexibility, with less complexity in encoding and decoding.

ON THE DESIGN OF BCH CODES POLYNOMIALS FOR DIGITAL TELEVISION DVB-T2 BROADCASTING SYSTEMS

Digital Video Broadcasting Terrestrial{Second Generation (DVB-T2) requires a high coding rate to transmit data of high-quality video. This paper evaluates Bose-Chaudhuri-Hocquenghem (BCH) codes for the DVB-T2 to measure the gain of BCH codes. This paper evaluates the BCH codes as outer coding to be combined with other different inner encoding schemes such as Low Density Parity Check (LDPC) codes and convolutional codes to measure the best suitable inner encoding scheme. This paper also studies the performances of BCH codes for DVB-T2 specified by two different standards, i.e., (a) The European Telecommunications Standards Institute (ETSI) Technical Specification (TS) 102 831 and (b) ETSI European Standard (EN) 302 755. To obtain better error correcting capability, we propose new BCH polynomials based on the general guideline from ETSI TS 102 831 for Galois Field GF(214). We perform computer simulations to evaluate bit-error-rate (BER) performances under additive white Gaussian noise (AWGN) channel and Indonesia DVB-T2 channel model. We revealed the superiority of BCH codes in high data rate transmission, which is required for DVB-T2, and found that BCH codes are better suited to the LDPC codes as inner encoding rather than to the convolutional codes. We also confirmed that BCH codes of DVB-T2 from ETSI TS 102 831 using the proposed BCH polynomials have better performances compared to the standard polynomial of ETSI EN 302 755. We are expecting that the obtained polynomials can be adopted by the BCH codes of Indonesia DVB-T2 system. These results are expected to support the Indonesian government in determining the parameters of the BCH codes of DVB-T2 for Indonesia.

An Efficient Design of Systematic Rateless Codes

The asymptotic performance of systematic rateless codes is first analysed using Gaussian approximation (GA) based on mutual information, which provides more accurate decoding thresholds than the method based on message mean. A modified linear program (LP) algorithm is proposed, where two key parameters are precomputed to efficiently search degree distributions with low overhead and appropriate average degree. The asymptotic analysis and simulation results show that the optimized code outperforms the codes obtained by conventional LP. Furthermore, the effects of outer code on overall code rate and decoding complexity are discussed.

Integrated Analysis of Performance and Resources in Large-Scale Quantum Computing

To see the feasibility of a large-scale quantum computing, it is required to accurately analyze the performance and the quantum resource. However, most of the analysis reported so far have focused on the statistical examination, i.e., simply calculating the performance and resource based on individual data, and even worse usually only a few components have been considered. In this work, to achieve more exact analysis, we propose an integrated analysis method for a practical quantum computing model with three components (\textit{algorithm}, \textit{error correction} and \textit{device}) under a realistic quantum computer system architecture. To implement the above method, we develop a quantum computing framework composed of three functional layers: compile, system and building block. This framework can support, for the first time, the mapping of quantum algorithm from physical qubit level to system architecture level with a given fault-tolerant scheme. Therefore, the proposed method can measure the effect of dynamic situation when the quantum computer practically runs. By using our method, we found that Shor algorithm to factorize 512-bit integer requires $8.78\times 10^ 5$ hours. We also show how the proposed method can be used for analyzing optimal concatenation level and code distance of fault-tolerant quantum computing.

A novel BCS code in a downlink LTE system over an LTE-MIMO channel

In general, a concatenated RS/BCH code consists of an outer RS code and an inner BCH code with separation by an interleaver. We create a novel BCS code using a new methodology by combining an outer BCH code with an inner RS code appended by an interleaver to randomize burst errors and help the RS code in correcting the errors. Generally, BCH codes handle binary data, whereas RS codes handle non-binary data. Hence, RS (7, 1) inner code is proposed to achieve compatibility with BCH (15, 5) outer codes and ultimately create a novel BCS code to handle binary data. The proposed BCS code is compared with familiar concatenated RS/BCH codes and single codes (RS and BCH) for BPSK and QPSK modulation schemes. Results show the downlink LTE system performance using the proposed BCS code is significantly better than the uncoded LTE system and single codes (RS and BCH). Moreover, the proposed BCS code also outperforms familiar concatenated RS/BCH codes for both schemes. In contrast, the system performance is improved further when the number of antennas in the MIMO channel is increased from $$2 \times 2$$ to $$4 \times 4$$ . Therefore, the proposed BCS code can be considered a stronger code with high reliability in wireless communication systems.

Interleaved Polar (I-Polar) Codes

By inserting interleavers between intermediate stages of the polar encoder, a new class of polar codes, termed interleaved polar (i-polar) codes, is proposed. By the uniform interleaver assumption, we derive the weight enumerating function (WEF) and the input-output weight enumerating function (IOWEF) averaged over the ensemble of i-polar codes. The average WEF can be used to calculate the upper bound on the average block error rate (BLER) of a code selected at random from the ensemble of i-polar codes. Also, we propose a concatenated coding scheme that employs $P$ high rate codes as the outer code and $Q$ i-polar codes as the inner code with an interleaver in between. The average WEF of the concatenated code is derived based on the uniform interleaver assumption. Simulation results show that BLER upper bounds can well predict BLER performance levels of the concatenated codes. The results show that the performance of the proposed concatenated code with $P=Q=2$ is better than that of the CRC-aided i-polar code with $P=Q=1$ of the same length and code rate at high signal-to-noise ratios (SNRs). Moreover, the proposed concatenated code allows multiple decoders to operate in parallel, which can reduce the decoding latency and hence is suitable for ultra-reliable low-latency communications (URLLC).

Quantum Computing with Rotation-Symmetric Bosonic Codes

Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase codes--which includes the well-known cat and binomial codes, among many others. The entangling gate in our scheme is code-agnostic and can be used to interface different rotation-symmetric encodings. In addition to a universal set of operations, we propose a teleportation-based error correction scheme that allows recoveries to be tracked entirely in software. Focusing on cat and binomial codes as examples, we compute average gate fidelities for error correction under simultaneous loss and dephasing noise and show numerically that the error-correction scheme is close to optimal for error-free ancillae and ideal measurements. Finally, we present a scheme for fault-tolerant, universal quantum computing based on concatenation of number-phase codes and Bacon-Shor subsystem codes.

Performance analysis of concatenated BCH and convolutional coded OFDM system

ABSTRACT Orthogonal Frequency Division Multiplexing (OFDM) is a widely used technique for wireless communications. But uncoded OFDM is not sufficient by itself, that is why channel coding is included to increase the system performance. In this study, concatenated Bose Chaudhuri Hocquenghem (BCH) and Convolutional Coded (CC) OFDM system is investigated for multipath fading channel with Additive White Gaussian Noise (AWGN). The simulation results show that the proposed concatenated code needs lower Signal-to-Noise Ratio (SNR) when compared with single BCH code, single convolutional code and even with other concatenated systems. Throughout the simulations BCH coding is performed with 128, 256, 512 Fast Fourier Transform (FFT) lengths; whereas convolutional coding is performed with 1/2, 1/3 coding rates. Furthermore, interleavers are added to the system to prevent the burst errors that occur over the channel. With the proposed system, the best result is obtained by using BCH(511,340) and CC(3,1,7) concatenation which is 8.2 dB SNR value for 10−3 Bit Error Rate (BER). This result is very close to ideal AWGN channel value, which is 8 dB for 10−3 BER.

Coding for Two-User Energy Harvesting Interference Channel

A two-user interference channel with energy harvesting transmitters, each equipped with a finite battery, is considered. Achievable rate regions (ARRs) considering independent and identically distributed Shannon strategies at both users and ignoring the memory in the battery state are obtained for both single-user decoding and joint decoding at the receivers. Explicit and implementable codes based on concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check code are designed, and it is demonstrated that rate pairs close to the boundary of ARR can be obtained with this approach. Furthermore, an improved alternative decoding scheme which exploits the memory in the battery state is developed, and it is shown to be highly superior to the simple decoding approach via numerical examples. Superiority of the newly developed practical channel coding solutions over the previously known alternative approaches are illustrated via extensive set of examples as well.

An analysis of code mixing and code switching used by teacher and students in english class

The purpose of conducting this study is to find out the kinds of code mixing and code switching used by teacher and students in English class and some factors that make the teacher and students use code mixing and code switching in English class. This research used qualitative method. The researcher use basic technique in analyzing the data which are recording the entire content, transcribing the utterances, classifying and organizing the data, grouping data and the last is analyzing data. Based on the data found by the researcher, the result of the research shows 4 types of code mixing and code switching namely outer code mixing (English with Indonesia and Indonesian with English) and external code switching (English into Indonesian and Indonesian into English). There are 51 utterances total of code mixing and switching in English class. And some factors that make they use code mixing and switching because the teacher often found out that the students confused or did not understand, the students lack of vocabulary and English knowledge, feel afraid of being wrong in using English and they are not used to talking only in English.

Iterative Decoding of LDPC-Based Product Codes and FPGA-Based Performance Evaluation

Low-density parity-check (LDPC) codes have the potential for applications in future high throughput optical communications due to their significant error correction capability and the parallel decoding. However, they are not able to satisfy the very low bit error rate (BER) requirement due to the error floor phenomenon. In this paper, we propose a low-complexity iterative decoding scheme for product codes consisting of very high rate outer codes and LDPC codes. The outer codes aim at eliminating the residual error floor of LDPC codes with quite low implementation costs. Furthermore, considering the long simulation time of computer simulation for evaluating very low BER, the hardware platform is built to accelerate the evaluation of the proposed iterative decoding methods. Simultaneously, the fixed-point effects of the decoding algorithms are also be evaluated. The experimental results show that the iterative decoding of the product codes can achieve a quite low bit error rate. The evaluation using field programmable gate array (FPGA) also proves that product codes with LDPC codes and high-rate algebraic codes can achieve a good trade-off between complexity and throughput.

DSEP Fulcrum: Dynamic Sparsity and Expansion Packets for Fulcrum Network Coding

Fulcrum coding combines a high-field outer Random Linear Network Coding (RLNC) that generates outer coding expansion packets with a small-field inner RLNC that combines the source packets and the outer coding expansion packets. This two-layer Fulcrum coding allows flexible decoding in receivers with heterogeneous computational capabilities. Fulcrum coding has so far only been studied for conventional dense RLNC, which randomly selects all coding coefficients, and only for a statically fixed number of outer expansion packets. However, the probability that the coding coefficient row of a newly received packet is linearly independent of prior received coding coefficient rows (a prerequisite for successful decoding) is highly dynamic. We propose to exploit the dynamics of this probability to reduce the computational complexity of Fulcrum coding. In particular, we vary the density of non-zero coding coefficients, i.e., equivalently, the sparsity of coding coefficients, and the number of outer expansion packets to keep the complexity low while maintaining a reasonably high decoding probability. We introduce the general principles of dynamic sparsity and expansion packets (DSEP) for Fulcrum coding as well as two specific example DSEP policies. Our evaluations indicate that DSEP Fulcrum can increase the encoding throughput tenfold and increase the decoding throughput 1.4 to 4.3 fold while achieving decoding probabilities that are typically less than 1% lower than the conventional Fulcrum decoding probabilities. We also find that DSEP achieves somewhat higher encoding and decoding throughputs than the CodornicesRq (Release 2.1) implementation of RaptorQ block coding for small blocks (generations) of source packets, while RaptorQ is substantially faster for large generation sizes. Furthermore, we develop and evaluate an elementary DSEP recoding mechanism that achieves a recoding throughput more than double the decoding throughput.

Flexible Multilevel Coding with Concatenated Polar-Staircase Codes for M-QAM

In this work, a multilevel coding (MLC) based coded modulation scheme with two degrees of freedom in rate flexibility is proposed and compared with a bit-interleaved coded modulation (BICM) scheme from a performance versus complexity perspective. The proposed MLC scheme is based on a rate flexible inner soft-decision polar code and utilizes an outer hard-decision staircase code structure as in the 400ZR concatenated forward error-correcting code. The performance of the MLC scheme is investigated for a range of inner code lengths, inner decoder list sizes, and signaling with 16 and 64 quadrature amplitude modulation, respectively. The MLC is designed such that a portion of the staircase encoded bits can bypass the inner code. The number of required inner soft-decision decoders can thus be reduced, thereby saving computational complexity. The proposed MLC scheme simultaneously offers up to a 53.7% reduction in the number of inner decoders and up to 0.55 dB of performance improvement when compared with the similar BICM approach.