Design Of Error Correcting Codes Research Articles

High-Performance and Flexible Design Scheme with ECC Protection in the Cache.

To improve the reliability of static random access memory (SRAM), error-correcting codes (ECC) are typically used to protect SRAM in the cache. While improving the reliability, we also need additional circuits to support ECC, including encoding and decoding logic. In a high-speed circuit such as a CPU, the L1 cache maintains the same frequency as the CPU, and the decoding of the ECC codes in the cache consumes considerable combinational logic, resulting in limited frequency and performance. This study proposes a high-performance and flexible design scheme with ECC protection in the cache, in which the cache has two working modes: a high-performance mode and a high-reliability mode. The high-performance mode uses simple ECC codes, which can maintain high frequency with low access latency. The high-reliability mode uses more complex ECC codes, which improves the error correction capability and enhances the reliability of the SRAM. To meet the application requirements of different scenarios, the proposed scheme supports the software in switching between the above two modes by configuring the register, which improves the flexibility of the system. The results of synthesis show that the theoretical maximum frequency of proposed ECC design scheme increased from approximately 1.4 GHz in the conventional ECC design scheme to approximately 2.2 GHz. Some of the error correction capability of the high-performance mode is traded off against a 57% increase in frequency. In the high-reliability mode, the error correction capability of the SRAM is enhanced; however, the latency of accessing the cache increases by one cycle.

Asymptotic Behavior of Spatial Coupling LDPC Coding for Compute-and-Forward Two-Way Relaying

Compute-and-forward (CAF) relaying is an effective way to increase bandwidth efficiency of wireless two-way relay channels. Design of error-correcting codes and their decoding algorithms suitable for CAF relaying schemes remains an important issue to be studied. In this paper, we will analyze an asymptotic behavior of LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric characteristics of the channel, we use the population dynamics DE combined with DE formulas for asymmetric channels to obtain the belief propagation (BP) thresholds. Additionally, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatially coupled codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels.

Protecting Memories against Soft Errors: The Case for Customizable Error Correction Codes

As technology scales, radiation induced soft errors create more complex error patterns in memories with a single particle corrupting several bits. This poses a challenge to the Error Correction Codes (ECCs) traditionally used to protect memories that can correct only single bit errors. During the last decade, a number of codes have been developed to correct the emerging error patterns, focusing initially on double adjacent errors and later on three bit burst errors. However, as the memory cells get smaller and smaller, the error patterns created by radiation will continue to change and thus new codes will be needed. In addition, the memory layout and the technology used may also make some patterns more likely than others. For example, in some memories, there maybe elements that separate blocks of bits in a word, making errors that affect two blocks less likely. Finally, for a given memory, depending on the data stored, some error patterns may be more critical than others. For example, if numbers are stored in the memory, in most cases, errors on the more significant bits have a larger impact. Therefore, for a given memory and application, to achieve optimal protection, we would like to have a code that corrects a given set of patterns. This is not possible today as there is a limited number of code choices available in terms of correctable error patterns and word lengths. However, most of the codes used to protect memories are linear block codes that have a regular structure and which design can be automated. In this paper, we propose the automation of error correction code design for memory protection. To that end, we introduce a software tool that given a word length and the error patterns that need to be corrected, produces a linear block code described by its parity check matrix and also the bit placement. The benefits of this automated design approach are illustrated with several case studies. Finally, the tool is made available so that designers can easily produce custom error correction codes for their specific needs.

High capacity DNA data storage with variable-length Oligonucleotides using repeat accumulate code and hybrid mapping

BackgroundWith the inherent high density and durable preservation, DNA has been recently recognized as a distinguished medium to store enormous data over millennia. To overcome the limitations existing in a recently reported high-capacity DNA data storage while achieving a competitive information capacity, we are inspired to explore a new coding system that facilitates the practical implementation of DNA data storage with high capacity.ResultIn this work, we devised and implemented a DNA data storage scheme with variable-length oligonucleotides (oligos), where a hybrid DNA mapping scheme that converts digital data to DNA records is introduced. The encoded DNA oligos stores 1.98 bits per nucleotide (bits/nt) on average (approaching the upper bound of 2 bits/nt), while conforming to the biochemical constraints. Beyond that, an oligo-level repeat-accumulate coding scheme is employed for addressing data loss and corruption in the biochemical processes. With a wet-lab experiment, an error-free retrieval of 379.1 KB data with a minimum coverage of 10x is achieved, validating the error resilience of the proposed coding scheme. Along with that, the theoretical analysis shows that the proposed scheme exhibits a net information density (user bits per nucleotide) of 1.67 bits/nt while achieving 91% of the information capacity.ConclusionTo advance towards practical implementations of DNA storage, we proposed and tested a DNA data storage system enabling high potential mapping (bits to nucleotide conversion) scheme and low redundancy but highly efficient error correction code design. The advancement reported would move us closer to achieving a practical high-capacity DNA data storage system.

An Adaptive Thermal-Aware ECC Scheme for Reliable STT-MRAM LLC Design

Considering the insatiable demand for high-performance computing, on-chip cache capacity increases rapidly. Spin-transfer-torque magnetoresistive random-access memory (STT-MRAM) is a promising cache candidate due to ultralow standby power, high-access speed, and integration density. Unfortunately, when the feature size of magnetic tunnel junction (MTJ) scales down to 1 Xnm, read current approaches write current closely, which may result in read disturbance threatening the reliability of STT-MRAM. Furthermore, the elevating on-chip temperature reduces the thermal stability of STT-MRAM remarkably and aggravates the read disturbance. Error correction code (ECC) is an effective technique to enhance memory reliability. In this paper, we take advantage of the thermal dependence of STT-MRAM and propose a thermally adaptive ECC design, called “Chameleon,” that can adjust the ECC protection strength dynamically to reduce the ECC storage overhead and improve the cache access performance and energy efficiency. Experimental results show that compared to the conservative nonadaptive ECC scheme, our design can improve both cache performance and energy consumption effectively.

Configurable-ECC: Architecting a Flexible ECC Scheme to Support Different Sized Accesses in High Bandwidth Memory Systems

Designing error correction code (ECC) to guarantee strong reliability for high bandwidth memory (HBM) is imperative in high performance computers, especially for systems equipped with graphics processing units (GPUs). The design of ECC is challenging because future GPUs are expected to implement a memory subsystem supporting fine and coarse-grained data accesses to match the difference in the spatial locality of GPGPU applications. Current ECC designs, however, are developed for a fixed data fetch granularity. To have a more flexible design, we propose a novel memory protection scheme, called Config(urable)-ECC, which provides strong reliability for both fine and coarse-grained data accesses. Config-ECC consists of two tiers of ECC protection. The tier-1 code is a strong product code that can correct errors due to small granularity faults and detect errors caused by large granularity faults. The tier-2 code is an XOR-based code that is employed to correct errors incurred by large granularity faults. Config-ECC provides stronger reliability and/or lower energy consumption compared to state-of-the-art fixed 32B and 64B ECC schemes. It reduces the HBM energy by 17-21 percent while reducing the failure in time (FIT) rate by 20 times compared to a state-of-the-art fixed 64B ECC scheme with an insignificant 1.2 percent performance overhead.

Geometric Approaches to Gibbs Energy Landscapes and DNA Oligonucleotide Design

DNA codeword design has been a fundamental problem since the early days of DNA computing. The problem calls for finding large sets of single DNA strands that do not crosshybridize to themselves, to each other or to others' complements. Such strands represent so-called domains, particularly in the language of chemical reaction networks (CRNs). The problem has shown to be of interest in other areas as well, including DNA memories and phylogenetic analyses because of their error correction and prevention properties. In prior work, a theoretical framework to analyze this problem has been developed and natural and simple versions of Codeword Design have been shown to be NP-complete using any single reasonable metric that approximates the Gibbs energy, thus practically making it very difficult to find any general procedure for finding such maximal sets exactly and efficiently. In this framework, codeword design is partially reduced to finding large sets of strands maximally separated in DNA spaces and, therefore, the size of such sets depends on the geometry of these spaces. Here, the authors describe in detail a new general technique to embed them in Euclidean spaces in such a way that oligonucleotides with high (low, respectively) hybridization affinity are mapped to neighboring (remote, respectively) points in a geometric lattice. This embedding materializes long-held metaphors about codeword design in analogies with error-correcting code design in information theory in terms of sphere packing and leads to designs that are in some cases known to be provably nearly optimal for small oligonucleotide sizes, whenever the corresponding spherical codes in Euclidean spaces are known to be so. It also leads to upper and lower bounds on estimates of the size of optimal codes of size under 20-mers, as well as to a few infinite families of DNA strand lengths, based on estimates of the kissing (or contact) number for sphere codes in high-dimensional Euclidean spaces. Conversely, the authors show how solutions to DNA codeword design obtained by experimental or other means can also provide solutions to difficult spherical packing geometric problems via these approaches. Finally, the reduction suggests a tool to provide some insight into the approximate structure of the Gibbs energy landscapes, which play a primary role in the design and implementation of biomolecular programs.

다양한 유전 연산자를 이용한 저전력 오류 정정 코드 설계

The memory is very sensitive to the soft error because the integration of the memory increases under low power environment. Error correcting codes (ECCs) are commonly used to protect against the soft errors. This paper proposes a new genetic ECC design method which reduces power consumption. Power is minimized using the degrees of freedom in selecting the parity check matrix of the ECCs. Therefore, the genetic algorithm which has the novel genetic operators tailored for this formulation is employed to solve the non-linear power optimization problem. Experiments are performed with Hamming code and Hsiao code to illustrate the performance of the proposed method.

Superadditivity of communication capacity using entangled inputs

The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information [1]. This capacity can be expressed using the mutual information between input and output for a single use of the channel: although correlations between subsequent input bits are used to correct errors, they cannot increase the capacity. For quantum channels, it has been an open question whether entangled input states can increase the capacity to send classical information [2]. The additivity conjecture [3,4] states that entanglement does not help, making practical computations of the capacity possible. While additivity is widely believed to be true, there is no proof. Here we show that additivity is false, by constructing a random counter-example. Our results show that the most basic question of classical capacity of a quantum channel remains open, with further work needed to determine in which other situations entanglement can boost capacity.

A Symbiotic Evolutionary Design of Error-Correcting Code with Minimal Power Consumption

In this paper, a new design for an error correcting code (ECC) is proposed. The design is aimed to build an ECC circuitry with minimal power consumption. The genetic algorithm equipped with the symbiotic mechanism is used to design a power-efficient ECC which provides single-error correction and double-error detection (SEC-DED). We formulate the selection of the parity check matrix into a collection of individual and specialized optimization problems and propose a symbiotic evolution method to search for an ECC with minimal power consumption. Finally, we conduct simulations to demonstrate the effectiveness of the proposed method.

A NEW GENETIC DESIGN FOR ERROR CORRECTING CODE FOR POWER MINIMIZATION

Error correcting codes (ECCs) are commonly used as a protection against the soft errors. Single error correcting and double error detecting (SEC–DED) codes are generally used for this purpose. Such circuits are widely used in industry in all types of memory, including caches and embedded memory. In this paper, a new genetic design for ECC is proposed to perform SEC–DED in the memory check circuit. The design is aimed at finding the implementation of ECC which consumes minimal power. We formulate the ECC design into a permutable optimization problem and employ special genetic operators appropriate for this formulation. Experiments are performed to demonstrate the performance of the proposed method.

Codeword Stabilized Quantum Codes

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.

Iterated local search and constructive heuristics for error correcting code design

Error Correcting Codes (ECCs) play an important role, for example, in the transmission of messages over telecommunication networks or in reading information from digital data media such as DVDs or CDs. The design of ECCs is computationally a hard problem. Due to its hardness, several metaheuristic approaches for its solution have been proposed in the literature. In this paper, we present different algorithms based on solution construction and iterated local search. The experimental evaluation shows that a simple multistart constructive heuristic is often between two and three orders of magnitude faster than current state-of-the-art metaheuristics when applied to rather small problem instances. When bigger problem instances are concerned, the proposed iterated local search algorithm has advantages over both the multistart constructive heuristic and state-of-the-art metaheuristics.

High code rate error correction code design for partial response systems

In recent years, code designers have been interested in finding high code rate solutions for coded partial response systems. The focus of the attention has been given to increasing the code rate of modulation codes. In this paper we turn our attention to increasing the code rate of error correction codes designed fur partial response systems. An analysis of low distance preceded input error events illustrates how an error correction code should exploit the structure of these error events in order to achieve an increase in rode rate. We describe a method of using a combination of interleaved Reed-Solomon codes interspersed with uncoded bits to achieve a higher code rate than the classical ECC solution. Simulation results suggest good performance of this scheme.

Parallel genetic simulated annealing: a massively parallel SIMD algorithm

Many significant engineering and scientific problems involve optimization of some criteria over a combinatorial configuration space. The two methods most often used to solve these problems effectively-simulated annealing (SA) and genetic algorithms (GA)-do not easily lend themselves to massive parallel implementations. Simulated annealing is a naturally serial algorithm, while GA involves a selection process that requires global coordination. This paper introduces a new hybrid algorithm that inherits those aspects of GA that lend themselves to parallelization, and avoids serial bottle-necks of GA approaches by incorporating elements of SA to provide a completely parallel, easily scalable hybrid GA/SA method. This new method, called Genetic Simulated Annealing, does not require parallelization of any problem specific portions of a serial implementation-existing serial implementations can be incorporated as is. Results of a study on two difficult combinatorial optimization problems, a 100 city traveling salesperson problem and a 24 word, 12 bit error correcting code design problem, performed on a 16 K PE MasPar MP-1, indicate advantages over previous parallel GA and SA approaches. One of the key results is that the performance of the algorithm scales up linearly with the increase of processing elements, a feature not demonstrated by any previous parallel GA or SA approaches, which enables the new algorithm to utilize massive parallel architecture with maximum effectiveness. Additionally, the algorithm does not require careful choice of control parameters, a significant advantage over SA and GA.

Very simple method to find the minimum polynomial of an arbitrary nonzero element of a finite field

A method is described of finding the minimum polynomial of an arbitrary, nonzero element of GF(2m). This method requires finite arithmetic on only a single element of the field, and not on each of the k+1 coefficients over GF(2m), where k is the degree of the minimum polynomial. Applications include the design of error-correcting codes and of apparatus to process them, as well as cryptographic systems.