Linear Network Error Correction Codes in Packet Networks

We propose an explicit construction of full-diversity space-time block codes, under the constraint of an error correction capability. Furthermore, these codes are constructed in order to be suitable for a serial concatenation with an outer linear forward error correcting (FEC) code. We apply the binary rank criterion, and we use the threaded layering technique and an inner linear FEC code to define a space-time error-correcting code. When serially concatenated with an outer linear FEC code, a product code can be built at the receiver, and adapted iterative receiver structures can be applied. An optimized hybrid structure mixing MMSE turbo equalization and turbo product code decoding is proposed. It yields reduced complexity and enhanced performance compared to previous existing structures.

To improve data reliability in NoC, extensively adopted method is the deployment of error correction codes. Errors present in the data flit are corrected by these codes and this is not applicable for correcting errors present in the header flit. So, there is a need for an coding method which will correct errors in data and also the header flit. Further, it is important to have a coding method that will decode the header flit faster compared to data flit, as header flit is used for processing the data flits. Existing single error correction and double error detection code is improved and presented in this paper to support faster error correction in header flit with retaining the same number of redundant bits. This improved code is synthesised and results are compared with existing code. The results show that the header flit are decoded faster compared to data flits as the critical path delay is reduced.

In recent days, polar codes have attracted the attention of Industry and Academia. It is one of a linear block error correction codes. Polar codes are one of the capacity achieving algorithms over a wide range of channels, making them very attractive from a theoretical perspective. Polar codes are shown to be instances of concatenated codes. It has been shown that the effect of a polar code can be enhanced by showing the multistage decoding algorithm with log-likelihood based Successive List decoding (SCL). However, SCL decoders are no longer optimal in terms of frame error rate. It is believed that the machine learning based algorithm can improve the FER for the decoded bit. Thus, the logistic regression algorithm is proposed in this paper. The proposed method offers an optimized solution to the decoded bits. The simulation result shows that with sufficient training, this method can provide a lower frame error rate for different code lengths.

Error compensation is one of effective and economical means to improve the machining accuracy of machine tools. The measurement accuracy of kinematic errors has great impact on the accuracy of machine tool error modeling. Some measurement errors are inevitably generated due to the distortion of the slide table and the limit of local measuring stroke. To solve these problems, an improved machine tool volumetric error compensation method is proposed in this paper, based on linear and squareness error correction method. The linear errors, including position errors and straightness errors, are corrected by considering the distance effect between optical mirror groups and the surface of worktable. The squareness errors are corrected through modifying local squareness errors measured with double ball bar to global squareness errors, with the aid of straightness errors measured with multi-laser calibrator. Then volumetric errors are obtained based on multi-body system theory, and volumetric diagonal errors are measured with laser interferometer. It is illustrated that the bidirectional systematic deviation of positioning of four volumetric diagonals reduced about 81.3%, 35.2%, 29.2%, and 4.5% respectively by using this improved machine tool volumetric error compensation method, and it is of obvious advantages in contrast with traditional compensation method with direct measurement data. The improved error compensation method proposed in this paper has universal applicability and has great significance on machine tool accuracy improvement.

Error-correcting codes (ECC) are widely used during data transfer in wireless communication systems as well as in computer memory architectures. The error-correcting process is based on sending data with extra parity bits and decoding the received data for error correction. The first error detection and correction code, introduced in 1950, Hamming Code (7,4) is a linear error-correcting code able to detect and correct a single-bit error by encoding 7-bit data from 4-bit data, including 3 parity bits. Previous efforts using unipolar resistive random access memory (ReRAM) based in-memory computation of Hamming Code (7,4) resulted in 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> times lower power consumption compared to GPU and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> times less than CPU-based computations. However further reduction of power consumption can be achieved by vector-matrix multiplication (VMM) using bipolar ReRAM arrays. In the VMM based approach, an encoding or decoding code matrix is stored in the array where it leverages the nonvolatile properties of ReRAM. With the VMM approach, the total number of computation cycles is not limited by the endurance of the ReRAM devices. Here we report the first experimental results of encoding and decoding Hamming code (7,4) using 1 transistor 1 hafnium oxide-based ReRAM (1T1R) arrays fabricated using 65nm CMOS technology. Our results show bipolar 1T1R arrays can correctly encode 4-bit message data to 7 bit encoded data as well as error position detection with overall 3 fold less power consumption than previously reported unipolar ReRAM crossbar array-based computation. Furthermore, we propose and simulate a peripheral circuit to convert the analog column output from a 1T1R array to single-bit binary output using the Cadence Spectre simulator. Our results pave the way for using a memristor-based fast and scalable hardware solution for encoding decoding of error-correcting codes

Error correction in existing point-to-point communication networks is done on a link-by-link basis, which is referred to in this paper as classical error correction. Inspired by network coding, we introduce in this two-part paper a new paradigm called network error correction. The theory thus developed subsumes classical algebraic coding theory as a special case. In Part I, we discuss the basic concepts and prove the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. By studying a few elementary examples, the relation between network error correction and classical error correction is investigated.

Modified Packet Combining (MPC) scheme is an error correction scheme, which can correct double or, higher bit errors. In some earlier work, a scheme known as Packet Reversed Packet Combining (PRPC) scheme that will correct error if occurs at same bit location of erroneous copies, was studied. Both PRPC and MPC scheme are believed to offer higher throughput and better error correction capability at high bit error rate (BER) and large packet size only. Exact analysis was performed to substantiate this claim of higher throughput and better error correction capability in high as well as in low bit error rate (BER) for large and medium packet size. To combat high bit error rate some researches proposed to use Error Correction Code (ECC) in place of Error Detection Code (EDC) in ARQ scheme. But no conclusive result is found to justify the idea in terms of throughput. The current investigation is an attempt to explore the basic gap. In this paper, we investigate the exact analysis of both PRPC and MPC in a Modified way over Conventional PRPC, and report the findings thereof. We propose a combined protocol of Modified PRPC and MPC, and find that it will offer higher throughput and better error correction capability at high and low BER with medium and large packet size as we have used MPC (Modified Packet Combining) scheme with PRPC (Packet Reverse Packet Combining) scheme in a Modified way by combining BEC (Backward Error Correction) with FEC (Forward Error Correction) Codes for Mobile Communication and Networks.

Error detection and correction which has been used in communication and memory design is becoming increasingly important in fault tolerant logic circuit design. As a result of the aggressive technology scaling, the current high-density integrated circuits are easily succumbed to faulty operations generated from many sources including stuck-at-faults, radiation induced faults, or malicious eavesdropper attacks. The currently used techniques like low-density parity-check (LDPC) and Hamming code based fault masking to mitigate bit flips in the digital circuits are either single bit error correcting or multiple error correctable with Bose-Choudhury-Hocquenghem (BCH) and Reed-solomon based methods with very large overheads. This paper introduce a novel cross code based method that can correct multiple errors with minimal compromise in error correction capability and area. The key idea of the novel method proposed in this paper is that do not correct all the errors but minimize their probability being escaped. Experimental results of the proposed methods show that the following: (1) area overhead is 101% for Hamming cross code and 106% for BCH cross code for a 90-bit finite field multiplier and (2) 150% for Hamming cross code and 170% for BCH cross codes for practically used 163-bit digit serial polynomial basis multiplier. Thus, the proposed methods are significantly efficient compared to Triple Modular Redundancy (TMR), LDPC, Hamming based methods in terms of area overhead and also the first attempted approach to a low complexity multiple error correctable digit serial multiplier to the best of the authors knowledge.

In this paper, a linear-prediction maximum power point tracking (MPPT) algorithm for photovoltaic (PV) power generation is presented. This allows rapid tracking without step-size reference. The new methodology has two parts: linear prediction and error correction. The first part estimates the maximum power point (MPP); this improves the MPPT response speed. The second part calibrates the error after the linear prediction; this enhances the calculation accuracy which leads to a faster MPP convergence. Theoretical analysis and simulations are put forward to validate the feasibility of the linear prediction method. Convergence, error correction, and steady and dynamic state evaluations are made. The results show that the algorithm can work effectively and have the advantages of fast response and high efficiency when compared to the Perturbation and Observe (P&O) algorithm.

Error correction coding, channel coding, also known as error control coding, is to add some redundant code elements, or check code elements, to form a correlated sequence of code elements—code words and to use the correlation property between code elements to detect and correct errors when decoding. Different error correction coding schemes have different error detection and correction capabilities. This paper designs a combination of parity check and cyclic redundancy check (CRC) to improve the error detection and correction capabilities with minimum cost, so that the system can transmit information more efficiently while also having high transmission reliability.

Robust codes are codes that can detect any nonzero errore with probability 1 − Q(e) > 0. This property makes them useful in protecting hardware systems from fault injection attacks which cause an arbitrary number of bit flips. This paper presents a new construction of non-linear robust q-ary codes with q = 2m and an error correction capability. The codes are built upon systematic linear codes [n, k, d]q whereas the n − k redundant symbols that were originally allocated to increase the minimum distance of the code are modified to provide both correction capability and robustness. The error masking probability of the codes is Q(e) upper bounded by 2/q for odd values of m and by 4/q for even m. Hence, they are more effective in detecting maliciously injected errors and have a higher code rate than codes obtained by concatenation of a linear error correcting code with a security oriented code.

This thesis summarizes research on the design and implementation of the unequal error protection (UEP) mechanism for the RaptorQ forward error correction (FEC) scheme. As part of this research, existing UEP mechanisms for various fountain codes were evaluated. Two new UEP methods were proposed for the RaptorQ coding scheme, and these methods were designed with the assumption that all of the symbols in a source block have the same priority. The first method, known as priority based overhead number (PBON), was based on the priority encoding transmission model, wherein the error-correction capability was altered by making the number of overhead symbols proportional to the priority of the information symbols. This method was extended to the RaptorQ codes with some changes and evaluated for failure probability and performance. The second method, known as priority based precode ratio (PBPR), was designed by changing the precode properties of the RaptorQ codes. The ratio of precode symbols to Luby-Transform symbols in the RaptorQ codes was changed to achieve different error correction capabilities for each priority group. The scheme with the higher number of precode symbols provided superior error-correction capabilities compared to those with fewer precode symbols. Both methods were empirically verified through simulation in the C++ programming language. The results demonstrated that the higher-importance class depicted a better error-correction capability than the lower-importance class.

We use a terahertz echo pulse as a transfer standard to correct linear time-base errors of a terahertz spectrometer. With this calibration technique, the linear error of the translate stage is corrected and the spectral repeatability of the spectrometer is improved. This calibration technique is able to correct each ‘shot’ of the terahertz pulse and can realize on-line calibration of the terahertz spectrum. The average of multiple measurements of carbon monoxide gas absorption lines was corrected and the deviation was reduced by a factor of 2.5 using this technique. This on-line calibration technique needs no additional optical components and causes no performance degradation of the terahertz spectrometer. It provides a simple and alternative method to the conventional interferometric technique and allows for accurate measurement of spectral properties of specimens in the terahertz region.

Finding the minimum distance of linear codes is in general a NP-hard problem, we propose an efficient algorithm to attack this problem. The principle of this approach is to search code words locally around the all-zero code word perturbed by a level of noise magnitude, in other words the maximum of noise that can be corrected by a Soft-In decoder, anticipating that the resultant nearest non-zero code words will most likely contain the minimum Hamming weight code word, whose Hamming weight is equal to the minimum distance of the linear code. A numerous results prove that the proposed algorithm is valid for general linear codes and it is very fast comparing to all others known techniques, therefore it is a good tool for computing. Comparing to Joanna's works, we proof that our algorithm has a low complexity with a fast time of execution. For some linear RQs, QDCs and BCHs codes with unknown minimum distance, we give a good estimation (true) of the minimum distance where the length is less than 439.

In this paper we relate how Equidistant Constant Weight Codes and Different Combinatorial Structures like Resolvable Balanced Incomplete Block Designs (RBIBD) , Nested Balanced Incomplete Block Designs (NBIBD) and Linear Codes are related with each other and then show how these Combinatorial Structures can be used as 2-Traceable (TA) Code.