Avoiding Flow Size Overestimation in the Count-Min Sketch with Bloom Filter Constructions

The Count-Min sketch is the most popular data structure for flow size estimation, a basic measurement task required in many networks. Typically the number of potential flows is large, eliminating the possibility to maintain a counter per flow within memory of high access rate. The Count-Min sketch is probabilistic and relies on mapping each flow to multiple counters through hashing. This implies potential estimation error such that the size of a flow is overestimated when all flow counters are shared with other flows with observed traffic. Although the error in the estimation can be probabilistically bounded, many applications can benefit from accurate flow size estimation and the guarantee to completely avoid overestimation. We describe a design of the Count-Min sketch with accurate estimations whenever the number of flows with observed traffic follows a known bound, regardless of the identity of these particular flows. We make use of a concept of Bloom filters that avoid false positives and indicate the limitations of existing Bloom filter designs towards accurate size estimation. We suggest new Bloom filter constructions that allow scalability with the support for a larger number of flows and explain how these can imply the unique guarantee of accurate flow size estimation in the well known Count-Min sketch.Ori Rottenstreich was partially supported by the German-Israeli Foundation for Scientic Research and Development (GIF), by the Gordon Fund for System Engineering as well as by the Technion Hiroshi Fujiwara Cyber Security Research Center and the Israel National Cyber Directorate. Pedro Reviriego would like to acknowledge the sup-port of the ACHILLES project PID2019-104207RB-I00 and the Go2Edge network RED2018-102585-T funded by the Spanish Ministry of Science and Innovation and of the Madrid Community research project TAPIR-CM grant no. P2018/TCS-4496

Ultrafast Codes for Multiple Adjacent Error Correction and Double Error Detection

(c) 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.[EN] Reliable computer systems employ error control codes (ECCs) to protect information from errors. For example, memories are frequently protected using single error correction-double error detection (SEC-DED) codes. ECCs are traditionally designed to minimize the number of redundant bits, as they are added to each word in the whole memory. Nevertheless, using an ECC introduces encoding and decoding latencies, silicon area usage and power consumption. In other computer units, these parameters should be optimized, and redundancy would be less important. For example, protecting registers against errors remains a major concern for deep sub-micron systems due to technology scaling. In this case, an important requirement for register protection is to keep encoding and decoding latencies as short as possible. Ultrafast error control codes achieve very low delays, independently of the word length, increasing the redundancy. This paper summarizes previous works on Ultrafast codes (SEC and SEC-DED), and proposes new codes combining double error detection and adjacent error correction. We have implemented, synthesized and compared different Ultrafast codes with other state-of-the-art fast codes. The results show the validity of the approach, achieving low latencies and a good balance with silicon area and power consumption.This work was supported in part by the Spanish Government under Project TIN2016-81075-R, and in part by the Primeros Proyectos de Investigacion, Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia (UPV), Valencia, Spain, under Project PAID-06-18 20190032.Saiz-Adalid, L.; Gracia-Morán, J.; Gil Tomás, DA.; Baraza Calvo, JC.; Gil, P. (2019). Ultrafast Codes for Multiple Adjacent Error Correction and Double Error Detection. IEEE Access. 7:151131-151143. https://doi.org/10.1109/ACCESS.2019.2947315S151131151143

2D Parity Product Code for TSV online fault correction and detection

Through-Silicon-Via (TSV) is one of the most promising technologies to realize 3D Integrated Circuits (3D-ICs).  However, the reliability issues due to the low yield rates and the sensitivity to thermal hotspots and stress issues are preventing TSV-based 3D-ICs from being widely and efficiently used. To enhance the reliability of TSV connections, using error correction code to detect and correct faults automatically has been demonstrated as a viable solution.This paper presents a 2D Parity Product Code (2D-PPC) for TSV fault-tolerance with the ability to correct one fault and detect, at least, two faults.  In an implementation of 64-bit data and 81-bit codeword, 2D-PPC can detect over 71 faults, on average. Its encoder and decoder decrease the overall latency by 38.33% when compared to the Single Error Correction Double Error Detection code.  In addition to the high detection rates, the encoder can detect 100% of its gate failures, and the decoder can detect and correct around 40% of its individual gate failures. The squared 2D-PPC could be extended using orthogonal Latin square to support extra bit correction

Error control coding for semiconductor memories

All modern computers have memories built from VLSI RAM chips. Individually, these devices are highly reliable and any single chip may perform for decades before failing. However, when many of the chips are combined in a single memory, the time that at least one of them fails could decrease to mere few hours. The presence of the failed chips causes errors when binary data are stored in and read out from the memory. As a consequence the reliability of the computer memories degrade. These errors are classified into hard errors and soft errors. These can also be termed as permanent and temporary errors respectively. In some situations errors may show up as random errors, in which both 1-to-O errors and 0-to-l errors occur randomly in a memory word. In other situations the most likely errors are unidirectional errors in which 1-to-O errors or 0-to-l errors may occur but not both of them in one particular memory word. To achieve a high speed and highly reliable computer, we need large capacity memory. Unfortunately, with high density of semiconductor cells in memory, the error rate increases dramatically. Especially, the VLSI RAMs suffer from soft errors caused by alpha-particle radiation. Thus the reliability of computer could become unacceptable without error reducing schemes. In practice several schemes to reduce the effects of the memory errors were commonly used. But most of them are valid only for hard errors. As an efficient and economical method, error control coding can be used to overcome both hard and soft errors. Therefore it is becoming a widely used scheme in computer industry today. In this thesis, we discuss error control coding for semiconductor memories. The thesis consists of six chapters. Chapter one is an introduction to error detecting and correcting coding for computer memories. Firstly, semiconductor memories and their problems are discussed. Then some schemes for error reduction in computer memories are given and the advantages of using error control coding over other schemes are presented. In chapter two, after a brief review of memory organizations, memory cells and their physical constructions and principle of storing data are described. Then we analyze mechanisms of various errors occurring in semiconductor memories so that, for different errors different coding schemes could be selected. Chapter three is devoted to the fundamental coding theory. In this chapter background on encoding and decoding algorithms are presented. In chapter four, random error control codes are discussed. Among them error detecting codes, single* error correcting/double error detecting codes and multiple error correcting codes are analyzed. By using examples, the decoding implementations for parity codes, Hamming codes, modified Hamming codes and majority logic codes are demonstrated. Also in this chapter it was shown that by combining error control coding and other schemes, the reliability of the memory can be improved by many orders. For unidirectional errors, we introduced unordered codes in chapter five. Two types of the unordered codes are discussed. They are systematic and nonsystematic unordered codes. Both of them are very powerful for unidirectional error detection. As an example of optimal nonsystematic unordered code, an efficient balanced code are analyzed. Then as an example of systematic unordered codes Berger codes are analyzed. Considering the fact that in practice random errors still may occur in unidirectional error memories, some recently developed t-random error correcting/all unidirectional error detecting codes are introduced. Illustrative examples are also included to facilitate the explanation. Chapter six is the conclusions of the thesis. The whole thesis is oriented to the applications of error control coding for semiconductor memories. Most of the codes discussed in the thesis are widely used in practice. Through the thesis we attempt to provide a review of coding in computer memories and emphasize the advantage of coding. It is obvious that with the requirement of higher speed and higher capacity semiconductor memories, error control coding will play even more important role in the future

Codes for Limited Magnitude Error Correction in Multilevel Cell Memories

Multilevel cell (MLC) memories have been advocated for increasing density at low cost in next generation memories. However, the feature of several bits in a cell reduces the distance between levels; this reduced margin makes such memories more vulnerable to defective phenomena and parameter variations, leading to an error in stored data. These errors typically are of limited magnitude, because the induced change causes the stored value to exceed only a few of the level boundaries. To protect these memories from such errors and ensure that the stored data is not corrupted, Error Correction Codes (ECCs) are commonly used. However, most existing codes have been designed to protect memories in which each cell stores a bit and thus, they are not efficient to protect MLC memories. In this paper, an efficient scheme that can correct up to magnitude-3 errors is presented and evaluated. The scheme is based by combining ECCs that are commonly used to protect traditional memories. In particular, Interleaved Parity (IP) bits and Single Error Correction and Double Adjacent Error Correction (SEC-DAEC) codes are utilized; both these codes are combined in the proposed IP-DAEC scheme to efficiently provide a strong coding function for correction, thus exceeding the capabilities of most existing coding schemes for limited magnitude errors. The SEC-DAEC code is used to detect the cell in error and correct some bits, while the IP bits identify the remaining erroneous bits in the memory cell. The use of these simple codes results in an efficient implementation of the decoder compared to existing techniques as shown by the evaluation results presented in this paper. The proposed scheme is also competitive in terms of number of parity check bits and memory redundancy. Therefore, the proposed IP-DAEC scheme is a very efficient alternative to protect and correct MLC memories from limited magnitude errors.Pedro Reviriego was partially supported by the TEXEO project (TEC2016-80339-R) funded by the Spanish Research Plan and by the Madrid Community research project TAPIR-CM grant no. P2018/TCS-4496

Fixed-latency system for high-speed serial transmission between FPGA devices with Forward Error Correction

This paper presents the design of a compact pro-tocol for fixed-latency, high-speed, reliable, serial transmissionbetween simple field-programmable gate arrays (FPGA) devices.Implementation of the project aims to delineate word boundaries,provide randomness to the electromagnetic interference (EMI)generated by the electrical transitions, allow for clock recov-ery and maintain direct current (DC) balance. An orthogonalconcatenated coding scheme is used for correcting transmissionerrors using modified Bose–Chaudhuri–Hocquenghem (BCH)code capable of correcting all single bit errors and most ofthe double-adjacent errors. As a result all burst errors of alength up to 31 bits, and some of the longer group errors,are corrected within 256 bits long packet. The efficiency of theproposed solution equals 46.48%, as 119 out of 256 bits arefully available to the user. The design has been implementedand tested on Xilinx Kintex UltraScale+ KCU116 Evaluation Kitwith a data rate of 28.2 Gbps. Sample latency analysis has alsobeen performed so that user could easily carry out calculationsfor different transmission speed. The main advancement of thework is the use of modified BCH(15, 11) code that leads to higherror correction capabilities for burst errors and user friendlypacket length

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder

Modifying Hamming code and using the replication method to protect memory against triple soft errors

As technology scaling increases computer memory’s bit-cell density and reduces the voltage of semiconductors, the number of soft errors due to radiation induced single event upsets (SEU) and multi-bit upsets (MBU) also increases. To address this, error-correcting codes (ECC) can be used to detect and correct soft errors, while x-modular-redundancy improves fault tolerance. This paper presents a technique that provides high error-correction performance, high speed, and low complexity. The proposed technique ensures that only correct values get passed to the system output or are processed in spite of the presence of up to three-bit errors. The Hamming code is modified in order to provide a high probability of MBU detection. In addition, the paper describes the new technique and associated analysis scheme for its implementation. The new technique has been simulated, evaluated, and compared to error correction codes with similar decoding complexity to better understand the overheads required, the gained capabilities to protect data against three-bit errors, and to reduce the misdetection probability and false-detection probability of four-bit errors