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

Reliable Physical Layer Network Coding

When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the IEE

Single photon continuous variable quantum key distribution based on energy-time uncertainty relation

In previous quantum key distribution (QKD) protocols, information is encoded on either the discrete-variable of single-photon signal or continuous-variables of multi-photon signal. Here, we propose a new QKD protocol by encoding information on continuous-variables of a single photon. In this protocol, Alice randomly encodes her information on either the central frequency of a narrow-band single photon pulse or the time-delay of a broadband single photon pulse, while Bob randomly chooses to do either frequency measurement or time measurement. The security of this protocol rests on the energy-time uncertainty relation, which prevents Eve from simultaneously determining both frequency and time information with arbitrarily high resolution. In practice, this scheme may be more robust against various channel noises, such as polarization and phase fluctuations.Comment: 4 pages, 3 figure