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Unidirectional error correcting/detecting codes
An extensive theory of symmetric error control coding has been developed in the last few decades. The recently developed VLSI circuits, ROM, and RAM memories have given an impetus to the extension of error control coding to include asymmetric and unidirectional types of error control. The maximal numbers of unidirectional errors which can be detected by systematic codes using r checkbits are investigated. They are found for codes with k, the number of information bits, being equal to 2[superscript r] and 2[superscript r] + 1. The importance of their characteristic in unidirectional error detection is discussed. A new method of constructing a systematic t-error correcting/all-unidirectional error detecting(t-EC/AUED) code, which uses fewer checkbits than any of the previous methods, is developed. It is constructed by appending t + 1 check symbols to a systematic t-error correcting and (t+l)-error detecting code. Its decoding algorithm is developed. A bound on the number of checkbits for a systematic t-EC/AUED code is also discussed. Bose-Rao codes, which are the best known single error correcting/all-unidirectional error detecting(SEC/AUED) codes, are completely analyzed. The maximal Bose-Rao codes for a fixed weight and for all weights are found. Of course, the base group and the group element which make the Bose-Rao code maximal are found, too. The bounds on the size of SEC/AUED codes are discussed. Nonsystematic single error correcting/d-unidirectional error detecting codes are constructed. Three methods for constructing the systematic t-error correcting/d-unidirectional error detecting(t-EC/d-UED) codes are developed. From these, simple and efficient t-EC/(t+2)-UED codes are derived. The decoding algorithm for one of these methods, which can be applied to the other two methods with slight modification, is described. A lower bound on the number of checkbits for a systematic t-EC/d-UED code is derived. Finally, future research efforts are proposed
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
On q-ary codes correcting all unidirectional errors of a limited magnitude
We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of
unidirectional errors of level l. That is, the transmission channel is such
that the received word cannot contain both a component larger than the
transmitted one and a component smaller than the transmitted one. Moreover, the
absolute value of the difference between a transmitted component and its
received version is at most l.
We introduce and study q-ary codes capable of correcting all unidirectional
errors of level l. Lower and upper bounds for the maximal size of those codes
are presented.
We also study codes for this aim that are defined by a single equation on the
codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting
binary asymmetric errors). We finally consider the problem of detecting all
unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian
Academy of Sciences, special issue dedicated to Rom Varshamo
Unordered Error-Correcting Codes and their Applications
We give efficient constructions for error correcting
unordered {ECU) codes, i.e., codes such that any
pair of codewords are at a certain minimal distance
apart and at the same time they are unordered. These
codes are used for detecting a predetermined number
of (symmetric) errors and for detecting all unidirectional
errors. We also give an application in parallel
asynchronous communications
RFID Key Establishment Against Active Adversaries
We present a method to strengthen a very low cost solution for key agreement
with a RFID device.
Starting from a work which exploits the inherent noise on the communication
link to establish a key by public discussion, we show how to protect this
agreement against active adversaries. For that purpose, we unravel integrity
-codes suggested by Cagalj et al.
No preliminary key distribution is required.Comment: This work was presented at the First IEEE Workshop on Information
Forensics and Security (WIFS'09) (update including minor remarks and
references to match the presented version
A coding approach for detection of tampering in write-once optical disks
We present coding methods for protecting against tampering of write-once optical disks, which turns them into a secure digital medium for applications where critical information must be stored in a way that prevents or allows detection of an attempt at falsification. Our method involves adding a small amount of redundancy to a modulated sector of data. This extra redundancy is not used for normal operation, but can be used for determining, say, as a testimony in court, that a disk has not been tampered with
Acoustic Integrity Codes: Secure Device Pairing Using Short-Range Acoustic Communication
Secure Device Pairing (SDP) relies on an out-of-band channel to authenticate
devices. This requires a common hardware interface, which limits the use of
existing SDP systems. We propose to use short-range acoustic communication for
the initial pairing. Audio hardware is commonly available on existing
off-the-shelf devices and can be accessed from user space without requiring
firmware or hardware modifications. We improve upon previous approaches by
designing Acoustic Integrity Codes (AICs): a modulation scheme that provides
message authentication on the acoustic physical layer. We analyze their
security and demonstrate that we can defend against signal cancellation attacks
by designing signals with low autocorrelation. Our system can detect
overshadowing attacks using a ternary decision function with a threshold. In
our evaluation of this SDP scheme's security and robustness, we achieve a bit
error ratio below 0.1% for a net bit rate of 100 bps with a signal-to-noise
ratio (SNR) of 14 dB. Using our open-source proof-of-concept implementation on
Android smartphones, we demonstrate pairing between different smartphone
models.Comment: 11 pages, 11 figures. Published at ACM WiSec 2020 (13th ACM
Conference on Security and Privacy in Wireless and Mobile Networks). Updated
reference
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