777 research outputs found
Quantum stabilizer codes and beyond
The importance of quantum error correction in paving the way to build a
practical quantum computer is no longer in doubt. This dissertation makes a
threefold contribution to the mathematical theory of quantum error-correcting
codes. Firstly, it extends the framework of an important class of quantum codes
-- nonbinary stabilizer codes. It clarifies the connections of stabilizer codes
to classical codes over quadratic extension fields, provides many new
constructions of quantum codes, and develops further the theory of optimal
quantum codes and punctured quantum codes. Secondly, it contributes to the
theory of operator quantum error correcting codes also called as subsystem
codes. These codes are expected to have efficient error recovery schemes than
stabilizer codes. This dissertation develops a framework for study and analysis
of subsystem codes using character theoretic methods. In particular, this work
establishes a close link between subsystem codes and classical codes showing
that the subsystem codes can be constructed from arbitrary classical codes.
Thirdly, it seeks to exploit the knowledge of noise to design efficient quantum
codes and considers more realistic channels than the commonly studied
depolarizing channel. It gives systematic constructions of asymmetric quantum
stabilizer codes that exploit the asymmetry of errors in certain quantum
channels.Comment: Ph.D. Dissertation, Texas A&M University, 200
A Comparison Study of LDPC and BCH Codes
The need for efficient and reliable digital data communication systems has been rising
rapidly in recent years. There are various reasons that have brought this need for the
communication systems, among them are the increase in automatic data processing
equipment and the increased need for long range communication. Therefore, the
LDPC and BCH codes were developed for achieving more reliable data transmission
in communication systems. This project covers the research about the LDPC and
BCH error correction codes. Algorithm for simulating both the LDPC and BCH
codes were also being investigated, which includes generating the parity check
matrix, generating the message code in Galois array matrix, encoding the message
bits, modulation and decoding the message bits for LDPC. Matlab software is used
for encoding and decoding the codes. The percentage of accuracy for LDPC
simulation codes are ranging from 95% to 99%. The results obtained shows that the
LDPC codes are more efficient and reliable than the BCH codes coding method of
error correction because the LDPC codes had a channel performance very close to the
Shannon limit. LDPC codes are a class of linear block codes that are proving to be
the best performing forward error correction available. Markets such as broadband
wireless and mobile networks operate in noisy environments and need powerful error
correction in order to improve reliability and better data rates. Through LDPC and
BCH codes, these systems can operate more reliably, efficiently and at higher data
rates
PERFORMANCE COMPARISON OF NON-INTERLEAVED BCH CODES AND INTERLEAVED BCH CODES
This project covers the research about the BCH error correcting codes and the
performance of interleaved and non-interleaved BCH codes. Both long and short
BCH codes for multimedia communication are examined in an A WGN channel.
Algorithm for simulating the BCH codes was also being investigated, which includes
generating the parity check matrix, generating the message code in Galois array
matrix, encoding the message blocks, modulation and decoding the message blocks.
Algorithm for interleaving that includes interleaving message, including burst errors
and deinterleaving message is combined with the BCH codes algorithm for
simulating the interleaved BCH codes. The performance and feasibility of the coding
structure are tested. The performance comparison between interleaved and noninterleaved
BCH codes is studied in terms of error performance, channel performance
and effect of data rates on the bit error rate (BER). The Berlekamp-Massey Algorithm
decoding scheme was implemented. Random integers are generated and encoded with
BCH encoder. Burst errors are added before the message is interleaved, then enter
modulation and channel simulation. Interleaved message is then compared with noninterleaved
message and the error statistics are compared. Initially, certain amount of
burst errors is used. "ft is found that the graph does not agree with the theoretical bit
error rate (BER) versus signal-to-noise ratio (SNR). When compared between each
BCH codeword (i.e. n = 31, n = 63 and n = 127), n = 31 shows the highest BER while
n = 127 shows the lowest BER. This happened because of the occurrence of error
bursts and also due to error frequency. A reduced size or errors from previous is used
in the algorithm. A graph similar to the theoretical BER vs SNR is obtained for both
interleaved and non-interleaved BCH codes. It is found that BER of non-interleaved
is higher than interleaved BCH codes as SNR increases. These observations show that
size of errors influence the effect of interleaving. Simulation time is also studied in
terms of block length. It is found that interleaved BCH codes consume longer
simulation time compared to non-interleaved BCH codes due to additional algorithm
for the interleaved BCH codes
Algebraic Codes For Error Correction In Digital Communication Systems
Access to the full-text thesis is no longer available at the author's request, due to 3rd party copyright restrictions. Access removed on 29.11.2016 by CS (TIS).Metadata merged with duplicate record (http://hdl.handle.net/10026.1/899) on 20.12.2016 by CS (TIS).C. Shannon presented theoretical conditions under which communication was possible
error-free in the presence of noise. Subsequently the notion of using error
correcting codes to mitigate the effects of noise in digital transmission was introduced
by R. Hamming. Algebraic codes, codes described using powerful tools from
algebra took to the fore early on in the search for good error correcting codes. Many
classes of algebraic codes now exist and are known to have the best properties of
any known classes of codes. An error correcting code can be described by three of its
most important properties length, dimension and minimum distance. Given codes
with the same length and dimension, one with the largest minimum distance will
provide better error correction. As a result the research focuses on finding improved
codes with better minimum distances than any known codes.
Algebraic geometry codes are obtained from curves. They are a culmination of years
of research into algebraic codes and generalise most known algebraic codes. Additionally
they have exceptional distance properties as their lengths become arbitrarily
large. Algebraic geometry codes are studied in great detail with special attention
given to their construction and decoding. The practical performance of these codes
is evaluated and compared with previously known codes in different communication
channels. Furthermore many new codes that have better minimum distance
to the best known codes with the same length and dimension are presented from
a generalised construction of algebraic geometry codes. Goppa codes are also an
important class of algebraic codes. A construction of binary extended Goppa codes
is generalised to codes with nonbinary alphabets and as a result many new codes
are found. This construction is shown as an efficient way to extend another well
known class of algebraic codes, BCH codes. A generic method of shortening codes
whilst increasing the minimum distance is generalised. An analysis of this method
reveals a close relationship with methods of extending codes. Some new codes from
Goppa codes are found by exploiting this relationship. Finally an extension method
for BCH codes is presented and this method is shown be as good as a well known
method of extension in certain cases
A survey of digital television broadcast transmission techniques
This paper is a survey of the transmission techniques used in digital television (TV) standards worldwide. With the increase in the demand for High-Definition (HD) TV, video-on-demand and mobile TV services, there was a real need for more bandwidth-efficient, flawless and crisp video quality, which motivated the migration from analogue to digital broadcasting. In this paper we present a brief history of the development of TV and then we survey the transmission technology used in different digital terrestrial, satellite, cable and mobile TV standards in different parts of the world. First, we present the Digital Video Broadcasting standards developed in Europe for terrestrial (DVB-T/T2), for satellite (DVB-S/S2), for cable (DVB-C) and for hand-held transmission (DVB-H). We then describe the Advanced Television System Committee standards developed in the USA both for terrestrial (ATSC) and for hand-held transmission (ATSC-M/H). We continue by describing the Integrated Services Digital Broadcasting standards developed in Japan for Terrestrial (ISDB-T) and Satellite (ISDB-S) transmission and then present the International System for Digital Television (ISDTV), which was developed in Brazil by adopteding the ISDB-T physical layer architecture. Following the ISDTV, we describe the Digital Terrestrial television Multimedia Broadcast (DTMB) standard developed in China. Finally, as a design example, we highlight the physical layer implementation of the DVB-T2 standar
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