168 research outputs found
Developing Efficient Algorithms of Decoding the Systematic Quadratic Residue Code with Lookup Tables
The lookup table methods for decoding binary systematic Quadratic Residue (QR) code are
presented in this paper. The key ideas behind this decoding technique are based on one to one corresponding
mapping between the syndromes and the correctable error patterns. Such algorithms determine the error locations
directly by lookup tables without the operations of addition and multiplication over a finite field. Moreover, the
methods to dramatically reduce the memory requirement by shift-search decoding are utilized. Two new algorithm
have been verified through a software simulation in C language. The new approach is modular, regular and naturally
suitable for System on Chip (SOC) software implementation
An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes
In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM).
In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders
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
Asymmetric Encryption for Wiretap Channels
Since the definition of the wiretap channel by Wyner in 1975, there has been much
research to investigate the communication security of this channel. This thesis presents
some further investigations into the wiretap channel which improve the reliability of
the communication security. The main results include the construction of best known
equivocation codes which leads to an increase in the ambiguity of the wiretap channel
by using different techniques based on syndrome coding.
Best known codes (BKC) have been investigated, and two new design models which
includes an inner code and outer code have been implemented. It is shown that best
results are obtained when the outer code employs a syndrome coding scheme based on
the (23; 12; 7) binary Golay code and the inner code employs the McEliece cryptosystem
technique based on BKC0s.
Three techniques of construction of best known equivocation codes (BEqC) for syndrome
coding scheme are presented. Firstly, a code design technique to produce new (BEqC)
codes which have better secrecy than the best error correcting codes is presented. Code
examples (some 50 codes) are given for the case where the number of parity bits of the
code is equal to 15. Secondly, a new code design technique is presented, which is based
on the production of a new (BEqC) by adding two best columns to the parity check
matrix(H) of a good (BEqC), [n; k] code.
The highest minimum Hamming distance of a linear code is an important parameter
which indicates the capability of detecting and correcting errors by the code. In general,
(BEqC) have a respectable minimum Hamming distance, but are sometimes not as good
as the best known codes with the same code parameters. This interesting point led to
the production of a new code design technique which produces a (BEqC) code with the
highest minimum Hamming distance for syndrome coding which has better secrecy than
the corresponding (BKC). As many as 207 new best known equivocation codes which
have the highest minimum distance have been found so far using this design technique.Ministry of Higher Education and Scientific Research, Kurdistan Regional Government, Erbil-Ira
The Telecommunications and Data Acquisition Report
Deep Space Network (DSN) progress in flight project support, tracking and data acquisition research and technology, network engineering, hardware and software implementation, and operation is discussed. In addition, developments in Earth-based radio technology as applied to geodynamics, astrophysics and the radio search for extraterrestrial intelligence are reported
The Telecommunications and Data Acquisition Report
This quarterly publication provides archival reports on developments in programs managed by JPL's Telecommunications and Mission Operations Directorate (TMOD), which now includes the former Telecommunications and Data Acquisition (TDA) Office. In space communications, radio navigation, radio science, and ground-based radio and radar astronomy, it reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standards activity at JPL for space data and information systems and reimbursable DSN work performed for other space agencies through NASA. The preceding work is all performed for NASA's Office of Space Communications (OSC). TMOD also performs work funded by other NASA program offices through and with the cooperation of OSC. The first of these is the Orbital Debris Radar Program funded by the Office of Space Systems Development. It exists at Goldstone only and makes use of the planetary radar capability when the antennas are configured as science instruments making direct observations of the planets, their satellites, and asteroids of our solar system. The Office of Space Sciences funds the data reduction and science analyses of data obtained by the Goldstone Solar System Radar. The antennas at all three complexes are also configured for radio astronomy research and, as such, conduct experiments funded by the National Science Foundation in the U.S. and other agencies at the overseas complexes. These experiments are either in microwave spectroscopy or very long baseline interferometry. Finally, tasks funded under the JPL Director's Discretionary Fund and the Caltech President's Fund that involve TMOD are included. This and each succeeding issue of 'The Telecommunications and Data Acquisition Progress Report' will present material in some, but not necessarily all, of the aforementioned programs
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