Analog Error Correction Code
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Error Correction Code Definition
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181 pages; 3456229 Abstract: Practical communication channels are inevitably subject to noise uncertainty, interference, and/or other channel impairments. The essential technology to enable a reliable communication over an unreliable physical channel is termed as
Error Correction Code Algorithm
channel coding or error correction coding (ECC). The profound concept that underpins channel error correction code in string theory coding is distance expansion. That is, a set of elements in some space having small distances among them are mapped error correcting code found in string theory to another set of elements in possibly a different space with larger distances among the elements. Distance expansion in terms of digital error correction has been a common practice, but the principle is http://ieeexplore.ieee.org/iel4/26/15084/00701312.pdf?arnumber=701312 by no means limited to the discrete domain. In a broader context, a channel code may be mapping elements in an analog source space to elements in an analog code space. As long as a similar distance expansion condition is satisfied, the code space is expected to provide an improved level of distortion tolerance than the original source space. For example, one may treat the combination http://gradworks.umi.com/34/56/3456229.html of quantization, digital coding and modulation as a single nonlinear analog code that maps real-valued sources to complex-valued coded symbols. Such a concept, thereafter referred to as analog error correction coding (AECC), analog channel coding, or, simply, analog coding, presents a generalization to digital error correction coding (DECC). This dissertation investigates several intriguing aspects of DECC and especially of AECC. The research of DECC focuses on turbo codes and low-density-parity-check (LDPC) codes, two of the best performing codes known to date. In the topic of turbo codes, this dissertation studies on interleaver design, which plays an important role in the overall performance of turbo codes (at small to medium code lengths) but does not affect the decoding architecture. Before this work, the theoretical foundation of interleaver design and evaluation were rather incomplete, e.g. efficient approaches in measuring “randomness” (one of the most important characteristics for interleavers) were rigorously established. This work proposes two powerful metrics, cycle correlation sum (CCS) and variance of the second order spread spectrum (VSSS), to quantify spread and randomness, two fundamental properties of interleavers, while accounting for the iterative nature of turbo decoding and the weight spectrum of turbo encoding. We evaluat
Full PapersApplied Algebra, Algebraic Algorithms and Error-Correcting Codes Volume 357 of the series Lecture Notes in Computer Science pp 239-249 Date: 01 http://link.springer.com/content/pdf/10.1007/3-540-51083-4_63.pdf June 2005Multiple error correction with Analog CodesWerner HenkelAffiliated withInstitut für Netzwerk- und Signaltheorie, Technische Hochschule Darmstadt Buy this eBook * Final gross prices may vary according to local VAT. Get Access Abstract After pointing out the expected advantages of complex coding compared to usual RS- or BCH-codes over finite fields, it has been shown that ”Analog Codes” are able to correct error correction multiple errors (bursts) also if additional background noise is superimposed. Simulations made obvious that the amplitude of the noise has to be of considerably lower amplitude than the ‘bursts’ to be corrected. Furthermore, it has been stated that intermediate solutions during execution of the recursive Berlekamp-Massey-Algorithm are not meaningless but represent a measure for the conditioning of the corresponding sub-Toeplitz system. error correction code Page %P Close Plain text Look Inside Chapter Metrics Provided by Bookmetrix Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions About this Book Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Supplementary Material (0) References (8) References[1]Wolf, J.K., ”Redundancy, the Discrete Fourier Transform, and Impulse Noise Cancellation”, IEEE Trans. on Comm., vol. COM-31, No. 3, pp. 458–461, March 1983.[2]Wolf, J.K., ”Analog Codes”, IEEE Int. Conf. on Comm. (ICC '83), Boston, MA, USA, 19–22 June 1983, pp. 310–312 vol. 1.[3]Hildebrandt, F.B., Introduction to numercal analysis, McGraw-Hill, New York, Toronto, London, 1956.[4]Golub, G.H., van Loan, C.F., Matrix Computations, North Oxford Academic Publishing, Oxford, 1983[5]Massey, J.L., ”Shift-Register Synthesis and BCH Decoding”, IEEE Trans. on Inf. Theory, vol. IT-15, No. 1, pp. 122–127, January 1969.[6]Marshall, T.G., ”Real number transform and convolutional codes”, in Proc. 24th Midwest Symp. Circuits Syst., S. Karne, Ed., Albuquerque, NM, June 29–30, 1981.[7]Maekawa, Y., Sakaniwa, K., “An Extension of DFT Code and the Evaluation of its Pe