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Analog Error Correction

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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 forward error correction example an unreliable physical channel is termed as channel coding or error correction

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coding (ECC). The profound concept that underpins channel coding is distance expansion. That is, a set of elements error correcting code example in some space having small distances among them are mapped to another set of elements in possibly a different space with larger distances among the elements. Distance expansion in terms http://ieeexplore.ieee.org/iel4/26/15084/00701312.pdf?arnumber=701312 of digital error correction has been a common practice, but the principle is 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 http://gradworks.umi.com/34/56/3456229.html to provide an improved level of distortion tolerance than the original source space. For example, one may treat the combination 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 c

Full PapersApplied Algebra, Algebraic Algorithms and Error-Correcting Codes Volume 357 of the series Lecture Notes in Computer Science pp 239-249 Date: 01 June 2005Multiple error correction http://link.springer.com/content/pdf/10.1007/3-540-51083-4_63.pdf 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 multiple errors (bursts) also if additional background noise error correction 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. Page %P Close Plain text Look Inside Chapter Metrics Provided by Bookmetrix forward error correction 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 Performance”, Int. Symp. on Information Theory, Brighton, England June 24–28, 1985.[8]Cybenko, G., ”The numerical stability of the Levinson-Durbin Algorithm for Toeplitz systems of equations”, SI

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