Error Correction Dsp
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Request full-text Coding of Real-Number Sequences for Error Correction: A Digital Signal Processing ProblemArticle in IEEE Journal on Selected Areas in Communications 2(2):381 - 392 · April 1984 with 38 https://www.researchgate.net/publication/3234895_Coding_of_Real-Number_Sequences_for_Error_Correction_A_Digital_Signal_Processing_Problem ReadsDOI: 10.1109/JSAC.1984.1146063 · Source: IEEE Xplore1st T. Marshall JrAbstractError-correcting codes defined over the real-number and complex-number fields are introduced. The possibility of utilizing realnumber arithmetic permits the codes to be implemented with operations normally available in standard programmable digital signal processors by methods which are discussed. Hadamard and discrete Fourier transform codes are presented for block coding, and the error correction latter are seen to be cyclic and to include the class of BCH codes. It is shown that maximum distance separable real-number BCH ( N, K ) codes exist for all nontrivial values of N and K . A large class of block and convolutional real-number single-error-correcting codes, derived from similar codes over GF(p) , are presented. Both error correction dsp block and convolutional codes are seen to be describable by the z -transform in a manner which emphasizes their similarities to conventional digital signal processing structures such as digital filters and digital filter banks. Methods for correcting weight t and t + 1 errors in a t error-correcting code are demonstrated and interpreted; in particular, the use of a VLSI digital signal processor for implementation of an algorithm for correcting almost all double adjacent error patterns in a single-error-correcting convolutional code is discussed.Do you want to read the rest of this article?Request full-text CitationsCitations129ReferencesReferences12What is odd about binary Parseval frames?"Indeed, the correspondence between vectors in Hilbert spaces and linear functionals given by the Riesz representation theorem provides a convenient way to characterize Parseval frames, sequences of vectors that behave in a way that is similar to orthonormal bases without requiring the vectors to be linearly independent [6]. Incorporating linear dependence relations is useful to permit more flexibility for expansions and to suppress errors that may model faulty signal transmissions in applications [20] [21] [1