29,828 research outputs found

    New Linear Codes from Matrix-Product Codes with Polynomial Units

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    A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented

    New Linear Codes from Matrix-Product Codes with Polynomial Units

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    A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented

    List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

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    A list decoding algorithm for matrix-product codes is provided when C1,...,CsC_1,..., C_s are nested linear codes and AA is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units

    Quasi-Cyclic Complementary Dual Code

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    LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized. Constructions of QCCD codes from codes over larger alphabets are given

    Deriving Good LDPC Convolutional Codes from LDPC Block Codes

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    Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework. Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this "convolutional gain," and we also discuss the --- mostly moderate --- decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010; revised August 2010, revised November 2010 (essentially final version). (Besides many small changes, the first and second revised versions contain corrected entries in Tables I and II.

    Deterministic Construction of Binary, Bipolar and Ternary Compressed Sensing Matrices

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    In this paper we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar m×nm\times n RIP fulfilling ±1\pm 1 matrices of order kk such that mO(k(log2n)log2klnlog2k)m\leq\mathcal{O}\big(k (\log_2 n)^{\frac{\log_2 k}{\ln \log_2 k}}\big). The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ({0,1,1}\{0,1,-1\} elements) that satisfy the RIP condition.Comment: The paper is accepted for publication in IEEE Transaction on Information Theor
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