521 research outputs found

    Symbol synchronization in convolutionally coded systems

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    Alternate symbol inversion is sometimes applied to the output of convolutional encoders to guarantee sufficient richness of symbol transition for the receiver symbol synchronizer. A bound is given for the length of the transition-free symbol stream in such systems, and those convolutional codes are characterized in which arbitrarily long transition free runs occur

    Concatenation of convolutional and block codes Final report

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    Comparison of concatenated and sequential decoding systems and convolutional code structural propertie

    Quasi-Cyclic Codes

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    Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some asymptotic results, a few minimum distance bounds and further applications such as the trace representation and characterization of certain subfamilies of quasi-cyclic codes are elaborated. This survey will appear as a chapter in "A Concise Encyclopedia of Coding Theory" to be published by CRC Press.Comment: arXiv admin note: text overlap with arXiv:1906.0496

    On the Minimum Distance of Array-Based Spatially-Coupled Low-Density Parity-Check Codes

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    An array low-density parity-check (LDPC) code is a quasi-cyclic LDPC code specified by two integers qq and mm, where qq is an odd prime and m≀qm \leq q. The exact minimum distance, for small qq and mm, has been calculated, and tight upper bounds on it for m≀7m \leq 7 have been derived. In this work, we study the minimum distance of the spatially-coupled version of these codes. In particular, several tight upper bounds on the optimal minimum distance for coupling length at least two and m=3,4,5m=3,4,5, that are independent of qq and that are valid for all values of q≄q0q \geq q_0 where q0q_0 depends on mm, are presented. Furthermore, we show by exhaustive search that by carefully selecting the edge spreading or unwrapping procedure, the minimum distance (when qq is not very large) can be significantly increased, especially for m=5m=5.Comment: 5 pages. To be presented at the 2015 IEEE International Symposium on Information Theory, June 14-19, 2015, Hong Kon

    Concatenated codes with convolutional inner codes

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