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In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called ldquoinjection distance,rdquo introduced by Silva and Kschischang. A Gilbert-Varshamov bound for such codes is derived. Using the code-construction framework of Etzion...
Randomized linear network code for single source multicast was introduced and analyzed in Ho et al. (IEEE Transactions on Information Theory, October 2006) where the main results are upper bounds for the failure probability of the code. In this paper, these bounds are improved and tightness of the new bounds is studied by analyzing the limiting behavior of the failure probability as the field size...
This paper applies the sigma mapping of M-QAM in linear diversity-embedded space-time block codes (LDE-STBC) to achieve different diversity levels and various coding gains for unequal error protection (UEP). By controlling the basis vectors of sigma mapping, the bit error rate (BER) performance of each bit in a layer can be made to satisfy its quality-of-service (QoS) requirement. Moreover, with the...
In this paper, we study the error correction and detection capabilities of block codes for a general transmission system inspired by network error correction. For a given weight measure on the error vectors, we define a corresponding minimum weight decoder. Then we obtain a complete characterization of the capabilities of a block code for error correction and error detection. Our results imply that...
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