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We introduce a family of sparse random linear network codes with outer-code. Due to the bold role of the incomplete gamma function in their design, we call these codes “Gamma codes”. We show that Gamma codes outperform all the existing linear-complexity network coding solutions in terms of reception overhead, while keeping the encoding and decoding complexity linear in the block length.
Based on a new vision of the inactivation decoding process, we set a new degree distribution design criterion for the LT part of Raptor codes. Under an infinite block length assumption, a family of degree distributions that satisfy the new design criterion is analytically derived. The finite length performance of this family is investigated by using computer simulations and is shown to outperform...
In this paper, an extension of raptor codes is introduced which keeps all the desirable properties of raptor codes, including the linear complexity of encoding and decoding per information bit, unchanged. The new design, however, improves the performance in terms of the reception rate. Our simulations show a 10% reduction in the needed overhead at the benchmark block length of 64,520 bits and with...
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