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A Polynomial Formula for Finite-Length BATS Code Performance
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DOI：10.1109/LCOMM.2016.2619698.png)
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Abstract
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Batched sparse (BATS) codes have been proposed for communication through networks with packet loss. BATS codes include a matrix generalization of fountain codes as the outer code and random linear network coding at the intermediate network nodes as the inner code. BATS codes, however, do not possess a universal degree distribution that achieves the optimal rate for any distribution of the transfer matrix ranks, so that fast performance evaluation of finite-length BATS codes is important for optimizing the degree distribution. The state-of-the-art finite-length performance evaluation method has a computational complexity of O(K(2)n(2)M), where K, n, and M are the number of input symbols, the number of batches, and the batch size, respectively. We propose a polynomial-form formula for finite-length BATS codes performance evaluation with the computational complexity of O(K(2)n ln n). Numerical results demonstrate that the polynomial-form formula can be significantly faster than the previous methods.
Keywords:
Network coding
BATS code
finite-length analysis
LT code
belief propagation
polynomial form
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