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- W1503869652 abstract "We consider a transmitter broadcasting random linear combinations (over a field of size $d$) formed from a block of $c$ packets to a collection of $n$ receivers, where the channels between the transmitter and each receiver are independent erasure channels with reception probabilities $mathbf{q} = (q_1,ldots,q_n)$. We establish several properties of the random delay until all $n$ receivers have recovered all $c$ packets, denoted $Y_{n:n}^{(c)}$. First, we provide lower and upper bounds, exact expressions, and a recurrence for the moments of $Y_{n:n}^{(c)}$. Second, we study the delay per packet $Y_{n:n}^{(c)}/c$ as a function of $c$, including the asymptotic delay (as $c to infty$), and monotonicity (in $c$) properties of the delay per packet. Third, we employ extreme value theory to investigate $Y_{n:n}^{(c)}$ as a function of $n$ (as $n to infty$). Several results are new, some results are extensions of existing results, and some results are proofs of known results using new (probabilistic) proof techniques." @default.
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- W1503869652 date "2017-03-01" @default.
- W1503869652 modified "2023-09-27" @default.
- W1503869652 title "Delay on Broadcast Erasure Channels Under Random Linear Combinations" @default.
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- W1503869652 doi "https://doi.org/10.1109/tit.2016.2634007" @default.
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