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• W2073060063 abstract "We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, s <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> - t <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> and s <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> - t <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> . Current characterizations of the multiple unicast capacity region in this setting have a large number of inequalities, which makes them hard to explicitly evaluate. In this work we consider a slightly different problem. We assume that we only know certain minimum cut values for the network, e.g., mincut(S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> , T <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>j</sub> ), where S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> ⊆ {si, s <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> } and T <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>j</sub> ⊆ {t <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> , t <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> } for different subsets S <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> and T <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>j</sub> . Based on these values, we propose an achievable rate region for this problem based on linear codes. Towards this end, we begin by defining a base region where both sources are multicast to both the terminals. Following this we enlarge the region by appropriately encoding the information at the source nodes, such that terminal t <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> is only guaranteed to decode information from the intended source s <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> , while decoding a linear function of the other source. The rate region takes different forms depending upon the relationship of the different cut values in the network." @default.
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• W2073060063 date "2011-10-01" @default.
• W2073060063 modified "2023-10-16" @default.
• W2073060063 title "An achievable region for the double unicast problem based on a minimum cut analysis" @default.
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• W2073060063 doi "https://doi.org/10.1109/itw.2011.6089359" @default.
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