Two Classes of Optimal Multi-Input Structures for Node Computations in Message Passing Algorithms
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916320384122880 |
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| author | Lu, Teng He, Xuan Tang, Xiaohu |
| author_facet | Lu, Teng He, Xuan Tang, Xiaohu |
| contents | In this paper, we delve into the computations performed at a node within a message-passing algorithm. We investigate low complexity/latency multi-input structures that can be adopted by the node for computing outgoing messages y = (y1, y2, . . . , yn) from incoming messages x = (x1, x2, . . . , xn), where each yj , j = 1, 2, . . . , n is computed via a multi-way tree with leaves x excluding xj . Specifically, we propose two classes of structures for different scenarios. For the scenario where complexity has a higher priority than latency, the star-tree-based structures are proposed. The complexity-optimal ones (as well as their lowest latency) of such structures are obtained, which have the near-lowest (and sometimes the lowest) complexity among all structures. For the scenario where latency has a higher priority than complexity, the isomorphic-directed-rooted-tree-based structures are proposed. The latency-optimal ones (as well as their lowest complexity) of such structures are obtained, which are proved to have the lowest latency among all structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two Classes of Optimal Multi-Input Structures for Node Computations in Message Passing Algorithms Lu, Teng He, Xuan Tang, Xiaohu Information Theory In this paper, we delve into the computations performed at a node within a message-passing algorithm. We investigate low complexity/latency multi-input structures that can be adopted by the node for computing outgoing messages y = (y1, y2, . . . , yn) from incoming messages x = (x1, x2, . . . , xn), where each yj , j = 1, 2, . . . , n is computed via a multi-way tree with leaves x excluding xj . Specifically, we propose two classes of structures for different scenarios. For the scenario where complexity has a higher priority than latency, the star-tree-based structures are proposed. The complexity-optimal ones (as well as their lowest latency) of such structures are obtained, which have the near-lowest (and sometimes the lowest) complexity among all structures. For the scenario where latency has a higher priority than complexity, the isomorphic-directed-rooted-tree-based structures are proposed. The latency-optimal ones (as well as their lowest complexity) of such structures are obtained, which are proved to have the lowest latency among all structures. |
| title | Two Classes of Optimal Multi-Input Structures for Node Computations in Message Passing Algorithms |
| topic | Information Theory |
| url | https://arxiv.org/abs/2407.08941 |