Vector Flows That Compute the Capacity of Discrete Memoryless Channels
One of the fundamental problems of information theory, since its foundation by C. Shannon, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In this paper, we investigate the properti...
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MDPI AG
2025-03-01
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| author | Guglielmo Beretta Marcello Pelillo |
| author_facet | Guglielmo Beretta Marcello Pelillo |
| author_sort | Guglielmo Beretta |
| collection | DOAJ |
| description | One of the fundamental problems of information theory, since its foundation by C. Shannon, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In this paper, we investigate the properties of a novel approach to computing the capacity, based on a continuous-time dynamical system. Interestingly, the proposed dynamical system can be regarded as a continuous-time version of the classical Blahut–Arimoto algorithm, and we can prove that the former shares with the latter an exponential rate of convergence if certain conditions are met. Moreover, a circuit design is presented to implement the dynamics, hence enabling analog computation to estimate the capacity. |
| format | Article |
| id | doaj-art-9a7c402fc06b49018eff35f12b80ddf9 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-9a7c402fc06b49018eff35f12b80ddf92025-08-20T03:13:51ZengMDPI AGEntropy1099-43002025-03-0127436210.3390/e27040362Vector Flows That Compute the Capacity of Discrete Memoryless ChannelsGuglielmo Beretta0Marcello Pelillo1DAIS, Università Ca’ Foscari di Venezia, Via Torino 155, 30170 Venezia, ItalyDAIS, Università Ca’ Foscari di Venezia, Via Torino 155, 30170 Venezia, ItalyOne of the fundamental problems of information theory, since its foundation by C. Shannon, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In this paper, we investigate the properties of a novel approach to computing the capacity, based on a continuous-time dynamical system. Interestingly, the proposed dynamical system can be regarded as a continuous-time version of the classical Blahut–Arimoto algorithm, and we can prove that the former shares with the latter an exponential rate of convergence if certain conditions are met. Moreover, a circuit design is presented to implement the dynamics, hence enabling analog computation to estimate the capacity.https://www.mdpi.com/1099-4300/27/4/362analog computationcapacityconvex optimizationdiscrete memoryless channeldynamical systemsmutual information |
| spellingShingle | Guglielmo Beretta Marcello Pelillo Vector Flows That Compute the Capacity of Discrete Memoryless Channels Entropy analog computation capacity convex optimization discrete memoryless channel dynamical systems mutual information |
| title | Vector Flows That Compute the Capacity of Discrete Memoryless Channels |
| title_full | Vector Flows That Compute the Capacity of Discrete Memoryless Channels |
| title_fullStr | Vector Flows That Compute the Capacity of Discrete Memoryless Channels |
| title_full_unstemmed | Vector Flows That Compute the Capacity of Discrete Memoryless Channels |
| title_short | Vector Flows That Compute the Capacity of Discrete Memoryless Channels |
| title_sort | vector flows that compute the capacity of discrete memoryless channels |
| topic | analog computation capacity convex optimization discrete memoryless channel dynamical systems mutual information |
| url | https://www.mdpi.com/1099-4300/27/4/362 |
| work_keys_str_mv | AT guglielmoberetta vectorflowsthatcomputethecapacityofdiscretememorylesschannels AT marcellopelillo vectorflowsthatcomputethecapacityofdiscretememorylesschannels |