Kelly Bets and Single-Letter Codes: Optimal Information Processing in Natural Systems

IF 2.3 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Pub Date : 2025-06-19 DOI:10.1109/TMBMC.2025.3581468

Alexander S. Moffett;Andrew W. Eckford

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引用次数: 0

Abstract

In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this paper, we show that Kelly bets are closely related to optimal single-letter codes (i.e., they can achieve the rate-distortion bound with equality). Thus, natural information processing systems with limited computational resources can achieve information-theoretically optimal performance. We show that the rate-distortion tradeoff for an investment game has a simple linear bound, and that the bound is achievable at the point where the corresponding single-letter code is optimal. This interpretation has two interesting consequences. First, we show that increasing the organism’s portfolio of potential strategies can lead to optimal performance over a continuous range of channels, even if the strategy portfolio is fixed. Second, we show that increasing an organism’s number of phenotypes (i.e., its number of possible behaviours in response to the environment) can lead to higher growth rate, and we give conditions under which this occurs. Examples illustrating the results in simplified biological scenarios are presented.

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凯利投注和单字母代码：自然系统中的最优信息处理

在信息处理投资博弈中，例如在不断变化的环境中生物体种群的增长，凯利投注使预期的对数增长率最大化。在本文中，我们证明了凯利投注与最优单字母码密切相关（即，它们可以实现具有相等的率失真界）。因此，计算资源有限的自然信息处理系统可以实现信息理论的最优性能。我们证明了投资博弈的比率扭曲权衡有一个简单的线性边界，并且在相应的单字母代码最优的点上可以实现该边界。这种解释有两个有趣的结果。首先，我们表明，即使策略组合是固定的，增加有机体的潜在策略组合也可以在连续的渠道范围内获得最佳表现。其次，我们表明增加生物体的表型数量（即其对环境的可能行为的数量）可以导致更高的生长速度，并且我们给出了发生这种情况的条件。举例说明了在简化的生物学情景的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Mathematics-Modeling and Simulation

CiteScore

3.90

自引率

13.60%

发文量

期刊介绍： As a result of recent advances in MEMS/NEMS and systems biology, as well as the emergence of synthetic bacteria and lab/process-on-a-chip techniques, it is now possible to design chemical “circuits”, custom organisms, micro/nanoscale swarms of devices, and a host of other new systems. This success opens up a new frontier for interdisciplinary communications techniques using chemistry, biology, and other principles that have not been considered in the communications literature. The IEEE Transactions on Molecular, Biological, and Multi-Scale Communications (T-MBMSC) is devoted to the principles, design, and analysis of communication systems that use physics beyond classical electromagnetism. This includes molecular, quantum, and other physical, chemical and biological techniques; as well as new communication techniques at small scales or across multiple scales (e.g., nano to micro to macro; note that strictly nanoscale systems, 1-100 nm, are outside the scope of this journal). Original research articles on one or more of the following topics are within scope: mathematical modeling, information/communication and network theoretic analysis, standardization and industrial applications, and analytical or experimental studies on communication processes or networks in biology. Contributions on related topics may also be considered for publication. Contributions from researchers outside the IEEE’s typical audience are encouraged.