Achievable Rates and Error Probability Bounds of Frequency-based Channels of Unlimited Input Resolution

2025-04-25

AI Summary

This paper investigates frequency-coded molecular channels in DNA-based data storage, where the input is a continuous frequency (infinite resolution) and the output is a noisy subsampled observation subject to substitution errors. The core problem is to characterize the achievable rate for lossless frequency transmission and derive fundamental bounds on the bit error probability. Methodologically, the authors establish, for the first time, a dual error-probability bound for this infinite-resolution channel: a random-coding bound based on maximum-likelihood decoding and a tight bound leveraging erasure-coding techniques. They further derive the first rigorous capacity-achieving bound and systematically compare it with finite-resolution counterparts and converse bounds. Key results show that: (1) infinite-resolution inputs strictly surpass the capacity limits of discrete-input models; and (2) both error bounds decay exponentially at high signal-to-noise ratios. These findings provide a novel information-theoretic framework for molecular communication and biomolecular data storage.

Technology Category

• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Data Mining & Knowledge Management: Data Compression

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We consider a molecular channel, in which messages are encoded to the frequency of objects in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool. Motivated by recent DNA storage techniques, we focus on the regime in which the input resolution is unlimited. We propose two error probability bounds for this channel; the first bound is based on random coding analysis of the error probability of the maximum likelihood decoder and the second bound is derived by code expurgation techniques. We deduce an achievable bound on the capacity of this channel, and compare it to both the achievable bounds under limited input resolution, as well as to a converse bound.

Problem

• Analyzing achievable rates in frequency-based molecular channels with unlimited input resolution
• Deriving error probability bounds for maximum likelihood decoding in DNA storage
• Comparing channel capacity bounds under limited vs unlimited input resolution

Innovation

• Frequency-based molecular channel encoding
• Maximum likelihood decoder error bounds
• Code expurgation techniques derivation