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The number of degrees of freedom (NDoF) in a communication channel fundamentally limits the number of independent spatial modes available for transmitting and receiving information. Although the NDoF can be computed numerically for specific configurations using singular value decomposition (SVD) of the channel operator, this approach provides limited physical insight. In this paper, we introduce a simple analytical estimate for the NDoF between arbitrarily shaped transmitter and receiver regions in free space.

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.

This paper studies achievable rates of nanopore-based DNA storage when nanopore signals are decoded using a tractable channel model that does not rely on a basecalling algorithm. Specifically, the noisy nanopore channel (NNC) with the Scrappie pore model generates average output levels via i.i.d. geometric sample duplications corrupted by i.i.d. Gaussian noise (NNC-Scrappie). Simplified message passing algorithms are derived for efficient soft decoding of nanopore signals using NNC-Scrappie.

In this paper, we consider a recent channel model of a nanopore sequencer proposed by McBain, Viterbo, and Saunderson (2024), termed the noisy nanopore channel (NNC). In essence, an NNC is a duplication channel with structured, Markov inputs, that is corrupted by memoryless noise. We first discuss a (tight) lower bound on the capacity of the NNC in the absence of random noise. Next, we present lower and upper bounds on the channel capacity of general noisy nanopore channels.