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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.

The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein’s work in 2001, this number is determined by the size of the maximum intersection between the error balls of any two distinct input sequences of the channel. In this work, we study the sequence reconstruction problem for the q-ary single-deletion single-substitution channel for any fixed integer q≥2.

In DNA sequencing, we often need to infer an unknown sequence from a collection of its corrupted copies. Each copy cannot faithfully tell the truth due to DNA fragmentation, point mutations, and measurement errors. The theoretical guarantee of unique reconstruction is thus of concern. This motivated the study of sequence reconstruction problems three decades ago. Recently, synthetic DNA has been regarded as an ultra-dense data storage medium. Sequence reconstruction is a crucial step in achieving reliable and efficient data readout.

Recent advancements in DNA storage show that composite DNA letters can significantly enhance storage capacity. We model this process as a multinomial channel and propose an optimization algorithm to determine its capacity-achieving input distribution (CAID) for an arbitrary number of output reads. Our empirical results match a scaling law that determines that the support size grows exponentially with capacity.

In this work, we present a generalization of the recently proposed quantum Tanner codes by Leverrier and Zémor, which contains a construction of asymptotically good quantum low-density parity-check codes. Quantum Tanner codes have so far been constructed equivalently from groups, Cayley graphs, or square complexes constructed from groups. We show how to enlarge this to graphs with labeled local views and a family of square complexes, which is the largest possible in a certain sense.

Emerging DNA storage technologies use composite DNA letters, where information is represented by a probability vector, leading to higher information density and lower synthesis costs. However, it faces the problem of information leakage in sharing the DNA vessels among untrusted vendors. This paper introduces an asymptotic ramp secret sharing scheme (ARSSS) for secret information storage using composite DNA letters.

In this paper, we study error exponents for an index-based concatenated coding based class of DNA storage codes in which the number of reads performed can be variable. That is, the decoder can sequentially perform reads and choose whether to output the final decision or take more reads, and we are interested in minimizing the average number of reads performed rather than a fixed pre-specified value.