Daniella Bar-Lev

Daniella Bar-Lev, Farzad Farnoud, Ryan Gabrys

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to partition the support of the distribution and assign dyadic probabilities to minimize total variation distance while achieving a prescribed rate. We formulate this task as a tree-based partitioning problem and develop a polynomial-time additive approximation scheme for the rate-constrained setting in the constant-rate regime. Our results provide provable guarantees for near-optimal dyadic approximations and, as an application, yield a principled framework for LLM-based steganography, where the rate maps to bits of hidden information embedded per token and the total variation bound controls statistical detectability.

Daniella Bar-Lev

We study the problem of coded information retrieval for block-structured data, motivated by DNA-based storage systems where a database is partitioned into multiple files that must each be recoverable as an atomic unit. We initiate and formalize the block-structured retrieval problem, wherein $k$ information symbols are partitioned into two files $F_1$ and $F_2$ of sizes $s_1$ and $s_2 = k - s_1$. The objective is to characterize the set of achievable expected retrieval time pairs $\bigl(E_1(G), E_2(G)\bigr)$ over all $[n,k]$ linear codes with generator matrix $G$. We derive a family of linear lower bounds via mutual exclusivity of recovery sets, and develop a nonlinear geometric bound via column projection. For codes with no mixed columns, this yields the hyperbolic constraint $s_1/E_1 + s_2/E_2 \le 1$, which we conjecture to hold universally whenever $\max\{s_1,s_2\} \ge 2$. We analyze explicit codes, such as the identity code, file-dedicated MDS codes, and the systematic global MDS code, and compute their exact expected retrieval times. For file-dedicated codes we prove MDS optimality within the family and verify the hyperbolic constraint. For global MDS codes, we establish dominance by the proportional local MDS allocation via a combinatorial subset-counting argument, providing a significantly simpler proof compared to recent literature and formally extending the result to the asymmetric case. Finally, we characterize the limiting achievability region as $n \to \infty$: the hyperbolic boundary is asymptotically achieved by file-dedicated MDS codes, and is conjectured to be the exact boundary of the limiting achievability region.

Daniella Bar-Lev, Itai Orr, Omer Sabary et al.

DNA-based storage is an emerging technology that enables digital information to be archived in DNA molecules. This method enjoys major advantages over magnetic and optical storage solutions such as exceptional information density, enhanced data durability, and negligible power consumption to maintain data integrity. To access the data, an information retrieval process is employed, where some of the main bottlenecks are the scalability and accuracy, which have a natural tradeoff between the two. Here we show a modular and holistic approach that combines Deep Neural Networks (DNN) trained on simulated data, Tensor-Product (TP) based Error-Correcting Codes (ECC), and a safety margin mechanism into a single coherent pipeline. We demonstrated our solution on 3.1MB of information using two different sequencing technologies. Our work improves upon the current leading solutions by up to x3200 increase in speed, 40% improvement in accuracy, and offers a code rate of 1.6 bits per base in a high noise regime. In a broader sense, our work shows a viable path to commercial DNA storage solutions hindered by current information retrieval processes.