Constrained coding is a subfield of coding theory that tackles efficient communication under constraints. While fixed constraints (e.g., a fixed set of substrings may not appear in transmitted messages) have a general optimal solution, there is increasing demand for supportingparametricconstraints that are dependent on the message length and portray some property (e.g., no log(n)consecutive zeros). Several works have tackled such parametric constraints throughiterativealgorithms, yet they require complex constructions specific to each constraint to guarantee convergence throughmonotonic progression. In this paper, we propose a universal framework for tacklinganyparametric constraint problem through a new simple iterative algorithm. By reducing an execution of this iterative algorithm to an acyclic graph traversal, we prove a surprising result that guarantees convergence with low average time complexityeven without requiring any monotonic progression. We demonstrate the effectiveness of this universal framework, with much of our focus on the special case of single-symbol redundancy, while also considering a variety of bothlocalandglobalconstraints. We begin by exploring the local constraints involving illegal substrings of variable length, where the construction essentially iteratively replaces forbidden windows. This local algorithm is applied to various fundamental constraints, achieving state-of-the-art results through simple adaptations of the universal algorithm. We then continue by exploring global constraints, and demonstrate the effectiveness of the proposed construction on repeat-free encoding, reverse-complement encoding and DNA data storage. Overall, the proposed framework generates state-of-the-art constructions with significant ease while also enabling the simultaneous integration of multiple constraints for the first time.

We address the challenge of optimizing the capacity-achieving input distribution for a multinomial channel under the constraint of limited input support size, which is a crucial aspect in the design of DNA storage systems. We propose an algorithm that further elaborates the Multidimensional Dynamic Assignment Blahut-Arimoto (M-DAB) algorithm [1]. Our proposed algorithm integrates variational autoencoder for determining the optimal locations of input distribution, into the alternating optimization of the input distribution locations and weights.

Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While fixed constraints (e.g., a fixed set of substrings may not appear in transmitted messages) have a general optimal solution, there is increasing demand for supporting parametric constraints that are dependent on the message length and portray some property that the substrings must satisfy (e.g., no log (n) consecutive zeros). Several works have tackled such parametric constraints through iterative algorithms following the sequence-replacement approach, yet this approach requires complex constraint-specific properties to guarantee convergence through monotonic progression. In this paper, we propose a universal framework for tackling any parametric constraint problem with far fewer requirements, through a simple iterative algorithm. By reducing an execution of this iterative algorithm to an acyclic graph traversal, we prove a surprising result that guarantees convergence with efficient average time complexity even without requiring any monotonic progression. We demonstrate how to apply this algorithm to the run-length-limited, minimal Hamming weight, local almost-balanced Hamming weight constraints, as well as repeat-free and secondary-structure constraints. Overall, this framework enables state-of-the-art results with minimal effort.