ABSTRACT This paper explores the practical application of source polar codes to entropy coding tasks in modern transform coding pipelines. Transform coding remains the predominant and rapidly evolving framework for compressing complex real‐world data. Despite the strong theoretical guarantees of polar codes, conventional polarization‐based compression techniques follow a “construct‐then‐use” paradigm, which proves inefficient and inaccurate when applied to transform coding scenarios characterized by highly dynamic entropy models. To overcome this limitation, we propose a construction‐free, plug‐and‐play polar compression scheme. Rather than relying on precomputed polarized entropies, our method selects output symbols based on probability vectors generated by a conditional entropy model. These vectors can be computed with low complexity and exact numerical precision, enabling efficient adaptation across diverse entropy coding tasks. The proposed approach offers greater flexibility than classical methods and achieves superior performance in the finite‐length regime.

Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also introduces significant challenges for existing successive cancellation (SC) based decoding schemes. Motivated by the need for a general SC decoding solution, we present a comprehensive decoding strategy for monotone chain polar codes that can handle arbitrary numbers of terminals, non-binary alphabets, and decoding along arbitrary monotone chains. Specifically, we formulate the SC decoding task as a series of inference subtasks over the polar transform and propose a computational graph framework based on probability propagation principles. This approach highlights the impact of variable switching during decoding and shows that time complexity varies between $O(N\log{N})$ and $O(N^2)$, depending on the specific chain structure. Moreover, we demonstrate that the widely used $O(N)$ space optimization is not universally applicable to monotone chain polar codes, which prompts us to introduce a constant-time decoder forking strategy based on the proposed logical computation graphs. This strategy enables time-efficient list decoding without relying on $O(N)$-space techniques. Numerical results verify the superior performance of the proposed scheme compared with the classical lazy-copy scheme.