Entropy Polarization-Based Data Compression Without Frozen Set Construction
Zichang Ren, Yuping Zhao
TL;DR
This work tackles practical data compression with polar codes by removing the need for frozen-set construction. It introduces a construction-free polar compression scheme that selects encoder output symbols based on the decoder's behavior, quantified through a data-dependent entropy measure $\hbar_i(u_{1:i-1})$ and a high-entropy set $\mathcal{G}$ defined by a threshold $\hbar_{\mathrm{th}}$, transmitting $u_{\mathcal{G}}$ and $\hbar_{\mathrm{th}}$. A rate-1 SC decoding process enables the encoder to compute $\hbar_i$ without frozen-set construction, achieving $O(N \log N)$ complexity and sequential decoding at the receiver to determine $\mathcal{G}$. The authors extend the framework with matching principles for non-standard decoders and non-binary sources, introduce a fixed-threshold variant for practical storage, and demonstrate via simulations that the proposed scheme attains compression rates near the source entropy and outperforms prior polar compression methods in several regimes.
Abstract
Classical source polar codes require the construction of frozen sets for given sources. While this scheme offers excellent theoretical performance, it faces challenges in practical data compression systems, including sensitivity to the accuracy and computational complexity of the construction algorithm. In this letter, we explore the feasibility of construction-free polar compression schemes. By optimally selecting output symbols based on the decoder's behavior, the proposed scheme not only enhances flexibility but also achieves significant improvements in compression rates. Several enhancements are introduced to facilitate the practical implementation of the proposed scheme. Numerical results demonstrate the superior performance compared to existing polar compression approaches.