AI 中文总结
本文将通用随机编码扩展至两阶段逐次精炼设置，基于LZ78复杂度构造无类型编码，证明其可达区域优于有限状态建模方法的姊妹论文结果。
AI 中文摘要
本工作将先前提出的用于单序列逐样本有损压缩的通用随机编码集合扩展至两阶段（逐次精炼）设置，该扩展并非十分直接，后续将对此作出说明。该构造包含三层：其一，基于类型类和典型序列语言的完整、自包含的直接/逆匹配，这是Rimoldi经典表征的两阶段类似物（应用于块的超字母表）；其二，通过基于Lempel-Ziv（LZ78）复杂度而非第一层依赖的类型类均匀测度的随机编码方案实现相同码率，因为基于LZ的集合对源统计和失真测度具有通用性，码本本身无块长参数，且可直接实现；其三，我们给出完全无类型的可达性构造（其搜索准则中不出现任何ℓ-向量的联合类型），并证明其与同一逆完全匹配，覆盖可达区域的所有点：第一层的同一逆已约束了任何编码，包括无类型方案，因此无需单独论证以证明匹配。我们还描述（未给出证明）如何将无类型构造扩展至任意固定数量r>2的阶段。最后，我们证明本文的可达区域是一篇姊妹论文所得区域的超集，该姊妹论文基于有限状态建模方法处理类似两阶段问题，将已知的单阶段支配结果扩展至两阶段。
英文摘要
This work extends an earlier proposed universal random-coding ensemble for sample-wise lossy compression of individual sequences to the two-stage (successive-refinement) setting --- an extension that is not quite straightforward, as explained in the sequel. The construction has three layers. First, a complete, self-contained direct/converse match in the language of type classes and typical sequences, a two-stage analogue of Rimoldi's classical characterization (applied in the superalphabet of blocks). Second, a realization of the same rates via a random-coding scheme built from the Lempel--Ziv (LZ78) complexity rather than the type-class uniform measure the first layer relies on, since an LZ-based ensemble is universal across source statistics and distortion measures, carries no block-length parameter in the codebook itself, and is directly implementable. Third, we give a fully type-free achievability construction (no joint types of $\ell$-vectors appear anywhere in its search criterion) and show it matches the same converse exactly, reaching every point of the achievable region: the same converse from the first layer already binds any code, type-free schemes included, so no separate argument is needed to certify the match. We also describe (without proof) how to extend the type-free construction to any fixed number $r>2$ of stages. Finally, we show this paper's achievable region is a superset of the one obtained by a companion paper, which is based on a finite-state modeling approach to a similar two-stage problem, extending a known single-stage domination result to two stages.
Comments35 pages; to be submitted
