AI 中文总结
该研究针对有损压缩问题，广义化了稀疏回归码（SPARCs）的构造，推导了平方误差失真的非渐近界，优化功率分配提升了SPARCs的有限长度性能，为其低复杂度变体提供了失真保证。
AI 中文摘要
我们研究稀疏回归码（SPARCs）在简单贪婪编码规则下的有损压缩问题，包括基于相关性和基于距离的两类方法。我们对SPARC构造进行了广义化，考虑了一类“加性正交”回归码，标准SPARCs是该类的特例。针对这类码，我们通过跟踪各阶段编码残差的演化，推导了平方误差失真的非渐近界。我们的结果凸显了功率分配在控制失真中的作用，使我们能够根据码的参数优化分配方案。优化后的分配提升了SPARCs的有限长度压缩性能，且我们的界为SPARCs的低复杂度变体（如符号SPARCs和K-稀疏SPARCs）提供了失真保证。
英文摘要
We study sparse regression codes (SPARCs) for lossy compression under simple greedy encoding rules, including both correlation-based and distance-based methods. We generalize the SPARC construction, and consider the class of \emph{additive orthogonal} regression codes, of which standard SPARCs are a special case. For this class of codes, we derive nonasymptotic bounds on the squared-error distortion by tracking the evolution of the encoding residual across stages. Our results highlight the role of power allocation in controlling the distortion, allowing us to optimize the allocation based on the parameters of the code. The optimized allocation improves the finite-length compression performance of SPARCs, and our bounds provide distortion guarantees for lower complexity variants of SPARCs, like signed SPARCs and $K$-sparse SPARCs.
