发表机构
Klipsch School of Electrical and Computer Engineering, New Mexico State University; School of Electrical, Computer and Energy Engineering, Arizona State University; Departments of Mathematics and Electrical Engineering, University of Notre Dame（新墨西哥州立大学克利普施电气与计算机工程学院; 亚利桑那州立大学电气、计算机与能源工程学院; 圣母大学数学与电气工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出多项式域有限长度提升积QLDPC码的结构化构造方案，基于商环构建，经实例验证可通过基准解码器在去极化信道实现良好性能。
AI 中文摘要
本文提出了有限长度的多项式域提升积量子低密度奇偶校验（QLDPC）码的公式化方案。我们在商环F₂[D]/(Dᴸ+1)上构建该码，其中多项式基矩阵按元素提升为二进制循环块。该表示为提升积奇偶校验矩阵提供了紧凑的代数描述，并允许在二进制展开前分析CSS正交性。我们证明标准循环提升映射与多项式共轭兼容，这意味着所得二进制矩阵满足CSS交换约束。以约束长度为7、码率为1/2的NASA卷积码为例说明该构造，并提供了来自3×4多项式奇偶校验矩阵的数值示例。随后在去极化信道上使用多种基准解码器评估了所选构造码的有限长度性能。所得框架提供了一种从小型多项式基矩阵构造有限长度提升积QLDPC码的结构化方法。
英文摘要
This paper presents a finite-length polynomial-domain formulation of lifted-product quantum low-density parity-check (QLDPC) codes. We formulate the code construction over the quotient ring F 2[D]/(D L + 1), where polynomial base matrices are lifted entrywise to binary circulant blocks. This representation gives a compact algebraic description of the lifted-product parity-check matrices and allows CSS orthogonality to be analyzed before binary expansion. We show that the standard circulant lifting map is compatible with polynomial conjugation, which implies that the resulting binary matrices satisfy the CSS commutation constraint. The construction is illustrated with a constraint length 7, rate 1/2 NASA convolutional code example, and numerical examples are provided from a 3 x 4 polynomial parity-check matrix. The finite-length performance of selected constructed codes is then evaluated over the depolarizing channel using various benchmark decoders. The resulting framework gives a structured method to construct finite-length lifted-product QLDPC codes from small polynomial base matrices.
