用随机哈达玛变换+6比特量化,实现无数据依赖的实时音频压缩。
AudioTQ: A Data-Oblivious 6-Bit CPU Audio Codec via Randomized Hadamard Rotation and Lloyd-Max Quantization
- 在时域通过随机哈达玛变换统一信号分布,适配固定量化器。
- 7比特虚拟索引压缩至8比特容器,实测可减小74.4%体积,保30dB音质。
- 无需硬件加速,适合嵌入式或低延迟音频处理场景。
传统有损音频压缩依赖心理声学模型与频域表示(如MP3、AAC、Opus),虽高效但计算复杂且领域特定。本文提出AudioTQ,一种数据无关的时域有损音频编解码器。受大语言模型权重量化(如TurboQuant)启发,AudioTQ采用正交随机快速沃尔什-哈达玛变换(FWHT)将波动的时域振幅转化为可预测的标准正态分布,从而支持坐标级标量量化。使用离线训练的均方误差最优6比特Lloyd-Max量化器,并引入1比特量化联合最小二乘(QJL)残差校正层。生成的7比特虚拟索引被打包进原生8比特容器,对齐标准CPU寄存器边界,确保无需硬件并行加速即可实现实时单线程运行。文中详细分析了24比特专业音频流的位级重建方法,推导了FWHT蝴蝶网络结构及稀疏输入下的数学失效模式,并通过基准测试验证:最高可实现74.4%物理尺寸缩减,同时保持约30 dB的信噪比(SQNR)。
原文摘要 · Abstract (English)
Lossy audio compression algorithms traditionally rely on psychoacoustic modeling and frequency-domain representations (e.g., MP3, AAC, and Opus) to discard information that is imperceptible to the human auditory system. While highly effective, these approaches are computationally complex and domain-specific. In this paper, we present the design and mathematical formulation of AudioTQ, a data-oblivious lossy audio codec that operates directly in the time domain. Inspired by Large Language Model (LLM) weight quantization techniques (specifically the TurboQuant framework), AudioTQ uniformizes volatile time-domain amplitudes into a predictable standard normal distribution using an orthonormal, randomized Fast Walsh-Hadamard Transform (FWHT) rotation. This enables coordinate-wise scalar quantization using an offline-trained, MSE-optimal 6-bit Lloyd-Max quantizer, augmented by a 1-bit Quantized Joint Least-Squares (QJL) residual correction layer. The resulting 7-bit virtual indices are packed into native 8-bit containers, aligning with standard CPU register boundaries to ensure real-time single-threaded execution without hardware parallel accelerators. We detail the bitwise reconstruction of 24-bit studio stems, analyze the butterfly network of the FWHT, derive the mathematical failure modes under sparse inputs, and present benchmarks showing up to 74.4% physical size reduction alongside a Signal-to-Quantization-Noise Ratio (SQNR) of ~30 dB.
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