Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a convolutional manner. The number of partitioned components determines the memory of SC codes. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. While adopting higher memories results in improved SC code performance, obtaining finite-length, high-performance SC codes with high memory is known to be computationally challenging. We break this computational bottleneck by developing a novel probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low-complexity optimization algorithms that minimize the number of detrimental objects to construct high-memory, high-performance quasi-cyclic SC codes. We apply our framework to various objects of interests, from the simplest short cycles, to more sophisticated objects such as concatenated cycles aiming at finer-grained optimization. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and optimized SC codes with uniform partitioning. The performance gain is shown to be universal over a variety of channels, from canonical channels such as additive white Gaussian noise and binary symmetric channels, to practical channels underlying flash memory and magnetic recording systems.
翻译:以阈值饱和和现象和低纬度窗口解码算法著称的空间组合(SC)代码,是流式应用程序和数据存储系统的理想方法。SC代码的构建方式是分割一个基本区块代码,然后以递进方式重新排列和混合分隔区块组件。分割区块数决定了SC代码的内存。在本文中,我们调查SC代码的性能和分区矩阵密度分布之间的关系。在采用更高的记忆量在改进SC代码性能方面的结果,获得具有高记忆的有限、高性能的SC代码在计算上具有挑战性。我们通过开发一个新的概率框架来打破这一计算瓶颈,该框架通过渐渐渐下降的方式获得(局部)最佳密度分布。我们从随机偏差的偏差矩阵中开始决定SC代码的内存内存质。我们采用低兼容度优化的算法,将有害物体的数量减少到最小度、高性能准周期、高性能、高性能、高性能的SC代码。我们将我们的框架应用到各种利益对象,从精密的短周期、高性级级的SC代码,我们打破了这个计算瓶的计算瓶的计算瓶,打破了这个计算瓶的计算瓶,到最精度的Slodial- cal- cal- cal- cal- cal-smaxx,以显示式的Slical-smax,以显示的系统显示的系统,以正制成的平式的系统,以Slical-s-smax制成的周期,通过等的系统,以正的系统,以正制成为正的系统,以正制为正制式的平式的周期,以正制式的平式的平式的系统,以正制式的系统,以正制为正制式的周期,以制式的系统,以正制制制式的平式的系统,以正制为正制为制为制为制为制式制式制式制式制式制式制为制为制。