大规模并行探测存储通道的信息论
Information theory of massively parallel probe storage channels
摘要：
受探针存储概念的启发，我们研究了使用N个纳米机械探针（N ~ 4000）的大阵列进行信息检索的问题。在纳米尺度上，不可能避免阵列定位中的误差，因此在给定采样时刻由阵列的探针检索的所有信号都受到相同量的随机位置抖动的影响。因此，大规模并行探测存储设备是由于全球定位误差而在信道输出之间具有长范围相关性的噪声通信信道的示例。我们发现，这些相关性有深刻的影响，通道的属性。例如，在高信噪比的限制下，信道的信息容量确实接近每个探测1比特，但该方法的速率仅是信道噪声强度的多项式。此外，具有块大小N >> 1使得码字对应于阵列中的所有探测器的瞬时输出的任何纠错码表现出与码率无关的错误平层。我们说明了这一现象明确使用里德-所罗门码的性能是很容易模拟数值。我们还讨论了全局抖动信道的容量实现纠错码及其复杂性。
英文摘要：
Motivated by the concept of probe storage, we study the problem of information retrieval using a large array of N nano-mechanical probes, N ~ 4000. At the nanometer scale it is impossible to avoid errors in the positioning of the array, thus all signals retrieved by the probes of the array at a given sampling moment are affected by the same amount of random position jitter. Therefore a massively parallel probe storage device is an example of a noisy communication channel with long range correlations between channel outputs due to the global positioning errors. We find that these correlations have a profound effect on the channel's properties. For example, it turns out that the channel's information capacity does approach 1 bit per probe in the limit of high signal-to-noise ratio, but the rate of the approach is only polynomial in the channel noise strength. Moreover, any error correction code with block size N >> 1 such that codewords correspond to the instantaneous outputs of the all probes in the array exhibits an error floor independently of the code rate. We illustrate this phenomenon explicitly using Reed-Solomon codes the performance of which is easy to simulate numerically. We also discuss capacity-achieving error correction codes for the global jitter channel and their complexity.
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