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Information theory of massively parallel probe storage channels

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.