Abstract
Exponential growth in data generation and large-scale data science has created an unprecedented need for inexpensive, low-power, low-latency, high-density information storage. This need has motivated significant research into multi-level memory devices that are capable of storing multiple bits of information per device. The memory state of these devices is intrinsically analog. Furthermore, much of the data they will store, along with the subsequent operations on the majority of this data, are all intrinsically analog-valued. Ironically though, in the current storage paradigm, both the devices and data are quantized for use with digital systems and digital error-correcting codes. Here, we recast the storage problem as a communication problem. This then allows us to use ideas from analog coding and show, using phase change memory as a prototypical multi-level storage technology, that analog-valued emerging memory devices can achieve higher capacities when paired with analog codes. Further, we show that storing analog signals directly through joint coding can achieve low distortion with reduced coding complexity. Specifically, by jointly optimizing for signal statistics, device statistics, and a distortion metric, we demonstrate that single-symbol analog codings can perform comparably to digital codings with asymptotically large code lengths. These results show that end-to-end analog memory systems have the potential to not only reach higher storage capacities than discrete systems but also to significantly lower coding complexity, leading to faster and more energy efficient data storage.
Highlights
To measure the capacity of analog-valued PCM devices, we recast the storage problem as a communication problem (Fig. 2a)
The channel noise characteristics are determined by both the memory controller and memory devices, and multi-pulse read-verify control schemes have proven effective at achieving high capacities despite device-to-device variation and resistance drift[7,8]
To calculate a continuous probability density for P(R|VWL), we first performed Gaussian kernel density estimation (KDE) of the distribution of resistances resulting from each voltage level
Summary
To measure the capacity of analog-valued PCM devices, we recast the storage problem as a communication problem (Fig. 2a). The devices are perturbed by voltage pulses of different magnitudes drawn from the input probability distribution P(V). These pulses modulate a device’s resistance, resulting in an output resistance distribution ( ) P(R) = ∫ P R V P(V)dV. In the limit of an infinite blocklength code, the capacity is the number of bits of information per use of the device that can be communicated without error[6]. It is equivalently given by the maximum mutual information between the input and output distributions, C
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