1. Introduction

A modern computer system requires large amounts of main memory owing to its multi-core structure and complex applications. In particular, data-intensive applications such as big data and deep learning require a large amount of main memory to support large amounts of data [1-3]. As a result, the need for large-capacity main memory with low power consumption and high reliability has become important [4,5], and studies on the use of phase-change memory (PCM) as main memory have been actively conducted [6-8]. The cell size in PCM is smaller than DRAM, so the module can be denser, enabling a large memory capacity [9]. Furthermore, owing to the non-volatile characteristics of PCM, it is more advantageous than DRAM in terms of power efficiency and data retention time.

Despite these advantages, PCM suffers from low reliability, which needs to be addressed in order to use PCM as main memory. One of the main causes of reliability issues in PCM is read disturbance errors (RDEs) [10,11]. An RDE is a phenomenon whereby cells that are repeatedly read are damaged by thermal energy. RDEs occur when the number of reads exceeds a certain threshold. A conventional solution for RDEs is to scrub the cells in a word before the number of reads reaches the threshold. Memory scrubbing first reads a word, corrects bit errors with error-correcting code (ECC), and writes the corrected word back to the same location. Periodically scrubbing a word therefore prevents RDEs in that word.

However, periodical scrubbing requires read counters, which results in significant resource overhead because the number of reads must be counted in order to trigger scrubbing. In this paper, on-demand memory scrubbing that does not require read counters is proposed. Under the given RDE model with ECC, the probability distribution of the number of errors that occur with an additional read is derived. By using the derived probability distribution, the proposed solution suggests whether to scrub or not based on the current number of errors. Because the proposed solution only requires the number of errors, it does not need read counters, thereby eliminating nearly 1GB of resource overhead. The contributions from this paper are summarized as follows.

· A probabilistic model for RDEs is mathematically derived, and the optimal on-demand scrubbing policy is derived from the proposed model.

· Monte-Carlo (MC) simulation is conducted to verify the probabilistic model.

· The proposed on-demand scrubbing eliminates more than 1GB needed for read counters, while fixing more than 99.99% of RDEs.

The remainder of this paper is organized as follows. Section 2 introduces the background, and Section 3 presents the proposed on-demand scrubbing method. In Section 4, experimental results are given. Finally, Section 5 concludes the paper.

2. Background

In this section, the background for RDE error models and RDE mitigating schemes is presented.

2.2 RDE Mitigating Schemes

To mitigate RDE occurrences, a memory scrubbing method is used [12]. In conventional methods, each word utilizes a read counter. If the counter value reaches a certain threshold, the method reads a whole word and checks for errors via ECC. If errors are found, they are corrected and the word is rewritten. This read-and-fix process is called memory scrubbing. Conventional memory scrubbing, which uses a read counter, can remove RDEs effectively as long as the scrubbing threshold value is well chosen. However, as shown in Fig. 1, it requires a read counter per word, which means an extra 2B of storage must be allocated per word. Taking into account that the word size in PCM is typically between 64B and 256B, the extra storage takes about 1/32 to 1/128 of the total PCM capacity. Moreover, these read counters are updated frequently, and thus, DRAM should be used for them. Assuming 512GB of PCM capacity and a 128B word size, nearly 8GB of DRAM is used only for read counters, which is a significantly large overhead.

Fig. 1. Diagram of PCM and its read counters.

3. On-demand Memory Scrubbing

In this section, an on-demand memory scrubbing method that effectively eliminates read counters is described. First, the probability distribution under the Gaussian counter-based error model is derived, and then, an efficient on-demand scrubbing policy under the given probability distribution is suggested.

4. Simulation Results

In this section, MC simulation results regarding the proposed on-demand memory scrubbing are presented. For MC simulations, RDE threshold value $\textit{T}$ for each bit in a word was randomly sampled from the Gaussian distribution, $N\left(3000,~ \sigma ^{2}\right)$. Under the generated $\textit{T}$ values in a word, the number of errors ($\textit{L}$) was followed as the read count ($\textit{K}$) increased.

Table 3 shows the MC simulation results with respect to various standard deviation values. The number of MC trials was 1,000,000. The first column of Table 3 shows the number of errors in the current state. From the current state, if one more read causes a violation ($\textit{i.e.}$, the number of errors exceeds 21), the case is counted as a $\textit{violated read}$. The second, fifth, and eighth columns in Table 3 show the number of violated reads for standard deviations of 10, 20, and 50, respectively. For example, when the standard deviation was 10, the violated read value was 4 for an $\textit{L}$ of 7. This means that in these four cases, the error number changed directly from 7 to a value larger than 21. The columns labeled Probability of VR show the ratio of violated reads with respect to the total number of trials. The column Average Read Threshold represents the average read counts among the violations. For example, when the standard deviation was 10, the average read threshold was 2,973 for an $\textit{L}$ of 7. This means that the average read count over four violations was 2,973.

From the MC simulation results in Table 3, two observations can be drawn. First, the distribution of violated reads changed with respect to the standard deviation. As the standard deviation of the underlying Gaussian model increased, the violations occurred late. In other words, when the standard deviation was relatively large, more errors could be endured until scrubbing. The other observation is that the average read threshold value remained almost the same while $\textit{L}$ increased. This means that even if we accumulate more errors before scrubbing, in order to reduce scrubbing frequency, the actual reduction in the scrubbing frequency is negligible. From this observation, the optimal on-demand scrubbing point for $\textit{L}$ is the point where a violation first occurs. Therefore, the optimal on-demand scrubbing points for each standard deviation value for $\textit{L}$ are 7, 10, and 13, respectively.

It should be noted that the MC simulation results presented in Table 3 verify the probability distribution described in Section 3.1. The probabilities of violations derived from the probability distributions shown in Table 1 give values similar to those in Table 3. For the average read threshold value drawn from the probability distribution in Table 2, the results verify that the value does not increase significantly when $\textit{L}$ is greater than 6.

In addition to RDEs, there are other reliability issues regarding PRAM, such as write disturbance error (WDE). That is, for example, if the current number of errors is 8, then it is possible that four RDEs and four WDEs both occur. Under this circumstance, consider a case where the proposed on-demand scrubbing policy initiates scrubbing. The policy thinks that all eight errors were caused by RDEs, but in this case, only four errors were caused by RDEs. Therefore, the probability that an additional read will cause an ECC violation is even less when other errors are considered. In summary, the proposed approach, which only considers RDEs, is a conservative approach, and other errors do not compromise the reliability of the proposed on-demand scrubbing.

5. Conclusion

To efficiently address RDEs, this paper proposes an on-demand scrubbing policy that does not require read counters. Assuming the memory capacity of PCM is 64GB, a read counter per word takes nearly 1GB of storage, which creates a significant resource overhead. In the proposed method, without this resource overhead, more than 99.99% of read disturbance errors can be fixed. From a mathematically derived probability distribution model of RDE occurrence, the optimal on-demand scrubbing policy is drawn up with respect to a certain standard deviation in RDE threshold values. MC simulation results also verified the derived probability distribution model. It should be noted that the probability of preventing violations can be increased by scrubbing more often. This means that there is a trade-off between reliability and performance, and the user can adaptively select the configuration according to the application.