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Exploiting Asymmetry in eDRAM Errors for Redundancy-Free Error-Tolerant Design

For some applications, errors have a different impact on data and memory systems depending on whether they change a zero to a one or the other way around; for an unsigned integer, a one to zero (or zero to one) error reduces (or increases) the value. For some memories, errors are also asymmetric; for example, in a DRAM, retention failures discharge the storage cell. The tolerance of such asymmetric errors can result in a robust and efficient system design. Error Control Codes (ECCs) are one common technique for memory protection against these errors by introducing some redundancy in memory cells. In this paper, the asymmetry in the errors in Embedded DRAMs (eDRAMs) is exploited for error-tolerant designs without using any ECC or parity, which are redundancy-free in terms of memory cells. A model for the impact of retention errors and refresh time of eDRAMs on the False Positive rate or False Negative rate of some eDRAM applications is proposed and analyzed. Bloom Filters (BFs) and read-only or write-through caches implemented in eDRAMs are considered as the first case studies for this model. For BFs, their tolerance to some zero to one errors (but not one to zero errors) is combined with the asymmetry of retention errors in eDRAMs to show that no ECC or parity is needed to protect the filter; moreover, the eDRAM refresh time can significantly be increased, thus reducing its power consumption. For caches, this paper shows that asymmetry in errors can be exploited also by using a redundancy-free error-tolerant scheme, which only introduces false negatives, but no false positives, therefore causing no data corruption. The proposed redundancy-free implementations have been compared with existing schemes for BFs and caches to show the benefits in terms of different figures of merit such as memory size, area, decoder/encoder complexity and delay. Finally, in the last case study, we show that the asymmetry of retention errors can be used to develop additional error correction capabilities in Modular Redundancy Schemes.