Count2Multiply: Reliable In-memory High-Radix Counting

Big data processing has exposed the limits of compute-centric hardware acceleration due to the memory-to-processor bandwidth bottleneck. Consequently, there has been a shift towards memory-centric architectures, leveraging substantial compute parallelism by processing using the memory elements directly. Computing-in-memory (CIM) proposals for both conventional and emerging memory technologies often target massively parallel operations. However, current CIM solutions face significant challenges. For emerging data-intensive applications, such as advanced machine learning techniques and bioinformatics, where matrix multiplication is a key primitive, memristor crossbars suffer from limited write endurance and expensive write operations. In contrast, while DRAM-based solutions have successfully demonstrated multiplication using additions, they remain prohibitively slow. This paper introduces Count2Multiply, a technology-agnostic digital-CIM method for performing integer-binary and integer-integer matrix multiplications using high-radix, massively parallel counting implemented with bitwise logic operations. In addition, Count2Multiply is designed with fault tolerance in mind and leverages traditional scalable row-wise error correction codes, such as Hamming and BCH codes, to protect against the high error rates of existing CIM designs. We demonstrate Count2Multiply with a detailed application to CIM in conventional DRAM due to its ubiquity and high endurance. We also explore the acceleration potential of racetrack memories due to their shifting properties, which are natural for Count2Multiply, and their high endurance. Compared to the state-of-the-art in-DRAM method, Count2Multiply achieves up to 10x speedup, 3.8x higher GOPS/Watt, and 1.4x higher GOPS/area, while the RTM counterpart offers gains of 10x, 57x, and 3.8x.