Channel Coding for Binary Neural Networks Implemented with Noisy Memristor Crossbars

In the context of in-memory computing, this paper investigates binary neural networks (BNNs) implemented with memristor crossbars. A key issue in these architectures is the difficulty in setting crossbar conductance values with an arbitrary precision, which introduces computational noise into the BNN layers. The paper first introduces a theoretical analysis of the impact of noise on the final computation, deriving an analytical expression for the error probability at the output of a BNN layer. This expression is validated through MonteCarlo simulations, demonstrating its accuracy in predicting error probabilities. Furthermore, the paper introduces a novel linear block code designed to mitigate the effects of noise in conductance values. This coding scheme is accompanied by a dedicated low-complexity belief propagation decoder that operates over the set of integers. Simulation results indicate a significant improvement in bit error rate for the proposed coding method compared to hard thresholding.