Analysis of voltage- and clock-scaling-induced timing errors in stochastic LDPC decoders

Low Density Parity Check (LDPC) decoders have an inherent capability of correcting the transmission errors that occur, when communicating over a hostile wireless channel. This capability allows LDPC-coded schemes to employ lower transmission energies than uncoded schemes, at the cost of introducing a significant processing energy consumption during LDPC decoding. Traditional energy-reduction techniques, such as voltage and clock scaling can be employed for reducing the LDPC decoder´s energy consumption. However, these techniques may induce timing errors, which can degrade the LDPC decoder´s error correction capability. Our previous work has demonstrated that in contrast to other types of LDPC decoders, stochastic decoders have an inherent tolerance to timing errors, allowing them to maintain a high error correction capability in clockscaling scenarios. In this paper, we investigate this timing error tolerance in voltage-scaling scenarios, by extending our previous model of timing errors using extensive SPICE simulations. Furthermore, we use these SPICE simulations to characterize the processing energy consumption of stochastic LDPC decoders for the first time. We demonstrate that a modified stochastic LDPC decoder can operate at 0.8 V and a clock period of 915.11 ps, while maintaining the error correction capability of a conventional stochastic decoder operating at 1 V and a clock period of 1019.2 ps, offering a 36.7% reduction in processing energy consumption.