Energy Consumption Modeling of 2-D and 3-D Decoder Circuits

Energy consumption evaluation for data processing tasks, such as encoding and decoding, is a critical consideration in designing very large scale integration (VLSI) circuits. Incorporating both information theory and circuit perspectives, a new general energy consumption model is proposed to capture the energy consumption of channel decoder circuits. For the binary erasure channel, lower bounds of energy consumption are derived for two-dimensional (2D) and three-dimensional (3D) decoder circuits under specified error probabilities, along with scaling rules for energy consumption in each case. Based on the proposed model, the lower bounds of energy consumption for staged serial and parallel implementations are derived, and a specific threshold value is identified to determine the parallel or serial decoding in decoder circuits. Staged serial implementations in 3D decoder circuits achieve a higher energy efficiency than fully parallel implementations when the processed data exceed 48 bits. Simulation results further demonstrate that the energy efficiency of 3D decoders improves with increasing data volume. When the number of input bits is 648, 1296 and 1944, the energy consumption of 3D decoders is reduced by 11.58%, 13.07%, and 13.86% compared to 2D decoders, respectively. The energy consumption of 3D decoders surpasses that of 2D decoders when the decoding error probability falls below a specific threshold of 0.035492. These results provide a foundational framework and benchmarks for analyzing and optimizing the energy consumption of 2D and 3D channel decoder circuits, enabling more efficient VLSI circuit designs.