Fundamental limits on the power consumption of encoding and decoding

We provide fundamental information-theoretic bounds on the required circuit wiring complexity and power consumption for encoding and decoding of error-correcting codes. These bounds hold for all codes and all encoding and decoding algorithms implemented within the paradigm of our VLSI model. This model essentially views computation on a 2-D VLSI circuit as a computation on a network of connected nodes. The bounds are derived based on analyzing information flow in the circuit. They are then used to show that there is a fundamental tradeoff between the transmit and encoding/decoding power, and that the total (transmit + encoding + decoding) power must diverge to infinity at least as fast as cube-root of log 1/p_e, where P_e is the average block-error probability. On the other hand, for bounded transmit-power schemes, the total power must diverge to infinity at least as fast as square-root of log 1/P_e due to the burden of encoding/decoding.