Thermodynamic costs of message-passing decoding depend on hardware and input
Thermodynamic characterization of message-passing: Framework and initial study
Information Theory
Summary
Decoding messages in computers or communication systems uses energy, and some of this energy is wasted due to how the system starts up and processes information. The authors study how the way a decoder is built and the type of errors it faces affect this wasted energy. They use a mathematical approach to measure the minimum energy loss and show that different hardware designs can cause more or less waste even if the decoding works the same way. This work helps design decoders that use less energy by considering both their operation and physical layout.
What this means in practice
- •For hardware engineers: Design decoders by choosing hardware states that minimize energy waste for given decoding algorithms and input patterns.
- •For communication system designers: Optimize error-correcting decoders to balance decoding performance with thermodynamic efficiency given channel error characteristics.
Authors
Kalana G. Abeywardena, Stark C. Draper
Abstract
We study the thermodynamic efficiency of message-passing decoders using the mismatch cost framework. This framework quantifies the excess entropy generated when a system operates away from the thermodynamically optimal initial distribution. It provides a computable lower bound on irrecoverable energy loss. The decoder is modeled as a main decoding program with local message updates implemented as subroutines. Memory is treated as an external copying subsystem whose thermodynamic cost is excluded. Studying the $[7,4]$ Hamming code transmitted over a binary erasure channel, we show how the channel-induced initialization statistics and the step-wise evolution of the algorithmic state distribution during decoding determine the total mismatch cost. We further show that different thermodynamically optimal state distributions, representing different underlying physical implementations of the decoder, can produce different thermodynamic costs for identical decoding dynamics. Conditioning the input distribution on correctable and non-correctable erasure patterns further reveals distinct thermodynamic signatures. These results demonstrate that thermodynamic cost is jointly governed by decoding dynamics, input statistics, and hardware characteristics. This points to opportunities for thermodynamically-informed decoder design to realize energy-efficient physical implementations.