# Thermodynamics of majority-logic decoding in information erasure

## TL;DR

This paper analyzes how majority-logic decoding affects the efficiency and speed of information erasure in macroscopic bits, showing it offers advantages in finite-time processes and can improve the precision-speed-efficiency trade-off.

## Contribution

It demonstrates that majority-logic decoding enhances finite-time erasure performance and can surpass single-unit transformations in speed and efficiency, especially under optimal protocols.

## Key findings

- Majority-logic decoding reduces minimal erasure duration for a given error.
- It improves erasure efficiency in fast and low-error regimes.
- Benefits persist under optimal heat-dissipation protocols.

## Abstract

We investigate the performance of majority-logic decoding in both reversible and finite-time information erasure processes performed on macroscopic bits that contain $N$ microscopic binary units. While we show that for reversible erasure protocols single-unit transformations are more efficient than majority-logic decoding, the latter is found to offer several benefits for finite-time erasure processes: Both the minimal erasure duration for a given erasure and the minimal erasure error for a given erasure duration are reduced, if compared to a single unit. Remarkably, the majority-logic decoding is also more efficient in both the small erasure error and fast erasure region. These benefits are also preserved under the optimal erasure protocol that minimizes the dissipated heat. Our work therefore shows that majority-logic decoding can lift the precision-speed-efficiency trade-off in information erasure processes.