Bit Propagation over a Noisy Grid
a day ago
- #information theory
- #noisy transmission
- #grid propagation
- The problem involves transmitting a bit over a noisy grid, starting from the origin and propagating outward as a wave.
- In 1D, the original bit cannot be recovered from the last bit in a long chain due to exponential decay to 50% correctness.
- In 2D, using a majority function and random tie-breaking, information is lost, and homogeneous function assignments cannot preserve the bit.
- For 3D, simulations show that at high temperatures, correctness drops to 50%; at low temperatures, behavior is unclear, possibly indicating a phase change.
- Noise along axes (1D chains) propagates into the grid, affecting the wavefront, especially with undefined nodes simplifying analysis.
- Undefined nodes eliminate random walks, leading to structured patterns on the wavefront, suggesting impossibility of recovery.
- The analysis is tentative; concerns include the simplification of undefined nodes and the need for rigorous proofs or alternative models.