A random coding theorem for "modulo-two adder" source network

TL;DR

This paper aimed to establish a coding theorem for modulo-two adder source networks but was withdrawn due to a critical proof error, highlighting the importance of rigorous validation in theoretical research.

Contribution

The paper attempted to derive a new coding theorem for modulo-two adder source networks, proposing a bound on error probability.

Findings

The initial proof contained an unconsidered contribution from certain pairs.

Adding the missing contribution aligns the rate region with the Slepian-Wolf region.

The paper was withdrawn due to a crucial error in the proof.

Abstract

This paper has been withdrawn by the author, due a crucial error in the proof of the main Theorem (Sec. 3). In particular, in deriving the bound on the probability of error (Eq. 10) the contribution of those pairs (x', y') that are not equal to (x, y) has not been considered. By adding the contribution of these pairs, one can verify that a region of rates similar to the Slepian-Wolf region will emerge. The author would like to acknowledge a critical review of the paper by Mr. Paul Cuff of Stanford University who first pointed out the error.