# Generalized Compute-Compress-and-Forward

## TL;DR

This paper introduces a generalized compute-compress-and-forward (GCCF) scheme that enhances wireless network performance by broadening compression capabilities, achieving optimal compression rates, and outperforming existing methods like CCF.

## Contribution

The paper develops a new GCCF framework with multiple quantization-and-modulo operations, demonstrating its optimality and broader rate region compared to prior CCF schemes.

## Key findings

- GCCF achieves a broader compression rate region than CCF.
- GCCF is optimal in minimizing total compression rate.
- Numerical results show GCCF outperforms existing schemes.

## Abstract

Compute-and-forward (CF) harnesses interference in wireless communications by exploiting structured coding. The key idea of CF is to compute integer combinations of codewords from multiple source nodes, rather than to decode individual codewords by treating others as noise. Compute-compress-and-forward (CCF) can further enhance the network performance by introducing compression operations at receivers. In this paper, we develop a more general compression framework, termed generalized compute-compress-and-forward (GCCF), where the compression function involves multiple quantization-and-modulo lattice operations. We show that GCCF achieves a broader compression rate region than CCF. We also compare our compression rate region with the fundamental Slepian-Wolf (SW) region. We show that GCCF is optimal in the sense of achieving the minimum total compression rate. We also establish the criteria under which GCCF achieves the SW region. In addition, we consider a two-hop relay network employing the GCCF scheme. We formulate a sum-rate maximization problem and develop an approximate algorithm to solve the problem. Numerical results are presented to demonstrate the performance superiority of GCCF over CCF and other schemes.