Compute-and-Forward Network Coding Design over Multi-Source Multi-Relay Channels

Abstract

Network coding is a new and promising paradigm for modern communication networks by allowing intermediate nodes to mix messages received from multiple sources. Compute-and-forward strategy is one category of network coding in which a relay will decode and forward a linear combination of source messages according to the observed channel coefficients, based on the algebraic structure of lattice codes. The destination will recover all transmitted messages if enough linear equations are received. In this work, we design in a system level, the compute-and-forward network coding coefficients by Fincke-Pohst based candidate set searching algorithm and network coding system matrix constructing algorithm, such that by those proposed algorithms, the transmission rate of the multi-source multi-relay system is maximized. Numerical results demonstrate the effectiveness of our proposed algorithms.

Compute-and-Forward on a Multi-User Multi-Relay Channel

“…in [6]), iv) using the integer coefficients algorithm described in IV-2 but forcing relay m to compute an equation with a mm ≠ 0, i.e., R CoF Out (Alg. in [4]) v) using the algorithm described in [7] i.e., R CoF Out (Alg. in [7]) as functions of May 5, 2018 DRAFT Alg.…”

“…in [4]) v) using the algorithm described in [7] i.e., R CoF Out (Alg. in [7]) as functions of May 5, 2018 DRAFT Alg. OP Alg.…”

“…In [7], the authors propose a method to compute the integer coefficient vectors of the linear combinations. In this method, the relays jointly optimize the integer vectors in such a way that the transmission rate is maximized and the matrix formed by these vectors is full rank.…”

“…This method is not practical for large networks since additional signaling overhead is needed among the relays. In [4] and in contrast to [7], each relay independently (i.e. no coordination among the relays) computes an integer vector.…”

“…In May 5, 2018 DRAFT [6], we maximize the transmission rate by properly allocating the precoding factors (powers) at the users and computing the integer coefficients. The integer coefficients are jointly computed as in [7]. In this setting, each relay independently computes a linear combination.…”