A Design of Overlapped Chunked Code over Compute-and-Forward for Multi-Source Multi-Relay Networks†

This paper investigates the design of overlapped chunked codes (OCC) for multi-source multi-relay networks where a physical-layer network coding approach, compute-and-forward (CF) based on nested lattice codes (NLC), is applied for the simultaneous transmissions from the sources to the relays. This code is called OCC/CF. In this paper, OCC is applied before NLC before transmitting for each source. Random linear network coding is applied within each chunk. A decodability condition to design OCC/CF is provided. In addition, an OCC with a contiguously overlapping, but non-rounded-end fashion is employed for the design, which is done by using the probability distributions of the number of innovative codeword combinations and the probability distribution of the participation factor of each source to the codeword combinations received for a chunk transmission. An estimation is done to select an allocation, i.e., the number of innovative blocks per chunk and the number of blocks taken from the previous chunk for all sources, that is expected to provide the desired performance. From the numerical results, the design overhead of OCC/CF is low when the probability distribution of the participation factor of each source is dense at the chunk size for each source.