Multilevel Coding Schemes for Compute-and-Forward with Flexible Decoding

TL;DR

This paper introduces a multilevel coding scheme for wireless two-way relaying that allows the relay to compute different functions based on channel conditions, achieving higher rates without channel state information at the transmitter.

Contribution

It proposes a flexible multilevel coding scheme enabling the relay to decode various functions adaptively, improving rate performance over fixed-function approaches.

Findings

Numerical results show significant rate improvements with the proposed scheme.

The scheme is universally achievable over a set of channel gains.

Flexibility in function choice enhances throughput compared to fixed or GF(4) coding.

Abstract

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits computation (or, decoding) of a class of functions at the relay. The function to be computed (or, decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or by adapting the function at the relay but coding over GF(4).