Integer Forcing: Effective SNR Distribution and Practical Block-Based Schemes

TL;DR

This paper analyzes the effective SNR distribution in Integer Forcing (IF) receivers, introduces simple bounds and practical block-based schemes that reduce complexity and improve performance at low SNR.

Contribution

It provides bounds on the effective SNR distribution in IF, and proposes practical block-based schemes that simplify optimization and enhance low-SNR performance.

Findings

Bounds on effective SNR distribution are derived.

Block-based schemes reduce complexity and do not require rate reduction.

Simulations show block-wise schemes outperform at low SNR.

Abstract

Integer Forcing (IF) is a novel linear receiver architecture, where instead of separating the codewords sent by each transmitter, and decoding them individually, forces integer-valued linear combinations at each receive antenna, and decodes the linear combinations. The original codewords are obtained by inverting the integer-valued matrix. While demonstrating superior performance, IF requires complex optimization in order to find the optimal linear combinations, and demands either using multi-level nested lattice codes, or reducing the rates of all transmitters to equal the weakest one. Finally, the distribution of the resulting effective SNR is hard to evaluate. In this paper, we first give simple upper and lower bounds on the effective SNR of a single linear combination in IF. These expressions allow us to easily bound the distribution of the effective SNR for any given linear combination used. We then suggest two simple block-based IF schemes. These schemes, while sub-optimal, significantly reduce the complexity of the optimization process, and, more importantly, do not require reducing the rates of all transmitters, as decoding is done block-wise. Finally, we bound the distribution of the effective SNR of the decoding schemes, and show via simulations the superiority of block-wise schemes at low SNR.