How to Compute Modulo Prime-Power Sums

TL;DR

This paper introduces Quasi Group Codes (QGC), a new class of codes for computing modulo prime-power sums, demonstrating improved achievable rates in distributed source coding and MAC computation.

Contribution

The paper proposes Quasi Group Codes (QGC), a novel code class that is not closed under addition, with new bounds and improved performance over existing schemes.

Findings

QGC outperform previous coding schemes in certain scenarios.

Derived new packing and covering bounds for QGC.

Achieved better rates in distributed source coding and MAC computation.

Abstract

The problem of computing modulo prime-power sums is investigated in distributed source coding as well as computation over Multiple-Access Channel (MAC). We build upon group codes and present a new class of codes called Quasi Group Codes (QGC). A QGC is a subset of a group code. These codes are not closed under the group addition. We investigate some properties of QGC's, and provide a packing and a covering bound. Next, we use these bounds to derived achievable rates for distributed source coding as well as computation over MAC. We show that strict improvements over the previously known schemes can be obtained using QGC's.