# Separable Codes for the Symmetric Multiple-Access Channel

## TL;DR

This paper investigates bounds on the rate of q-ary s-separable codes for noiseless symmetric multiple-access channels, generalizing previous binary models to more complex symmetric functions of inputs.

## Contribution

It extends the theory of s-separable codes to q-ary alphabets and symmetric MAC models, providing new upper and lower bounds on their rates.

## Key findings

- Derived bounds for q-ary s-separable codes in symmetric MACs.
- Generalized binary separable code results to q-ary case.
- Enhanced understanding of code performance limits in symmetric MACs.

## Abstract

A binary matrix is called an s-separable code for the disjunctive multiple-access channel (disj-MAC) if Boolean sums of sets of s columns are all distinct. The well-known issue of the combinatorial coding theory is to obtain upper and lower bounds on the rate of s-separable codes for disj-MAC. In our paper, we generalize the problem and discuss upper and lower bounds on the rate of q-ary s-separable codes for models of noiseless symmetric MAC, i.e., when at each time instant the output signal of MAC is a symmetric function of its s input signals.