# Uniquely Decodable Ternary Codes for Synchronous CDMA Systems

## TL;DR

This paper introduces a new recursive ternary code design for overloaded synchronous CDMA systems that supports more users with low-complexity decoding, nearly matching the performance of maximum likelihood decoding.

## Contribution

It proposes a novel recursive code construction and a simple low-complexity decoder that outperforms existing codes in overloaded CDMA systems.

## Key findings

- Supports more users than existing codes
- Decoder complexity is significantly lower than ML decoder
- Performance nearly matches ML decoder in simulations

## Abstract

In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multiple-access (CDMA) systems. The proposed code set achieves larger number of users $K < K_{max}^t$ than any other known state-of-the-art ternary codes that offer low-complexity decoders in the noisy transmission. Moreover, we propose a simple decoder that uses only a few comparisons and can allow the user to uniquely recover the information bits. Compared to maximum likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has much lower computational complexity. We also derived the computational complexity of the proposed recursive decoder analytically. Simulation results show that the performance of the proposed decoder is almost as good as the ML decoder.