# Maximum Likelihood Decoder for Index Coded PSK Modulation for Priority Ordered Receivers

## TL;DR

This paper develops a maximum likelihood decoding method for index coded PSK modulation in broadcast channels, optimizing performance for prioritized receivers by selecting optimal code and mapping pairs based on PSK-ICG.

## Contribution

It introduces an algorithm to find optimal index code and mapping pairs that maximize PSK-ICG for prioritized receivers in index coded PSK modulation.

## Key findings

- The proposed algorithm achieves optimal PSK-ICG for the highest priority receiver.
- It ensures maximum possible gain for subsequent receivers in order of priority.
- The decision rule for ML decoding is derived for arbitrary mappings in the context of index coded PSK.

## Abstract

Index coded PSK modulation over an AWGN broadcast channel, for a given index coding problem (ICP) is studied. For a chosen index code and an arbitrary mapping (of broadcast vectors to PSK signal points), we have derived a decision rule for the maximum likelihood (ML) decoder. The message error performance of a receiver at high SNR is characterized by a parameter called PSK Index Coding Gain (PSK-ICG). The PSK-ICG of a receiver is determined by a metric called minimum inter-set distance. For a given ICP with an order of priority among the receivers, and a chosen $2^N$-PSK constellation we propose an algorithm to find (index code, mapping) pairs, each of which gives the best performance in terms of PSK-ICG of the receivers. No other pair of index code (of length $N$ with $2^N$ broadcast vectors) and mapping can give a better PSK-ICG for the highest priority receiver. Also, given that the highest priority receiver achieves its best performance, the next highest priority receiver achieves its maximum gain possible and so on in the specified order or priority.