Noisy Index Coding with PSK and QAM

TL;DR

This paper explores transmitting index coded bits over AWGN channels using PSK and QAM signals, demonstrating bandwidth reduction and coding gains for receivers with side information, with QAM outperforming PSK for larger effective signal sets.

Contribution

It introduces a method to transmit index coded bits as PSK or QAM signals, providing conditions for coding gain and an algorithm to optimize signal mapping, enhancing efficiency and receiver performance.

Findings

Bandwidth is reduced by half using this transmission method.

Receivers with side information gain coding advantage under certain conditions.

QAM transmission outperforms PSK when effective signal sets have eight or more points.

Abstract

Noisy index coding problems over AWGN channel are considered. For a given index coding problem and a chosen scalar linear index code of length $N$, we propose to transmit the $N$ index coded bits as a single signal from a $2^N$- PSK constellation. By transmitting the index coded bits in this way, there is an $N/2$ - fold reduction in the bandwidth consumed. Also, receivers with side information satisfying certain conditions get coding gain relative to a receiver with no side information. This coding gain is due to proper utilization of their side information and hence is called "PSK side information coding gain (PSK-SICG)". A necessary and sufficient condition for a receiver to get PSK-SICG is presented. An algorithm to map the index coded bits to PSK signal set such that the PSK-SICG obtained is maximized for the receiver with maximum side information is given. We go on to show that instead of transmitting the $N$ index coded bits as a signal from $2^N$- PSK, we can as well transmit them as a signal from $2^N$- QAM and all the results including the necessary and sufficient condition to get coding gain holds. We prove that sending the index coded bits as a QAM signal is better than sending them as a PSK signal when the receivers see an effective signal set of eight points or more.