Index Codes for the Gaussian Broadcast Channel using Quadrature Amplitude Modulation

TL;DR

This paper introduces new index coding schemes using multidimensional QAM for the Gaussian broadcast channel, improving message encoding flexibility and side information gain, and demonstrates near-capacity performance with simulations.

Contribution

It proposes linear index codes over integer rings for Gaussian broadcast channels that encode all messages uniformly and achieve high side information gain, unlike previous codes.

Findings

Achieves large side information gains with uniform message encoding.

Provides QAM index codes for up to 5 messages with power-of-two sizes.

Simulated 16-QAM index code operates within 4.3 dB of channel capacity.

Abstract

We propose index codes, based on multidimensional QAM constellations, for the Gaussian broadcast channel, where every receiver demands all the messages from the source. The efficiency with which an index code exploits receiver side information in this broadcast channel is characterised by a code design metric called "side information gain". The known index codes for this broadcast channel enjoy large side information gains, but do not encode all the source messages at the same rate, and do not admit message sizes that are powers of two. The index codes proposed in this letter, which are based on linear codes over integer rings, overcome both these drawbacks and yet provide large values of side information gain. With the aid of a computer search, we obtain QAM index codes for encoding up to 5 messages with message sizes 2^m, m <= 6. We also present the simulated performance of a new 16-QAM index code, concatenated with an off-the-shelf LDPC code, which is observed to operate within 4.3 dB of the broadcast channel capacity.