Index Codes for the Gaussian Broadcast Channel Using Quadrature Amplitude Modulation

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.

I. Introduction

CODING for broadcast channels, where receivers know some part of the transmitted messages a priori, is called index coding and is well-known for noiseless binary broadcast channels [1]– [3]. In the case of noisy binary broadcast, the index codes of [4] provide equal error correcting capability at all receivers and exploit the receiver side information to enhance the code rate, while the codes of [5]– [7] transform side information into improvements in error performance. The capacity of general index coding over Gaussian broadcast channel is unknown, but information theoretic results are available for some special cases [8]– [12]. Separation-based coding schemes using a (noiseless) index code and a broadcast channel code are, in general, sub-optimal, since the channel decoders do not utilize the receiver side information, and the channel coding rate is limited by the receiver with the worst signal-to-noise ratio. This motivates schemes that perform index coding at the physical layer.