An Optimal Two-Step Decoding at Receivers with Side Information in PSK-Modulated Index Coding

TL;DR

This paper investigates optimal decoding strategies for noisy index coding over PSK-modulated broadcast channels, considering side information noise and demonstrating that minimizing transmission count does not always minimize error probability with multi-level modulations.

Contribution

It introduces a two-step decoding approach for unprioritized receivers, derives error probability expressions with noisy side information, and shows the decoding strategy depends on SNR levels.

Findings

Multi-level modulation changes the relation between transmission count and error probability.

Optimal decoding strategy varies with the SNR of side information broadcast.

Derived explicit error probability expressions considering noisy side information.

Abstract

This paper studies noisy index coding problems over single-input single-output broadcast channels. The codewords from a chosen index code of length $N$ are transmitted after $2^N$-PSK modulation over an AWGN channel. In "Index Coded PSK Modulation for prioritized Receivers," the authors showed that when a length-$N$ index code is transmitted as a $2^N$-PSK symbol, the ML decoder at a receiver decodes directly to the message bit rather than following the two-step decoding process of first demodulating the PSK symbol and equivalently the index-coded bits and then doing index-decoding. In this paper, we consider unprioritized receivers and follow the two-step decoding process at the receivers. After estimating the PSK symbol using an ML decoder, at a receiver, there might be more than one decoding strategy, i.e., a linear combination of index-coded bits and different subsets of side information bits, that can be used to estimate the requested message. Thomas et al. in ["Single Uniprior Index Coding With Min Max Probability of Error Over Fading Channels,"] showed that for binary-modulated index code transmissions, minimizing the number of transmissions used to decode a requested message is equivalent to minimizing the probability of error. This paper shows that this is no longer the case while employing multi-level modulations. Further, we consider that the side information available to each receiver is also noisy and derive an expression for the probability that a requested message bit is estimated erroneously at a receiver. We also show that the criterion for choosing a decoding strategy that gives the best probability of error performance at a receiver changes with the signal-to-noise ratio at which the side information is broadcast.