# Binary-Tree Encoding for Uniform Binary Sources in Index Modulation Systems

## TL;DR

This paper introduces a binary-tree encoding method for index modulation in OFDM systems, optimizing pattern probabilities and power allocation to maximize data rates under uniform bit input constraints.

## Contribution

It proposes a novel binary-tree formalism for pattern mapping, develops approximate solutions for rate maximization, and introduces a heuristic for constrained probability distributions.

## Key findings

- Achieves maximum mutual information in low and high-SNR regimes.
- Offers significant rate improvements over conventional OFDM-IM.
- Develops a new binary-tree based encoding framework.

## Abstract

The problem of designing bit-to-pattern mappings and power allocation schemes for orthogonal frequency-division multiplexing (OFDM) systems that employ subcarrier index modulation (IM) is considered. We assume the binary source conveys a stream of independent, uniformly distributed bits to the pattern mapper, which introduces a constraint on the pattern transmission probability distribution that can be quantified using a binary tree formalism. Under this constraint, we undertake the task of maximizing the achievable rate subject to the availability of channel knowledge at the transmitter. The optimization variables are the pattern probability distribution (i.e., the bit-to-pattern mapping) and the transmit powers allocated to active subcarriers. To solve the problem, we first consider the relaxed problem where pattern probabilities are allowed to take any values in the interval [0,1] subject to a sum probability constraint. We develop (approximately) optimal solutions to the relaxed problem by using new bounds and asymptotic results, and then use a novel heuristic algorithm to project the relaxed solution onto a point in the feasible set of the constrained problem. Numerical analysis shows that this approach is capable of achieving the maximum mutual information for the relaxed problem in low and high-SNR regimes and offers noticeable benefits in terms of achievable rate relative to a conventional OFDM-IM benchmark.