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

Justin P. Coon*, Mihai Alin Badiu, Ye Liu, Ferhat Yarkin, Shuping Dang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 that 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- A nd high-SNR regimes and offers noticeable benefits in terms of achievable rate relative to a conventional OFDM-IM benchmark.

Original languageEnglish
Article number8704951
Pages (from-to)1270-1285
Number of pages16
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number6
Publication statusPublished - Oct 2019
Externally publishedYes


  • OFDM
  • achievable rate
  • binary tree
  • index modulation
  • mutual information


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