K-hot encoding of selected mapping index in orthogonal frequency division multiplexing for peak to average power reduction is a method of encoding the selected mapping index without the complexity of a reliable side channel, and was first proposed in . In , I review and expand on this method .
In SLM-KHE, SI indexes are encoded by creating energy disparity in sub-vectors, before mapping to several OFDM symbols. A selector transmits an OFDM symbol with the minimal peak to average power ratio. At the receiver, the OFDM symbol is demodulated by DFT, energy disparity is measured and used to decode the SI index used by the transmitter, and original vector phases are restored based on the SI index detected. A block diagram from  is shown below.
The full paper in pdf format can be found in  below, and incudes brief backgrounds on orthogonal frequency division multiplexing (OFDM), the peak to average power problem in OFDM, selected mapping with side information (SLM), selected mapping with k-hot encoding (SLM-KHE), analysis descriptions, results, and other references. Correspondence on this topic is welcome.
 S. Y. Le Goff, S. S. Al-Samahi, B. K. Khoo, C. C. Tsimenidis, and B. S. Sharif, "Selected Mapping without Side Information for PAPR Reduction in OFDM," Wireless Communications, IEEE Transactions on, vol. 8, no. 7, pp. 3320-3325, 2009.
 Morgan, Mike Review of Selected Mapping with k-hot extension factor encoding of SI index, self-published, April 8, 2017