Learning While Transmitting: Pilotless Polar Coded Modulation for Short Packet Transmission

Abstract

Short packets make channel learning expensive. In pilot-aided transmission (PAT), a non-negligible fraction of the packet is consumed by pilots, creating a direct pre-log loss and tightening the reliability margin needed for ultra-reliable low-latency communication. We propose a pilot-free polar-coded framework that replaces explicit pilots with \emph{coded pilots}. The message is carried by two polar-coded segments: a quadrature phase shift keying (QPSK) segment that is decodable without channel state information (CSI), and a higher-order quadrature amplitude modulation (QAM) segment that provides high spectral efficiency. The receiver employs \emph{hybrid decoding}: it first jointly infers CSI during successive-cancellation-based decoding of the QPSK segment by exploiting QPSK phase-rotation invariance together with polar frozen-bit constraints; the decoded QPSK symbols then act as \emph{implicit pilots} for coherent detection and decoding of the QAM segment. The split also makes rate adaptation practical by confining the symmetry/frozen-bit requirements for phase resolution to the QPSK segment, enabling puncturing and shortening without breaking the pilot-free mechanism. For multi-block fading, we optimize the split and code parameters via density evolution with Gaussian approximation (DEGA); for higher-order modulation, we use bit-interleaved coded modulation capacity approximation to obtain equivalent channel parameters. Incorporating channel-estimation error variance into the DEGA-based analysis, simulations over practical multi-block block-fading channels show gains up to $1.5$~dB over PAT in the short-blocklength regime.