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

TL;DR

This work tackles the pilot overhead problem in short-packet URLLC by proposing a pilot-free polar-coded modulation that splits each codeword into a QPSK blind-estimation component and a higher-order QAM data component. A two-phase hybrid decoder first extracts CSI from the QPSK segment via blind processing, then uses the decoded bits as implicit pilots to coherently decode the QAM segment, all while remaining compatible with rate-matching. The authors develop a DEGA-based optimization framework and a BI-AWGN/BICM approximation to design and analyze the split codes, validating the model with simulations that show up to 1.5 dB gains over PAT in multi-block fading and providing insights into rate allocation. The approach demonstrates that embedding channel learning into coding and modulation can reclaim pilot overhead, improving reliability and spectral efficiency for URLLC in realistic fading scenarios.

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.

Figures (8)

• Figure 1: Encoding structure of the proposed code-splitting method. Information bits are partitioned into two sub-messages that are independently encoded and modulated using different schemes. $\Pi$ is an interleaver for BICM BICM-Carie-98.
• Figure 2: Decoding flowchart showing sequential processing of QPSK and QAM portions with blind channel estimation.
• Figure 3: Code parameter optimization procedure.
• Figure 4: Comparison between theoretical BLER approximation (dashed lines) and Monte Carlo simulation (solid lines) for single block fading ($B=1$) with $M=600$ total coded bits and $M_1=32$ coded-pilot bits. Three code rates are shown: $R \in \{0.25, 0.5, 0.75\}$ bits/channel use. The theoretical analysis accurately predicts performance across all modulation orders and code rates.
• Figure 5: Comparison between theoretical BLER approximation and Monte Carlo simulation for three block fading ($B=3$) with $M=600$ coded bits and $M_b=16$ coded bits per block. The theoretical model maintains accuracy in multi-block fading scenarios across different modulation orders and code rates.