This paper presents a puncturing pattern design for polar codes in hybrid automatic repeat request (HARQ) systems. We divide the encoder output bit sequence into sub-blocks. The sub-block indices are then permuted to generate a set of equivalent puncturing patterns (EPPs), each of which guarantees high reliability for message bits. A puncturing pattern for each HARQ transmission is selected from the generated set of EPPs. A Gaussian-approximation based method is proposed to optimize the selection, ensuring that additional redundancy bits are sent in HARQ transmissions. The proposed design has low complexity due to the limited number of sub-blocks and can be implemented offline to generate a lookup table of puncturing patterns. Up to 0.5 dB improvements in the error-correcting performance are obtained compared with state-of-the-art techniques.

Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in polar code construction is understudied. In this work, we propose using a sequence modeling framework to iteratively construct a polar code for any given length and rate under various channel conditions. Simulations show that polar codes designed via sequential modeling using transformers outperform both 5G-NR sequence and Density Evolution based approaches for both AWGN and Rayleigh fading channels.

Short-block length communication is becoming increasingly important for applications such as machine-to-machine communication, among others. This paper studies polar-coded modulation in the short-block length regime for decode-forward, amplify-forward and compress-forward relays. Our work seamlessly combines multi-level signaling, polar coding/decoding, and the requirements of relaying, into encoders and decoders that exhibit excellent performance. Compared with the state of the art in decode-forward, our work demonstrates 2.5 dB improvement (at block length 512). For shorter block lengths 256 and 128, this work is the first reported implementation for any coded modulation and any relaying protocol. In the category of polar-coded full-duplex relaying, this work presents the first implementation at any block length and for any relaying protocol. For decode-forward, we propose and analyze joint iterative belief propagation decoding with polar codes, and successive list decoding with polarization-adjusted convolutional (PAC) codes. For amplify-forward, we utilize PAC codes and successive list decoding. For the three relaying protocols, the respective dispersion bounds are presented for comparison, and the error exponent of the multi-level relaying coded modulations are analyzed to shed light on the results. Extensive simulations verify the performance of the proposed coding schemes.

We investigate the performance of multi-level polar coded modulation in the decode-forward relay channel. We begin by numerically analyzing the rates assigned to polar codes of all levels via chain rule and error exponent. The construction of polar codes follows the 5G standard. A joint decoding based on maximum ratio combining with multistage decoding is proposed for the destination. We simulate the error performance under 16QAM with gray labeling and Ungerboeck's set partitioning. In the half-duplex mode, a gain of 2.5dB is observed compared with the state of the art, consisting of 0.7 dB gain due to multistage decoding and 1.8dB gain due to the choice of labeling. In addition, the error performance according to error exponent is compared with the chain rule. A dispersion bound for the decode-forward relaying is calculated.

We investigate the performance of discrete (coded) modulations in the full-duplex compress-and-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information exchange algorithm are described for the joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known compress-and-forward achievable rate by two factors consisting approximately of the sum of the shaping gain (due to the scalar quantization) and the separation of the LDPC code implementation from AWGN capacity.