The recent developments in the field of coding theory and sequence design have been marked by significant advancements in the construction and analysis of polar codes, polar lattices, and low ambiguity zone (LAZ) sequences. A notable trend is the exploration of novel mathematical constructs and techniques to enhance the performance and flexibility of these codes and sequences. For instance, the introduction of locally perfect nonlinear functions (LPNFs) has led to the development of new classes of LAZ sequence sets that are asymptotically optimal, addressing the need for efficient integrated sensing and communication (ISAC) systems. Similarly, the investigation into the simultaneous goodness of polar codes and polar lattices has provided explicit constructions that are optimal for both channel and source coding, leveraging the polarization technique. Furthermore, the study of polar-like lattices and their AWGN-goodness has deepened the understanding of their structural advantages, particularly in relation to polarization adjusted convolutional (PAC) lattices. On the practical side, there has been a push towards simplifying the implementation of polar codes in data compression systems, with proposals for construction-free polar compression schemes that offer improved flexibility and compression rates. Additionally, the theoretical underpinnings of the min-sum approximation in polar code decoding have been rigorously analyzed, providing insights into its effectiveness and limitations.

Noteworthy Papers

• Asymptotically Optimal Aperiodic and Periodic Sequence Sets with Low Ambiguity Zone Through Locally Perfect Nonlinear Functions: Introduces LPNFs to construct new classes of LAZ sequence sets, achieving asymptotic optimality and cyclically distinct properties.
• Construction of Simultaneously Good Polar Codes and Polar Lattices: Offers an explicit construction of codes and lattices that are optimal for both channel and source coding, based on the polarization technique.
• Revisit the AWGN-goodness of Polar-like Lattices: Provides a comprehensive analysis of polar-like lattices, highlighting the structural advantages of PAC lattices and their AWGN-goodness.
• Constant Weight Polar Codes through Periodic Markov Processes: Demonstrates that polarization can occur in constant weight codes derived from periodic Markov chains by fixing the initial state.
• Entropy Polarization-Based Data Compression Without Frozen Set Construction: Proposes a construction-free polar compression scheme that enhances flexibility and improves compression rates.
• An Analytical Study of the Min-Sum Approximation for Polar Codes: Offers a theoretical justification for the min-sum approximation in polar code decoding, detailing its impact on error probabilities and code construction.