Extensible Polar Codes for Dynamic User Loads in IDMA Systems

This paper introduces a class of extensible polar codes for dynamic interleave-division multiple-access (IDMA) systems specifically designed to support short packet transmissions. The code can be dynamically shortened or extended by leveraging the generator matrix extension feature, allowing the code structure to be adaptive to varying user loads. To significantly enhance system performance, we establish one-to-one bit-protect pairs by strategically exploiting the design signal-to-noise ratio (design-SNR) and bit-channel reliability. Particularly, bit-channels in the extension part exhibiting higher reliability are paired with less reliable bit-channels from the original information set, maximizing performance gains by carefully selecting bit-protect pairs. We devise a simplified, multi-user-oriented extrinsic information transfer (EXIT) chart to streamline the search process for these optimal pairs, facilitating more efficient analysis. Our numerical results underscore the superior block-error rate (BLER) performance of the proposed multi-user polarized matrix extension (PME) based polar codes than traditional polar codes integrated with repetition codes in IDMA systems. Notably, the proposed codes consistently achieve competitive performance across diverse conditions of SNRs, code lengths, and user loads, illustrating their robustness and adaptability in dynamic IDMA environments.