In this work we demonstrate how a lack of synchronization can in fact be advantageous in the problem of random access. Specifically, we consider a multiple-access problem over a frame-asynchronous 2-user binary-input adder channel in the unsourced setup (2-UBAC). Previous work has shown that under perfect synchronization the per-user rates achievable with linear codes over the 2-UBAC are limited by 0.5 bit per channel use (compared to the capacity of 0.75). In this paper, we first demonstrate that arbitrary small (even single-bit) shift between the user's frames enables (random) linear codes to attain full capacity of 0.75 bit/user. Furthermore, we derive density evolution equations for irregular LDPC codes, and prove (via concentration arguments) that they correctly track the asymptotic bit-error rate of a BP decoder. Optimizing the degree distributions we construct LDPC codes achieving per-user rates of 0.73 bit per channel use.

翻译：本文展示在随机接入问题中，缺乏同步实际上可以成为一种优势。具体而言，我们研究无源场景下帧非同步双用户二进制输入加法器信道（2-UBAC）的多址接入问题。先前工作表明，在完全同步条件下，基于2-UBAC的线性码可实现的每用户速率受限于每信道使用0.5比特（而信道容量为0.75）。本文首先证明，用户帧间任意小的偏移（甚至单比特偏移）即可使（随机）线性码达到每用户0.75比特的完整容量。此外，我们推导了非规则LDPC码的密度进化方程，并通过集中性论证证明其能准确追踪BP译码器的渐近误码率。通过优化度分布，我们构造出可实现每信道使用0.73比特每用户速率的LDPC码。