We propose an irregular repetition slotted ALOHA (IRSA) based random-access protocol for the binary adder channel (BAC). The BAC captures important physical-layer concepts, such as packet generation, per-slot decoding, and information rate, which are neglected in the commonly considered collision channel model. We divide a frame into slots and let users generate a packet, to be transmitted over a slot, from a given codebook. In a state-of-the-art scheme proposed by Paolini et al. (2022), the codebook is constructed as the parity-check matrix of a BCH code. Here, we construct the codebook from independent and identically distributed binary symbols to obtain a random-coding achievability bound. Our per-slot decoder progressively discards incompatible codewords from a list of candidate codewords, and can be improved by shrinking this list across iterations. In a regime of practical interests, our scheme can resolve more colliding users in a slot and thus achieves a higher average sum rate than the scheme in Paolini et al. (2022).

翻译：本文针对二进制加法信道(BAC)提出一种基于不规则重复时隙ALOHA(IRSA)的随机接入协议。BAC捕获了重要的物理层概念，如数据包生成、每时隙译码和信息速率等，这些在通常考虑的碰撞信道模型中均被忽略。我们将帧划分为多个时隙，并让用户从给定码本中生成一个数据包，在某个时隙上传输。在Paolini等人(2022)提出的最新方案中，码本被构造为BCH码的奇偶校验矩阵。本文通过独立同分布的二进制符号构造码本，从而获得随机编码的可达性界。我们的每时隙译码器从候选码字列表中逐步剔除不相容码字，并可通过跨迭代缩减该列表来改进性能。在实际感兴趣的场景下，我们的方案能在单个时隙中解决更多碰撞用户问题，因此相较于Paolini等人(2022)的方案实现了更高的平均和速率。