We study a one-shot joint source-channel coding setting where the source is encoded once and broadcast to $K$ decoders through independent channels. Success is predicated on at least one decoder recovering the source within a maximum distortion constraint. We find that in the one-shot regime, utilizing disjoint codebooks at each decoder yields a codebook diversity gain, distinct from the channel diversity gain that may be expected when several decoders observe independent realizations of the channel's output but share the same codebook. Coding schemes are introduced that leverage this phenomenon, where first- and second-order achievability bounds are derived via an adaptation of the Poisson matching lemma (Li and Anantharam, 2021) which allows for multiple decoders using disjoint codebooks. We further propose a hybrid coding scheme that partitions decoders into groups to optimally balance codebook and channel diversity. Numerical results on the binary symmetric channel demonstrate that the hybrid approach outperforms strategies where the decoders' codebooks are either fully shared or disjoint.

翻译：我们研究一种单次联合信源信道编码场景，其中信源被编码一次并通过独立信道广播至 $K$ 个解码器。成功的判定标准是至少有一个解码器能在最大失真约束内恢复信源。我们发现，在单次编码体制下，每个解码器使用互斥码本可产生码本分集增益，这与信道分集增益不同——后者可能出现在多个解码器观测到信道输出的独立实现但共享相同码本的情况下。本文提出了利用此现象的编码方案，其中通过改进泊松匹配引理（Li and Anantharam, 2021）推导出一阶与二阶可达界，该引理适用于使用互斥码本的多个解码器。我们进一步提出一种混合编码方案，将解码器分组以最优平衡码本分集与信道分集。在二进制对称信道上的数值结果表明，该混合方案优于解码器码本完全共享或完全互斥的策略。