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 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：我们研究了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给$K$个译码器。成功的条件是在最大失真约束下至少有一个译码器能够恢复信源。我们发现，在单次机制中，每个译码器使用不相交码本可以产生码本多样性增益，这与多个译码器观察信道输出的独立实现但共享相同码本时可能预期的信道多样性增益不同。本文引入了利用这一现象的编码方案，通过适配允许多个译码器使用不相交码本的泊松匹配引理，推导出一阶和二阶可达界。我们进一步提出一种将译码器分组以优化码本与信道多样性平衡的混合编码方案。在二进制对称信道上的数值结果表明，混合方法优于译码器码本完全共享或完全不相交的策略。