In leader-based State Machine Replication (SMR), the leader's outgoing bandwidth is a natural throughput bottleneck. Erasure coding can alleviate this by letting the leader send each processor one fragment of each block rather than a full copy. The data expansion rate, the ratio of total data sent to payload size, determines how close throughput can get to network bandwidth. We investigate the fundamental limits of bandwidth-efficient leader-based consensus. We prove that protocols with 2-round finality (one voting round) cannot achieve a data expansion rate below approximately~$2.5$, matching existing protocols. Protocols with 3-round finality (two voting rounds) can do significantly better: the second voting round provides a recovery mechanism, letting leaders attempt aggressive erasure codes and safely fall back to conservative ones when reconstruction fails, without compromising consistency. We present two 3-round protocols realising this. Carnot~1 solves Extractable SMR, in which any correct processor can efficiently reconstruct any finalised block from fragments held by correct processors, but processors need not hold full blocks locally; this suffices for settings such as data availability layers. Carnot~1 assumes $n \geq 4f+1$ (at most $f$ Byzantine) and requires no fragment dissemination beyond the initial messages. Carnot~2 solves full SMR, where every correct processor eventually receives every finalised transaction. It operates under optimal resilience $n \geq 3f+1$, at the cost of additional fragment dissemination when Byzantine processors interfere. Both protocols support stable leaders. Under favourable conditions, leaders can use expansion rates approaching $1$; under adversarial conditions, they revert to safe rates of approximately $1.33$ and $1.5$, respectively, both well below the $2.5$ lower bound for 2-round finality.

翻译：在基于领导者的状态机复制（SMR）中，领导者的输出带宽是自然吞吐瓶颈。纠删码可通过让领导者向每个处理器发送区块的一个片段（而非完整副本）来缓解这一问题。数据扩展率（总发送数据量与有效载荷大小之比）决定了吞吐量接近网络带宽的程度。我们研究了带宽高效领导者共识的基本极限。我们证明，具有两轮终结性（一轮投票）的协议无法实现低于约$2.5$的数据扩展率，这与现有协议一致。具有三轮终结性（两轮投票）的协议可显著优化：第二轮投票提供了恢复机制，允许领导者尝试激进的纠删码，并在重构失败时安全回退到保守码，且不影响一致性。我们提出了两种实现该机制的三轮协议。Carnot~1解决可提取SMR，其中任意正确处理器可以从正确处理器持有的片段高效重构任意最终确定的区块，但处理器无需本地保存完整区块；这足以满足数据可用性层等场景。Carnot~1假设$n \geq 4f+1$（最多$f$个拜占庭节点），且无需在初始消息外进行额外片段传播。Carnot~2解决完整SMR，其中每个正确处理器最终都会收到每个最终确定的交易。它在最优容错$n \geq 3f+1$下运行，代价是当拜占庭处理器干扰时需要额外传播片段。两种协议均支持稳定领导者。在有利条件下，领导者可使用接近$1$的扩展率；在对抗条件下，它们分别回退到约$1.33$和$1.5$的安全速率，两者均远低于两轮终结性协议的下限$2.5$。