In leader-based protocols for State Machine Replication (SMR), the leader's outgoing bandwidth is a natural throughput bottleneck. Erasure coding can alleviate this by allowing the leader to send each processor a single fragment of each block, rather than a full copy. The \emph{data expansion rate}, the ratio of total data sent to payload size, determines how close throughput can get to the underlying network bandwidth. We investigate the fundamental limits and possibilities for bandwidth-efficient leader-based consensus. On the negative side, we prove that protocols with 2-round finality (one round of voting) cannot achieve a data expansion rate below approximately 2.5, a bound that is matched by existing protocols. On the positive side, we show that protocols with 3-round finality (two rounds of voting) can push the data expansion rate arbitrarily close to 1. The key insight is that the second voting round provides a recovery mechanism: leaders can attempt aggressive erasure codes and safely fall back to more conservative ones when reconstruction fails, without compromising consistency. We present two protocols with 3-round finality realising this approach. Carnot 1 assumes $n \geq 4f+1$ processors (of which at most $f$ may be Byzantine) and achieves a clean design requiring no additional fragment dissemination beyond the initial protocol messages. Carnot 2 operates under the optimal resilience assumption $n \geq 3f+1$, at the cost of additional fragment dissemination when Byzantine processors interfere. Both protocols can incorporate stable leaders and optimistic proposals to maximise throughput and minimise latency. Under favourable conditions, with correct leaders and few actual faults, both protocols allow leaders to use data expansion rates approaching 1; under adversarial conditions, leaders can revert to safe expansion rates of approximately $1.33$ and $1.5$, respectively.

翻译：在基于领导者的状态机复制协议中，领导者的出站带宽是天然的吞吐量瓶颈。纠删码技术可以通过允许领导者向每个处理器发送每个数据块的单个片段而非完整副本，来缓解此瓶颈。数据扩展率（即发送的总数据量与有效载荷大小的比值）决定了吞吐量能够多接近底层网络带宽的理论上限。我们研究了基于领导者的带宽高效共识的基本极限与可能性。在负面结果方面，我们证明了具有两轮最终性（一轮投票）的协议无法实现低于约2.5的数据扩展率，该界限与现有协议的性能匹配。在正面结果方面，我们展示了具有三轮最终性（两轮投票）的协议可以将数据扩展率无限逼近于1。关键洞见在于第二轮投票提供了恢复机制：领导者可以尝试采用激进的纠删码方案，并在重构失败时安全回退至更保守的方案，同时不损害一致性。我们提出了两种实现此方法的三轮最终性协议。Carnot 1 假设存在 $n \geq 4f+1$ 个处理器（其中至多 $f$ 个可能为拜占庭故障），实现了简洁的设计，无需在初始协议消息之外额外分发片段。Carnot 2 在最优容错假设 $n \geq 3f+1$ 下运行，代价是在拜占庭处理器干扰时需要额外分发片段。两种协议均可结合稳定领导者与乐观提案机制，以最大化吞吐量并最小化延迟。在有利条件下（领导者正确且实际故障极少），两种协议均允许领导者使用接近1的数据扩展率；在对抗条件下，领导者可分别回退至约 $1.33$ 和 $1.5$ 的安全扩展率。