The paper explores the benefits of correlated decoding in improving the performance of logical algorithms in quantum computing. Correlated decoding leverages the deterministic propagation of errors during transversal entangling gates to reduce the space-time overhead of syndrome extraction. The authors analyze two decoders: the most-likely error (MLE) decoder and the hypergraph union-find with belief propagation (belief-HUF) decoder. They find that correlated decoding significantly improves the performance of both Clifford and non-Clifford transversal entangling gates. In particular, for deep logical Clifford circuits, correlated decoding reduces the number of syndrome extraction rounds per gate, leading to a substantial reduction in space-time cost. The results demonstrate that correlated decoding is a powerful tool for early fault-tolerant computation and has the potential to reduce the space-time cost of large-scale logical algorithms.The paper explores the benefits of correlated decoding in improving the performance of logical algorithms in quantum computing. Correlated decoding leverages the deterministic propagation of errors during transversal entangling gates to reduce the space-time overhead of syndrome extraction. The authors analyze two decoders: the most-likely error (MLE) decoder and the hypergraph union-find with belief propagation (belief-HUF) decoder. They find that correlated decoding significantly improves the performance of both Clifford and non-Clifford transversal entangling gates. In particular, for deep logical Clifford circuits, correlated decoding reduces the number of syndrome extraction rounds per gate, leading to a substantial reduction in space-time cost. The results demonstrate that correlated decoding is a powerful tool for early fault-tolerant computation and has the potential to reduce the space-time cost of large-scale logical algorithms.