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To facilitate applications in IoT, 5G, and beyond, there is an engineering need to enable high-rate, low-latency communications. Errors in physical channels typically arrive in clumps, but most decoders are designed assuming that channels are memoryless. As a result, communication networks rely on interleaving over tens of thousands of bits so that channel conditions match decoder assumptions. Even for short high rate codes, awaiting sufficient data to interleave at the sender and de-interleave at the receiver is a significant source of unwanted latency. Using existing decoders with non-interleaved channels causes a degradation in block error rate performance owing to mismatch between the decoder's channel model and true channel behaviour. Through further development of the recently proposed Guessing Random Additive Noise Decoding (GRAND) algorithm, which we call GRAND-MO for GRAND Markov Order, here we establish that by abandoning interleaving and embracing bursty noise, low-latency, short-code, high-rate communication is possible with block error rates that outperform their interleaved counterparts by a substantial margin. Moreover, while most decoders are twinned to a specific code-book structure, GRAND-MO can decode any code. Using this property, we establish that certain well-known structured codes are ill-suited for use in bursty channels, but Random Linear Codes (RLCs) are robust to correlated noise. This work suggests that the use of RLCs with GRAND-MO is a good candidate for applications requiring high throughput with low latency.