We present MINE (Memory-efficient INference Engine), a lossless entropy coding approach that accelerates single-stream inference of Large Language Models (LLMs), where existing lossless compression methods yield speedups only for specific data types such as \texttt{BF16} and under additional assumptions. Single-stream decoding is strongly memory-bound, since every weight must be streamed from memory once per generated token and requests cannot be batched in local or low-latency deployments. At the core of MINE is dtANS-LLM, a GPU entropy coding scheme adapted from the prior dtANS to the needs of LLM inference. It exploits the non-uniform distribution of weights, which persists even after quantization, and exposes hyper-parameters that trade compression ratio against decoding cost. We auto-tune these parameters for each tensor and GPU to obtain the Pareto front between model size and decoding latency. MINE integrates into vLLM as a plugin and selects the best kernel configuration for a given memory budget. On Llama~3.1~8B~Instruct with a 2.1-bit EntQuant checkpoint, MINE achieves speedups of 2.52$\times$ and 1.48$\times$ over the fastest baseline on an RTX~4060~Ti and an RTX~5090, at effective bitrates of 2.24 and 3.43~bits per weight. MINE is available as open source.

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