Improving the Runtime of Algorithmic Polarization of Hidden Markov Models
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We improve the runtime of the linear compression scheme for hidden Markov sources presented in a 2018 paper of Guruswami, Nakkiran, and Sudan. Under the previous scheme, compressing a message of length n takes O(n log n) runtime, and decompressing takes O(n^1 + δ) runtime for any fixed δ > 0. We present how to improve the runtime of the decoding scheme to O(n log n) by caching intermediate results to avoid repeating computation.
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