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From Bit to Block: Decoding on Erasure Channels

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arxiv 2501.05748 v2 pith:YW75WPBJ submitted 2025-01-10 cs.IT math.IT

classification cs.ITmath.IT
keywords blockerasureerrorchannelproofthresholdachieveapproach
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abstract

We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight of any $r$-dimensional subcode of $C$, for all small values of $r$. As a proof of concept, we use our machinery to obtain a new proof of the celebrated result that Reed-Muller codes achieve capacity on the erasure channel with respect to block error probability.

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  1. From Bit to Block: Capacity Achievement via Code Concatenation

    cs.IT 2026-07 unverdicted novelty 5.0 of 10

    Product coding converts bit-level capacity-achieving codes into block-level capacity-achieving codes at the same asymptotic rate, with an RM–BCH construction for BMS channels.

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