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From Bit to Block: Decoding on Erasure Channels
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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.
Forward citations
Cited by 2 Pith papers
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Capacity on BMS Channels via Code Symmetry and Nesting
The paper derives recursive two-look and three-look bounds showing Reed-Muller codes achieve capacity on BMS channels and a faster BSC decay rate via level-k inequalities.
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From Bit to Block: Capacity Achievement via Code Concatenation
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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