From Bit to Block: Capacity Achievement via Code Concatenation

Bin Zhang

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arXiv · 2607.05816

From Bit to Block: Capacity Achievement via Code Concatenation

Bin Zhang

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Abstract

This paper shows that bit-level reliability can be converted into block-level reliability for binary codes over BMS channels through Forney's concatenation scheme. The construction concatenates an inner code of rate R-o(1) and vanishing bit-error probability \epsilon with an outer code of rate 1-o(1) equipped with a bounded-distance decoder. We show that, when the outer correction radius exceeds \epsilon and a suitable large-deviation condition holds, the concatenated code has rate R-o(1) and vanishing block-error probability. Hence, a family with vanishing bit-error probability for rates below capacity can be converted into a capacity-achieving concatenated-code family. We further show that, when binary BCH codes are used as outer codes, inner codes with bit-error probability \epsilon=o(1/\log\log n) can be converted into a capacity-achieving concatenated family.

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Bin Zhang. 2026-07-07. From Bit to Block: Capacity Achievement via Code Concatenation. https://arxiv.org/abs/2607.05816

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