Abstract:We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.
From: Prachi Mishra [view email]
[v1]
Sat, 9 May 2026 18:53:56 UTC (28 KB)
[v2]
Thu, 21 May 2026 14:09:54 UTC (28 KB)
[v3]
Sat, 29 Aug 2026 05:22:42 UTC (29 KB)
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