Quantized-Constraint Concatenation And The Covering Radius Of Constrained Systems
summary
Quantized-Constraint Concatenation (QCC) treats the constrained-encoder as an irreversible quantizer that embeds ECC codewords into the constraint and counts those edits as noise, yielding error correction linear in block length (Theta(n)) rather than O(sqrt n). Performance hinges on the constraint’s covering radius (combinatorial worst-case, e.g. zero-k RLL ≈ 1/(k+1)) and its essential covering radius (probabilistic, much smaller—roughly 1/2^{k+2} for zero-k RLL). Existence of good ECCs follows from GV bounds; constructing efficient quantizers and computing radii for general constraints remain open.
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chapters (11)
- 0:00Introduction
- 0:21Constraint codes in storage
- 3:41Traditional concatenation issues
- 6:36Quantized-constraint concatenation
- 9:04Quantizer operation and error budgeting
- 11:53Covering radius of constrained systems
- 14:06Formal covering radius definition
- 16:58Deep holes and constraint spread
- 17:20Essential covering radius
- 21:02Results and open problems
- 24:10Q&A
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