Storage–repair tradeoff for (7,6,6) exact-repair codes

For exact-repair regenerating codes with (n,k,d)=(7,6,6), what is the optimal tradeoff between per-node storage and repair bandwidth? Recovery from any k nodes and exact reproduction from d helpers are required, with no linearity assumption.

Why it matters and what counts as progress

Why it matters: The seven-node case extends exact finite-parameter tradeoff knowledge beyond smaller regenerating-code systems.

What counts as progress: Determine the full tradeoff by matching information-theoretic converse bounds to code constructions and their space sharing.

How the problem developed

3 Dec 2013 · Partial result [1]
Chao Tian Characterized the exact storage-repair tradeoff for the smaller (4,3,3) regenerating-code case using an information-theoretic converse.
2015 · Partial result [2]
Chao Tian Characterized the (5,4,4) rate region, extending the exact-repair tradeoff results to a larger parameter set.
20 Oct 2026 · Tradeoff theorem [3]
Chao Tian Reported a complete converse for the (7,6,6) exact-repair storage-repair-bandwidth region without assuming linear codes; layered codes attain the bounds.

AI contribution

Exact Storage-Repair-Bandwidth Tradeoffs for (6,5,5) and (7,6,6) Exact-Repair Regenerating Codes

Chao Tian

The manuscript gives converse bounds that completely characterize the storage/repair-bandwidth tradeoffs of exact-repair regenerating codes for (n,k,d)=(6,5,5) and (7,6,6), without assuming linear codes. Previously known layered codes with space sharing attain the bounds.

AI involvementAI-led

ImportanceNotable

Technical verificationPartial

Human understandingFull