Outer bounds for exact repair codes
  We address the open problem of establishing the rate region for exact-repair regenerating codes for given parameters (n,k,d). Tian determined the rate region for a (4,3,3) code and found that it lies strictly within the functional-repair rate region. Using different methods, Sasidharan, Senthoor and Kumar proved a non-vanishing gap between the functional-repair outer bound and the exact-repair outer bound for codes with k>=3. Our main results are two improved outer bounds for exact-repair regenerating codes. They capture and then extend essential parts in the proofs by Tian and by Sasidharan, Senthoor and Kumar. We show that the bounds can be combined for further improvements. 
Iwan M. Duursma
cs.IT math.IT