Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases.Two outer Air Vent bounds are established, showing that separate coding can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth trade-off regions for the general MDC-SR problem.The core of the new converse results is an exchange lemma, which can be Milk Jug established using Han’s subset inequality.