Structural Properties of Erasure Codes for Streaming Communication
summary
Defines a sliding-window channel model that allows either a burst of length B or up to N isolated erasures in any window W and proves an upper bound R/(1−R)·(B+N) ≤ min(W,T+1) with a constructive lower bound within one unit of T. Builds layered convolutional codes called MiDAS codes (split each packet into U and V, repetition + erasure layers), requires field sizes on the order of T^3 for best constructions, and shows in simulations (delay 12, rate ≈1/2) a practical N=2, B=9 design that outperforms single-purpose codes; relates performance to column distance and column span.
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chapters (17)
- 0:00Intro
- 4:38Recap
- 6:21Field Size
- 9:34Example
- 10:26Code Construction
- 12:34Code Construction Example
- 15:26HighLevel Idea
- 16:59Extension
- 18:22Structural Properties
- 19:07Column Distance
- 20:24Column Span
- 21:49Statistical Models
- 22:39Simulation
- 24:12Freshman Channel
- 24:43Multicast Extension
- 25:12Other Extensions
- 26:28Conclusion