Staggered Diagonal Embedding Based Linear Field Size Streaming Codes

05/14/2020

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by   Vinayak Ramkumar, et al.

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An (a,b,τ) streaming code is a packet-level erasure code that can recover under a strict delay constraint of τ time units, from either a burst of b erasures or else of a random erasures, occurring within a sliding window of time duration w. While rate-optimal constructions of such streaming codes are available for all parameters {a,b,τ,w} in the literature, they require in most instances, a quadratic, O(τ^2) field size. In this work, we make further progress towards field size reduction and present rate-optimal O(τ) field size streaming codes for two regimes: (i) gcd(b,τ+1-a)> a (ii) τ+1 > a+b and b a ∈{0,a-1}.