In this paper, we design erasure-correcting codes for channels with burst and random erasures, when a strict decoding delay constraint is in place. We consider the sliding-window-based packet erasure model proposed by Badr et al., where any time-window of width w contains either up to a random erasures or an erasure burst of length at most b. One needs to recover any erased packet with a strict decoding delay deadline of τ, where erasures are as per the channel model. Presently existing rate-optimal constructions in the literature require, in general, a field-size which grows exponential in τ, as long as a/τ remains a constant. In this work, we present a new rate-optimal code construction covering all channel and delay parameters, which requires an O(τ2) field-size. As a special case, when (b - a) = 1, we have a field-size linear in τ. We also present two other constructions having linear fieldsize, under certain constraints on channel and decoding delay parameters. As a corollary, we obtain low field-size, rate-optimal convolutional codes for any given column distance and column span. Simulations indicate that the newly proposed streaming code constructions offer lower packet-loss probabilities compared to existing schemes, for selected instances of Gilbert-Elliott and Fritchman channels.

We study the problem of designing error-correcting codes over channels with burst and random erasures, when a strict decoding delay constraint τ is in place. Badr et al. introduced a channel model wherein for any sliding-window of width w, at most one of the following erasures patterns are permissible; (i) a burst erasure of length ≤ b or (ii) a total of ≤ a random erasures. We present a rate-optimal code construction under this model, which covers all feasible channel and delay parameters. In contrast to existing rate-optimal code families which require a field-size at least as large as O((τα)), our a construction needs a field-size quadratic in the decoding delay constraint. For some parameters, the construction can be over linear field-size.