Explicit Information-Debt-Optimal Streaming Codes With Small Memory
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For a convolutional code in the presence of a symbol erasure channel, the information debt I(t) at time t provides a measure of the number of additional code symbols required to recover all message symbols up to time t. Information-debt-optimal streaming (iDOS) codes are convolutional codes which allow for the recovery of all message symbols up to t whenever I(t) turns zero under the following conditions; (i) information debt can be non-zero for at most τ consecutive time slots and (ii) information debt never increases beyond a particular threshold. The existence of periodically-time-varying iDOS codes are known for all parameters. In this paper, we address the problem of constructing explicit, time-invariant iDOS codes. We present an explicit time-invariant construction of iDOS codes for the unit memory (m=1) case. It is also shown that a construction method for convolutional codes due to Almeida et al. leads to explicit time-invariant iDOS codes for all parameters. However, this general construction requires a larger field size than the first construction for the m=1 case.
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