Explicit Information-Debt-Optimal Streaming Codes With Small Memory

M. Nikhil Krishnan; Myna Vajha; Vinayak Ramkumar; P. Vijay Kumar

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arXiv · 2305.06303

Explicit Information-Debt-Optimal Streaming Codes With Small Memory

M. Nikhil Krishnan·Myna Vajha·Vinayak Ramkumar·P. Vijay Kumar

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Abstract

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 ($i$DOS) 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 $i$DOS codes are known for all parameters. In this paper, we address the problem of constructing explicit, time-invariant $i$DOS codes. We present an explicit time-invariant construction of $i$DOS 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 $i$DOS 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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BibTeX RIS

M. Nikhil Krishnan, Myna Vajha, Vinayak Ramkumar, P. Vijay Kumar. 2023-05-10. Explicit Information-Debt-Optimal Streaming Codes With Small Memory. https://arxiv.org/abs/2305.06303

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