Streaming codes are a class of packet-level erasure codes that ensure packet recovery over a sliding window channel which allows either a burst erasure of size $b$ or $a$ random erasures within any window of size $(\tau+1)$ time units, under a strict decoding-delay constraint $\tau$. The field size over which streaming codes are constructed is an important factor determining the complexity of implementation. The best known explicit rate-optimal streaming code requires a field size of $q^2$ where $q \ge \tau+b-a$ is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible $\{a,b,\tau\}$ parameters, over a field of size $q^2$ for prime power $q \ge \tau$. This is the smallest-known field size of a general explicit rate-optimal construction that covers all $\{a,b,\tau\}$ parameter sets. We achieve this by modifying the non-explicit code construction due to Krishnan et al. to make it explicit, without change in field size.
翻译：串流代码是一种保证在滑动窗口通道上回收包件的包级压缩码,它允许在严格解码-代用限制$\tau+$$(tau+1美元)下,在任何大小的窗口中,在严格解码-代用限制$\tau$(tau$)的情况下,在任何(tau+1美元)的时间单位内,破解大小或随机删除美元($($(tau+1美元))单位。构建流码的字段大小是决定执行复杂性的一个重要因素。最著名的最明确速流出流代码的字段大小需要1美元=2美元,其中$q\ge\tou+b-a美元是一个主要能量。在这项工作中,我们提出了一个明确的速率最佳流代码代码代码代码,用于所有可能的 $a,b,\tau $($) $($) $(tau) $($) $(tau) $(tau) $($) $(tau) $($) $($) $($) $($) $(tau) $($) $($) $(t) $(t) $(t) $($) $(t) $(t) $) $(t) $(t) $) o) ) poot) poilt) logt) commol commol commol comm) comm) 。
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