局部可解码性约束下的稀疏序列压缩
Compressing Sparse Sequences under Local Decodability Constraints
摘要：
我们考虑一个可变长度的信源编码问题受到本地可解码性的限制。特别是，我们调查的块长度缩放行为可达到的编码的$r$稀疏二进制序列，在约束条件下，任何源位可以被正确解码后，探测最多$d$码字位。我们认为自适应和非自适应访问模型，并推导出上界和下界，往往符合常数因子。值得注意的是，尽管在过去的三十年里进行了大量的研究，但我们的问题的固定块长度模拟的这种特征仍然未知。连接到通信复杂性也简要讨论。
英文摘要：
We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most $d$ codeword bits. We consider both adaptive and non-adaptive access models, and derive upper and lower bounds that often coincide up to constant factors. Notably, such a characterization for the fixed-blocklength analog of our problem remains unknown, despite considerable research over the last three decades. Connections to communication complexity are also briefly discussed.
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