In the binary deletion channel with parameter p (BDCp) every bit is deleted independently with probability p. [1] proved a lower bound of (1−p)/9 on the capacity of the BDCp, yet currently no explicit construction achieves this rate. In this work we give an explicit family of codes of rate (1 −p)/16, for every p. This improves upon the work of Guruswami and Li [2] that gave a construction of rate (1−p)/120. The codes in our family have polynomial time encoding and decoding algorithms.
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机译:在带有参数p(BDC的二进制删除通道中
p inf>
)每一位都以概率p独立删除。 [1]证明了BDC容量的下界(1-p)/ 9
p inf>
,但目前尚无明确的构造可达到此速度。在这项工作中,我们为每个p给出了速率(1 -p)/ 16的明确代码族。这改进了Guruswami和Li [2]的工作,该工作给出了速率(1-p)/ 120。我们家族中的代码具有多项式时间编码和解码算法。
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