带反馈非对称信道的最优纠错编码

Optimal Error-correcting Codes for Asymmetric Channels with Feedback

带反馈非对称信道的最优纠错编码等同于Ulam Renyi问题的半谎搜索模型的最少提问次数qhl(m) .本文证明了qhl(m)的取值分布具有非交叉性 .借助于这一良好的分布特性 ,原始的确定最少提问次数精确值问题可以被简化为确定一个临界数问题并且这个临界数的存在性和唯一性得到了证明 .同时本文也改进了Cicalese等人的结果 ,在更大的范围内明确地给出了最少提问次数qhl(m)

Optimal errorcorrecting codes for asymmetric channels with feedback are the same as minimum number q hl (m) of questions in searching with half lies,a variant of UlamRenyi problem.It is proved that the distribution of q hl (m) is of noncross property.The original problem of determining the exact value of q hl (m) can be simplified to determine a critical number by virtue of this better property and the existence and uniqueness of this critical number are also proved.Furthemore,the exact values of q hl (m) are explicitly given for more integers m,thus strengthening previous results given by Cicalese et al.