A noisy entropy inequality for boolean functions by Samorodnitsky is applied to binary codes. It is shown that a binary code that achieves capacity on the binary erasure channel admits optimal list size for list decoding on some binary symmetric channels (in a regime where this optimal list size is exponentially large).
翻译:Samorodnitsky 对布林函数的杂音 entropy 不平等性适用于二进制代码。 显示在二进制删除频道上实现能力的二进制代码允许某些二进制对称频道( 在这种最佳列表大小指数大的制度下) 列表解码的最佳列表大小 。