After a death sentence is affirmed in state collateral review, the prisoner may file for federal habeas corpus, which is a unique type of lawsuit that can be brought in federal courts. Federal habeas corpus is a species of collateral review, and it is the only way that state prisoners may attack a death sentence in federal court (other than petitions for certiorari to the United States Supreme Court after both direct review and state collateral review). The scope of federal habeas corpus is governed by the Antiterrorism and Effective Death Penalty Act of 1996, which restricted significantly its previous scope. The purpose of federal habeas corpus is to ensure that state courts, through the process of direct review and state collateral review, have done at least a reasonable job in protecting the prisoner's federal constitutional rights. Prisoners may also use federal habeas corpus suits to bring forth new evidence that they are innocent of the crime, though to be a valid defense at this late stage in the process, evidence of innocence must be truly compelling.
If prisoners use federal habeas corpus to present evidence that they're innocent, what must the evidence be?
truly compelling

Bermuda's modern black population contains more than one demographic group. Although the number of residents born in Africa is very small, it has tripled between 2000 and 2010 (this group also includes non-blacks). The majority of blacks in Bermuda can be termed "Bermudian blacks", whose ancestry dates back centuries between the 17th century and the end of slavery in 1834, Bermuda's black population was self-sustaining, with its growth resulting largely from natural expansion. This contrasts to the enslaved blacks of the plantation colonies, who were subjected to conditions so harsh as to drop their birth rate below the death rate, and slaveholders in the United States and the West Indies found it necessary to continue importing more enslaved blacks from Africa until the end of slavery (the same had been true for the Native Americans that the Africans had replaced on the New World plantations). The indigenous populations of many West Indian islands, and much of the South-East of what is now the United States that had survived the 16th- and 17th-century epidemics of European-introduced diseases then became the victims of large-scale slave raiding, with much of the region completely depopulated. When the supply of indigenous slaves ran out, the slaveholders looked to Africa). The ancestry of Bermuda's black population is distinguished from that of the British West Indian black population in two ways: firstly, the higher degree of European and Native American admixture; secondly, the source of the African ancestry.
Why were so many blacks repeatedly being imported from Africa?
conditions so harsh as to drop their birth rate below the death rate

Hoover began using wiretapping in the 1920s during Prohibition to arrest bootleggers. In the 1927 case Olmstead v. United States, in which a bootlegger was caught through telephone tapping, the United States Supreme Court ruled that FBI wiretaps did not violate the Fourth Amendment as unlawful search and seizure, as long as the FBI did not break into a person's home to complete the tapping. After Prohibition's repeal, Congress passed the Communications Act of 1934, which outlawed non-consensual phone tapping, but allowed bugging. In the 1939 case Nardone v. United States, the court ruled that due to the 1934 law, evidence the FBI obtained by phone tapping was inadmissible in court. After the 1967 case Katz v. United States overturned the 1927 case that had allowed bugging, Congress passed the Omnibus Crime Control Act, allowing public authorities to tap telephones during investigations as long as they obtain a warrant beforehand.
What tool did Hoover use to find bootleggers?
wiretapping