What does Othello think he deserves for killing Desdemona

At the root of Othello's experience concerning Desdemona's death by his own hand, he unfortunately ends up violating his core principle. Seeing his unjust act for what it truly is and being confronted with the two basic options of continuing in pain or ending his life, he feels too much pain to continue and hope to end the pain but committing suicide as a penance for his misdeed. The pain comes to his own idyllic notions of right and wrong, in his own perception he has committed a grave offense against the set of rules he has chosen to live by.
In his eyes he has failed himself in his efforts to live up to even basic human standards, i.e not murdering innocents as an important aspect.The religious and philosophic references by themselves and in conjunction with one another help bring out the case-specific struggles multiple characters have with their conception of right and wrong in conjunction with striving for happiness. Thought the ambitions themselves portraited by the characters are many and varied the commonality amongst almost all the characters is a wealth of ambition. Desdemona uniquely painted as a character with significantly less ambition is the most tragic to lose as she is not only the victim of circumstance but innocent, pleasant, and beautiful.
As Othello realizes how his faults have lead to a tragedy he is uniquely responsible for, the point of no return has been passed and his only resolution is death, happiness now only a dream as he faces his own dogam down to oblivion.

When Othello finally recognizes that Desdemona was not, as he has been led to believe by Iago, "false as water," he is very distressed and feels he must be punished for what he has done, crying

Whip me, ye devils,From the possession of this heavenly sight!Blow me about in winds! roast me in sulphur!Wash me in steep-down gulfs of liquid fire!

He says that "in my sense, tis happiness to die"—suggesting that he feels so terrible about his misdeeds that to live with them would be far more difficult than simply to die and be put out of his misery. Later, in prevailing upon those assembled to remember him exactly as he was, he describes how he once killed a Turk, an enemy of Venice, and then kills himself. This indicates that he believes himself to be, because of what he has done to undeserving Desdemona, also someone who has acted against the laws of the Venetian state, and consequently somebody who should be punished in the same way. So, Othello both believes that he should be put to death and also wants to die because to live seems more difficult. Death is the only "happiness" remaining to him.