This paper considers the design of practical schemes that enable two terminals, namely a source and a destination, to agree on a secret key in the presence of an eavesdropper (wire-tapper). The channel model considered is a fast Rayleigh fading wiretap channel with the constraints of quadrature phase-shift-keyed source symbols and hard-decision destination quantization. It is assumed that there exists a public feedback channel between the source and destination to facilitate the key-agreement process, however, any communication over the public channel is perfectly observed by the wiretapper. A key-agreement scheme employing irregular low-density parity-check (LDPC) codes is proposed, and its secrecy performance is measured in terms of the key rate between the source and destination and the leakage rate about the secret key at the wiretapper. A code search algorithm is also developed to design irregular LDPC codes to achieve good secrecy performance under various channel conditions.