Coding techniques for information-theoretic strong secrecy on wiretap channels

Belief propagation;Girth;Sparse graph codes;Low-density parity-check (LDPC) codes;Information-theoretic security;Coding theory;Information theory

Subramanian, Arunkumar ; Electrical and Computer Engineering

University:Georgia Institute of Technology

Department:Electrical and Computer Engineering

关键词: Belief propagation;    Girth;    Sparse graph codes;    Low-density parity-check (LDPC) codes;    Information-theoretic security;    Coding theory;    Information theory;   

Others  :  https://smartech.gatech.edu/bitstream/1853/42776/1/subramanian_arunkumar_201112_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Traditional solutions to information security in communication systems act in the application layer and are oblivious to the effects in the physical layer. Physical-layer security methods, of which information-theoretic security is a special case, try to extract security from the random effects in the physical layer. In information-theoretic security, there are two asymptotic notions of secrecy---weak and strong secrecyThis dissertation investigates the problem of information-theoretic strong secrecy on the binary erasure wiretap channel (BEWC) with a specific focus on designing practical codes. The codes designed in this work are based on analysis and techniques from error-correcting codes. In particular, the dual codes of certain low-density parity-check (LDPC) codes are shown to achieve strong secrecy in a coset coding scheme. First, we analyze the asymptotic block-error rate of short-cycle-free LDPC codes when they are transmitted over a binary erasure channel (BEC) and decoded using the belief propagation (BP) decoder. Under certain conditions, we show that the asymptotic block-error rate falls according to an inverse square law in block length, which is shown to be a sufficient condition for the dual codes to achieve strong secrecy.Next, we construct large-girth LDPC codes using algorithms from graph theory and show that the asymptotic bit-error rate of these codes follow a sub-exponential decay as the block length increases, which is a sufficient condition for strong secrecy. The secrecy rates achieved by the duals of large-girth LDPC codes are shown to be an improvement over that of the duals of short-cycle-free LDPC codes.