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 secrecy
This 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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/42776 |
| Date | 29 August 2011 |
| Creators | Subramanian, Arunkumar |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Dissertation |
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