EG-LDPC codes for the erasure wiretap channel

Abstract

The wiretap channel model, proposed by Wyner, has been studied by various authors from the perspectives of security, reliability and cryptographic protocols. A basic theme of these discussions has been information theoretically secure communication whose degree of secrecy can be theoretically proved. This paper explains a practical implementation of Euclidean Geometry (EG) — Low Density Parity Check (LDPC) codes for wiretap channels of type I and II. The focus has been on efficient encoding and decoding by taking advantage of the cyclic nature of EG codes. The generalized Hamming weights of EG codes can be bounded using those of primitive BCH codes. This provides security guarantees for EG codes in wiretap channels. The asymptotic threshold analysis from the LDPC viewpoint provides added guarantees at long blocklengths. Overall, EG-LDPC codes are promising candidates for low-complexity coding over wiretap channels.