On the Secrecy Gain of Isodual Lattices from Tail-Biting Convolutional Codes

The secrecy gain of Construction A isodual lattices obtained from rate 1/2 binary tail-biting convolutional codes is considered. The secrecy gain criterion has been proposed in lattice coding for the Gaussian wiretap channel to characterize the secrecy-goodness performance. The higher the secrecy gain, the smaller the eavesdropper’s success probability of correctly guessing the transmitted message. This work performs exhaustive code searches for even lengths up to 108 to find the best isodual codes obtained from rate 1/2 binary tail-biting convolutional codes of certain memory constraints in terms of secrecy gain and investigates the corresponding isodual lattices. Numerical results indicate that the best results found via this tail-biting technique perform similarly to the best-known isodual codes from the conventional pure double-circulant code construction up to length 40. This approach offers two advantages: (1) it provides reasonably good codes of “any” even lengths, and (2) practical maximal-likelihood decoding is available for these codes.