RANDOMNESS PROPERTIES OF NON-LINEAR CONVOLUTIONAL CODING

PETRUZZI, D. M.; CASTIÑEIRA MOREIRA, J.; LEVIN, D. G.

PROCEEDINGS VIII ISCTA

HW COMMUNICATIONS LTD.

Lugar: Ambleside, UK; Año: 2005 vol. 1 p. 200 - 205

<!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} @page Section1 {size:595.3pt 841.9pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> Abstract?In this paper we present convolutional coding schemes based on a non-linear finite state sequence machine designed over a Galois Field GF(q), whose output shows optimal randomness properties. Schemes with the maximum output sequence length (all zero input response) are presented for different Galois Fields. Two coefficients are used to quantitatively measure the proximity of the output behavior of these schemes with respect to the ideal white noise behavior. The proposed schemes outperform those presented by Frey in his paper, and achieve the optimal Quasi-Chaotic properties available for a given chaotic digital scheme. The proponed schemes have also a very little loss in BER performance so that they are a good alternative to the design of  systems for which encryption and error correction are important joint goals. They can be implemented with time variant coefficients in order to highly improve cryptographic properties of the transmission.