Chaotic Analog Error Correction Codes: The Mirrored Baker´s Codes

A new class of analog codes based on 2-dimensional discrete-time chaotic systems, the baker\´s map, are proposed. The fundamental idea is to effectively transform the "sensitivity-to-initial-condition" property of a chaotic system to serve the "distance expansion" condition required by a good error correction code. By cleverly applying the baker\´s map on the tent map to achieve a higher dimensional nonlinear mapping, and by engineering a simple mirrored replication structure to protect against the weaker dimension, the proposed "mirrored baker\´s codes" promise considerably better performance than the existing tent map codes. A maximum likelihood detector is derived, simplified and evaluated. Comparison with the present-day digital coding systems, including convolutional codes and turbo codes, reveals a remarkably on-par performance achieved by the proposed new codes.