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 \emph{``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.