  This paper presents a new paradigm for image transmission through analog
error correction codes. Conventional schemes rely on digitizing images through
quantization (which inevitably causes significant bandwidth expansion) and
transmitting binary bit-streams through digital error correction codes (which
do not automatically differentiate the different levels of significance among
the bits). To strike a better overall performance in terms of transmission
efficiency and quality, we propose to use a single analog error correction code
in lieu of digital quantization, digital code and digital modulation. The key
is to get analog coding right. We show that this can be achieved by cleverly
exploiting an elegant "butterfly" property of chaotic systems. Specifically, we
demonstrate a tail-biting triple-branch baker's map code and its
maximum-likelihood decoding algorithm. Simulations show that the proposed
analog code can actually outperform digital turbo code, one of the best codes
known to date. The results and findings discussed in this paper speak volume
for the promising potential of analog codes, in spite of their rather short
history.
