  Methods of communications using chaotic signals use an ability of a chaos
generator (encoder) and matched response system (decoder) to behave identically
despite the instability of chaotic oscillations. Chaotic oscillations cover a
wide spectral domain and can efficiently mask an information signal scrambled
by the chaotic encoder. At the same time the wide spectrum poses intrinsic
difficulties in the chaotic decoding if the chaotic signal is transmitted over
real communication channels with limited bandwidth. We address this problem
both numerically and experimentally. Two alternative ways to improve
communication with chaos over band-limited channels are investigated. The first
method employs a matching filter in the decoder which compensates channel
distortions of the transmitted signal. This modification does not change the
individual dynamics of chaotic systems in the synchronous state however the
information signal injected into the driving system, breaks the symmetry
between encoder and decoder and therefore exact recovery is impossible. We show
that this approach has limited ability for synchronization of chaotic encoder.
The second approach does not use adaptive compensation but relies on the design
of chaotic oscillators which produce narrow-band chaotic waveforms.
