Performance of quantizers on noisy channels using structured families of codes

Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. It is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing a channel code rate that is independent of the overall transmission rate. We show that for certain families of practical channel codes and binary lattice vector quantizers, the overall distortion can still be made to decay to zero exponentially fast as the transmission rate grows, although the exponent is a sub-linear function of the transmission rate. This is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows. Explicit channel code rate schedules are obtained for several well-known families of channel codes.