DISCRETE MULTIPLE TONE MODULATION WITH COSET CODING FOR THE SPECTRALLY SHAPED CHANNEL

In this paper we develop a discrete approach to multiple tone modulation for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and well known high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. The design of the energy distribution and coded information allocation over the subchannels is optimized for the finite block length case and for the coset code concatenation, leading to an implementable coding system with optimized performance for the channel with ISI. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels is evaluated at different values of bits per sample. Using sufficiently long blocks for a particular ISI pattern, it can be shown that the implementable techniques presented here achieve the cut-off rate for any channel with ISI in the presence of additive Gaussian noise. In addition, this discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes.