Capacity approaching signal constellations for channels with memory

The i.i.d. rate of a channel is the mutual information rate between the channel input and the channel output when the channel input symbols are independent, identically distributed (i.i.d.) and equally likely. We design a coding strategy that achieves rates higher than the i.i.d. rate of a partial response channel (intersymbol interference channel with inputs constrained to binary values), while still allowing simple encoding and decoding. The strategy breaks the code into an inner trellis code and an outer block code. This paper concentrates on the design of the inner trellis code. The trellis code is designed according to sub-optimal Markov state transition probabilities which are determined by a rate-optimizing iterative algorithm so that the i.i.d. rate of the trellis code is near the channel capacity. We construct the trellis code using integer approximations to these transition probabilities. This yields a signal constellation that reduces the shaping loss, so that a properly constructed outer code can achieve rates near the channel capacity. We demonstrate that the proposed trellis code, with an appropriately optimized outer irregular low-density parity-check code, achieves rates that surpass the channel i.i.d. information rate.