Approximation of Capacity for ISI Channels with One-bit Output Quantization

TL;DR

This paper proposes an approximation method for the capacity of ISI channels with 1-bit output quantization, enabling practical coding schemes for high bandwidth communication systems.

Contribution

It introduces a novel approximation of channel capacity that simplifies analysis and guides the design of practical coding schemes for quantized ISI channels.

Findings

Approximate capacity matches the true channel output with high probability.

Methods involve Gibbs distributions to compute the approximate capacity.

Provides Markovian schemes approaching the approximate capacity.

Abstract

Motivated by recent high bandwidth communication systems, Inter-Symbol Interference (ISI) channels with 1-bit quantized output are considered under an average-power-constrained continuous input. While the exact capacity is difficult to characterize, an approximation that matches with the exact channel output up to a probability of error is provided. The approximation does not have additive noise, but constrains the channel output (without noise) to be above a threshold in absolute value. The capacity under the approximation is computed using methods involving standard Gibbs distributions. Markovian achievable schemes approaching the approximate capacity are provided. The methods used over the approximate ISI channel result in ideas for practical coding schemes for ISI channels with 1-bit output quantization.