Thresholds for Iterative Equalization of Partial Response Channels Using Density Evolution

This paper focuses on the computing of the thresholds for iterative equalization and decoding of partial response channel, such as what are of interest in high density magnetic recording. Extensive simulations on the performance of turbo codes, low density parity check (LDPC) codes and single-parity check turbo product codes (TPC/SPC) over partial response channels reveal very encouraging bit error rate (BER) performance, but cast little insight into the fundamental limitation within the existing suboptimal decoding. This work uses the method of density evolution with Gaussian approximation to investigate the achievable capacity by taking into consideration of both the code’s structural properties and the iterative decoding algorithm. A unified framework involving different outer codes, including (punctured) convolutional codes (also known as serial turbo), LDPC codes and TPC/SPC codes, is presented. Certain interesting issues in the decoding optimization are investigated. The tightness demonstrated by the bound attributes density evolution to be a very useful tool to be extended for capacity analysis of a broad range of iterative processes.