On iterative equalization, estimation, and decoding

Abstract

We consider the problem of coded data transmission over an inter-symbol interference (ISI) channel with unknown and possibly time-varying parameters. We propose a low-complexity algorithm for joint equalization, estimation, and decoding using an estimator, which is separate from the equalizer. Based on existing techniques for analyzing the convergence of iterative decoding algorithms, we show how to find powerful system configurations. This includes the use of recursive precoders in the transmitter. We derive novel a-posteriori probability equalization algorithms for imprecise knowledge of the channel parameters. We show that the performance loss implied by not knowing the parameters of the ISI channel is entirely a loss in signal-to-noise ratio for which a suitably designed iterative receiver algorithm converges. 2958 0-7803-7802-4/03/$17.00

Performance and design of a reduced complexity iterative equalizer for precoded ISI channels

“…As the number of states in the RS-SISO detector is reduced, the area under the corresponding transfer function, A DET is reduced. The area is approximately equal between the non-precoded and precoded case [7] and in this example is 0.72 for the 16-state detector. When the number of states is reduced to 4, in both cases, A DET reduces to approximately 0.67.…”

“…The precoder may be described in terms of a feedback polynomial for a recursive encoder, as in [5], however when Q > 1 this becomes unwieldy. A simpler approach uses discrete time state-space equations [7]. A generic precoder, with order m P and S P = 2 mP states, can be described by the following equations…”

“…In order to achieve high data rates in a limited bandwidth, higher modulation orders must be employed. In [7] a binary precoder for 8-PSK modulation was considered and its performance presented. With the use of modulation orders greater than two, the complexity of a maximum a-posterior (MAP) channel detector using the BCJR algorithm [8] becomes prohibitive.…”

Bayesian Equalization for LDPC Channel Decoding

“…?? we have plotted the inverse covariance matrix in (13) for 1000 BPSK symbols transmitted trough a channel with L = 6, n = 15 training symbols and an E b /N0 = 6 dB (this result corresponds to a particularization of Section VI-B). We plot the inverse covariance, because the zero covariates represent conditional independent components in a Markov random field [?].…”

“…Since the advent of turbo processing, some Bayesian approaches have been proposed to embed and consider the uncertainties in the whole iterative process of equalization and decoding. Otnes and Tuchler propose an approximate solution to include the uncertainties in the computation of the APP [13]. Wang and Chen put forward a blind algorithm, based on an iterative marginalization of the channel posterior through Gibbs sampling, to compute an approximation to the APP [14].…”