Turbo decoding for partial response channels

Abstract

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent work on the application of turbo decoding techniques to partial response channels has focused on using a parallel concatenation of convolutional encoders as the outer code and the partial response channel as the inner code. This system requires three a posteriori probability (APP) detectors-one matched to the channel and two matched to the constituent encoders. A simplified system will be presented that uses as its outer code a single convolutional code and as its inner code the partial response channel. The simplified system requires only two APP detectors, offering significant savings in complexity and computation time. This single convolutional code system will be shown to perform as well as the more complicated system, offering substantial gains over uncoded systems. Simulation results for three magnetic recording channel models will be presented: a partial response channel with additive white Gaussian noise, an equalized Lorentzian channel model, and a media noise model called the microtrack model. Since the use of an outer Reed-Solomon code is anticipated in an actual system, the burst-error statistics are investigated. System performance with various interleaver designs and precoders is also investigated. Index Terms-Concatenated coding, iterative methods, partial response signaling, turbo codes. I. INTRODUCTION T URBO codes were introduced by Berrou et al. [1] in 1993 as two or more parallel concatenated convolutional codes (PCCC's) connected with an interleaver and decoded using an iterative technique. These codes are capable of operating near Shannon capacity on an additive white Gaussian noise (AWGN) channel. The term "turbo decoding" has subsequently come to refer to this iterative decoding process. Therefore, in this paper, Paper approved by S. S. Pietrobon, the Editor for Coding Theory and Techniques of the IEEE Communications Society.

Noise Correlation-Aided Iterative Decoding for Magnetic Recording Channels

“…In this section the performance of all three decoding schemes is evaluated using computer simulations and compared to that of the benchmark scheme of [18], which does not employ the knowledge of the noise correlation. The recording densities of 2.25 and 2.86 are used.…”

“…We also investigated the convergence behavior of these four decoding schemes using different precoders and found that they obeyed similar trends. (L=scheme [18] iteration I1 10-5, coding gains in the range of 1-1.8 dB can be attained at a recording density of 2.25, whereas higher gains of 1.8-3.7 dB are achieved at the higher recording density of 2.86. This indicates that the three decoding schemes are capable of exploiting the knowledge of noise correlation very effectively, leading to performance improvement of the turbo decoding system in the magnetic recording channels in comparison to that of the benchmark scheme.…”

“…1 comprises a parallel concatenated convolutional encoder, a MUX/puncturing block, a channel interleaver /r2, and a precoder [18]. The data bit sequence dl,d2,..., d denoted as dN having a length of N is encoded by the Recursive Systematic Convolutional encoders RSC1 and RSC2, where RSC2 is fed by the turbo interleaver zT The parity bits RSC1 and RSC2 are appropriately punctured and multiplexed with the data sequence for the sake of achieving a code rate of 8/9.…”

“…3 and 4 illustrate the BER performance of the three decoding schemes in comparison to that of the benchmark scheme in [18] and to the Noise Predictive Turbo Systems with Hard Feedback (NPTS/HF) proposed in [15] (here we used the linear prediction order of 3), at recording densities of 2.25 and 2.86, respectively. The recording densities of 2.25 and 2.86 which lie in the typical operational range of the recoding densities used for PR-4-equalized Lorentzian channels [8]- [10], [24], [26], are selected for the sake of comparison.…”

“…The a posteriori probability (APP) of the coded bits was calculated and used for estimating the average values of both the channel output and noise for the sake of improving the achievable performance. Although impressive performance results were attained, the number of iterations required was as high as [16][17][18][19][20]. In [16] Fig.…”