Stefano Valle

Multiple-rate low-density parity-check codes with constant blocklength

This paper describes and analyzes low-density parity-check code families that support variety of different rates while maintaining the same fundamental decoder architecture. Such families facilitate the decoding hardware design and implementation for applications that require communication at different rates, for example to adapt to changing channel conditions. Combining rows of the lowest-rate parity-check matrix produces the parity-check matrices for higher rates. An important advantage of this approach is that all effective code rates have the same blocklength. This approach is compatible with well known techniques that allow low-complexity encoding and parallel decoding of these LDPC codes. This technique also allows the design of programmable analog LDPC decoders. The proposed design method maintains good graphical properties and hence low error floors for all rates.

Efficient design of non-binary LDPC codes for magnetic recording channels, robust to error bursts

In this work we consider an optimized design of q-ary low-density parity-check (LDPC) codes that takes into account their burst error correction capability. In recent works, the performance of LDPC decoding in presence of noise bursts has been related to the structure of the parity-check matrix. In particular, two approaches to characterize the burst error correction capabilities have been proposed in the literature. Following these ideas, we compare different matrix designs in order to choose the best matrix constraints to be maximized in a PEG construction. Several non-binary LDPC codes, generated with the proposed design methods are compared. Their performance are analyzed in the context of magnetic recording channels, where they are considered a promising alternative to the Reed Solomon (RS) codes.

NB-LDPC: Absorbing set and importance sampling

The identification of error sources when sub-optimal decoding algorithms are used is an open point both in binary and non-binary LDPC. Here a mathematical definition for absorbing sets in the case of non-binary LDPC is given and several examples are proposed to illustrate it. The definition is consistent with the error patterns resulting from Montecarlo (MC) simulations at high SNR. The absorbing sets patterns, as defined here, are used to predict the error floor of NB-LDPC with the Importance Sampling (IS). The IS and the MC simulation results match up very well when both are available.

Comparison Between Viterbi Detectors for Magnetic Recording Channels Based on Regressive and Autoregressive Noise Models

A recent work presents a regressive noise model for the data-dependent correlated noise, at the output of a magnetic recording channel detector. We have generalized this channel model, considering digital equalization and a more efficient correlation matrix, in order to make a comparison with the usual detector in a more realistic environment. Simulation results show that the regressive detector performs better when the number of trellis states is lower than needed, while both approaches are comparable when the number of states matches the channel memory.

Performance of Reed–Solomon codes in concatenated schemes with nonideal interleaving

The prediction of the performance of a Reed–Solomon (RS) code has an analytical solution in case of statistical independence of the errors at the input of the RS decoder (RSD). In concatenated schemes, this condition is often obtained through an interleaving device disrupting the correlation between erroneous symbols. Sometimes the ideal depth of such interleaver is too large to implement and the RSD must operate in sub-optimal conditions, for which no analytical formulas are available. In this paper, we propose a statistical model that can manage under-dimensioned interleavers. With a mild set of hypotheses on the behaviour of the inner decoder (ID), we derive analytical expressions for the performance of the concatenated code. Input data for the model can be analytical or can be obtained by simulation. We apply the method to two different types of inner codes, namely turbo codes and RS codes, and we compare the results predicted by the model with those obtained through simulation, when available, showing a very good agreement. Copyright

Data-Dependent Noise-Predictive Symbol-Based Detector for Perpendicular Magnetic Recording Channels

This work introduces a new formulation of the well-known data-dependent noise-predictive (DDNP) approach to whiten noise in partial response channel detection. The new approach is tailored for whitening the branches in the recently introduced symbol-based detectors that are demonstrated to have optimal performance in concatenation with non-binary error correction codes, such as non-binary low density parity check (LDPC) codes. This paper describes a new approach in the context of the perpendicular magnetic channel, where a symbol-based BCJR is concatenated with a non-binary LDPC decoder. Several approximations based on conventional DDNP implementations are suggested to quantify the performance of the new algorithm.