Proving threshold saturation for nonbinary SC-LDPC codes on the binary erasure channel

We analyze nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group for transmission over the binary erasure channel. We prove threshold saturation of the belief propagation decoding to the potential threshold, by generalizing the proof technique based on potential functions recently introduced by Yedla et al. The existence of the potential function is also discussed for a vector sparse system in the general case, and some existence conditions are developed. We finally give density evolution and simulation results for several nonbinary SC-LDPC code ensembles

Frequency packing and multiuser detection for CPMs: how to improve the spectral efficiency of DVB-RCS2 systems

We consider a frequency division multiplexed system where each user adopts a continuous phase modulation (CPM) and multiuser detection is employed at the receiver side. The spectral efficiency (SE) is used as a performance measure to compare, from an information-theoretic point of view, different modulation formats. More precisely, we consider the new CPM formats recently included in the DVB-RCS2 standard. We describe a framework for computing the information rate (IR) and the SE of such systems, and use it for optimizing the channel spacing between adjacent users and the CPM phase response. Our analysis reveals that modulation formats adopted in the DVB-RCS2 standard are suboptimal in terms of SE, while if we allow multiuser detection excellent performance can be achieved by using simple binary formats and highly frequency packed signals. Furthermore, we consider practical schemes, where CPMs are serially concatenated with an outer code, and a low-complexity multiuser receiver is employed, showing that the theoretical limits predicted by the IR analysis can be approached

On the design of variable-rate optimal convolutional encoders for turbo codes

Recently, we proposed a new design technique to construct high-rate convolutional codes based on a structure formed by a block encoder and a simpler convolutional encoder (Graell i Amat, A. et al., IEEE Commun.. Lett., vol.5, no.11, p.453-5, 2001). The search technique was based on the optimization of the output weight enumerating function of the code. We now prove that every (n,n-1) convolutional code can be reduced to this structure. Following this result and suitably modifying our earlier search algorithm, we have been able to obtain the best (n, n-1) convolutional encoders to be used in the design of turbo codes. In this case, the search is aimed at the optimization of the input-output weight enumerating function of the encoders. We also derive an inverse puncturing method that can be applied to these high-rate convolutional codes to obtain a sequence of the (almost) best convolutional encoders. With such a method, a whole family of good encoders with different rates is obtained using the same encoder-decoder, thus permitting a great versatility that can be exploited in practical implementations