A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially coupled generalized LDPC codes with Bose-Chaudhuri-Hocquengham component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution.

Applying the max-product (and sum-product) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence or optimality of converged solutions or both. This paper presents an analysis of both attenuated max-product decoding and weighted min-sum decoding for low-density parity-check (LDPC) codes, which guarantees convergence to a fixed point when a weight factor, β, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution. For (dv, dc)-regular LDPC codes, the weight factor must satisfy β(dv-1)v-1)(dc-1) ≤ 1. In addition, the range of the weight factor for a provable ML decoding solution is extended to 0v-1) 1. In addition, counterexamples that show a fixed point might not be the ML decoding solution if β(dv-1) > 1 are given. Finally, connections are explored with recent work on the threshold of LP decoding.

Low-density parity-check (LDPC) convolutional codes (or spatially coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled scalar recursions. Our approach is based on constructing potential functions for both the coupled and uncoupled recursions. Our results actually show that the fixed point of the coupled recursion is essentially determined by the minimum of the uncoupled potential function and we refer to this phenomenon as Maxwell saturation. A variety of examples are considered including the density-evolution equations for: irregular LDPC codes on the BEC, irregular low-density generator-matrix codes on the BEC, a class of generalized LDPC codes with BCH component codes, the joint iterative decoding of LDPC codes on intersymbol-interference channels with erasure noise, and the compressed sensing of random vectors with independent identically distributed components.

Designing error-correcting codes for optical communication is challenging mainly because of the high data rates (e.g., 100 Gbps) required and the expectation of low latency, low overhead (e.g., 7% redundancy), and large coding gain (e.g., >9dB). Although soft-decision decoding (SDD) of low-density parity-check (LDPC) codes is an active area of research, the mainstay of optical transport systems is still the iterative hard-decision decoding (HDD) of generalized product codes with algebraic syndrome decoding of the component codes. This is because iterative HDD allows many simplifications and SDD of LDPC codes results in much higher implementation complexity. In this paper, we use analysis and simulation to evaluate tightly-braided block codes with BCH component codes for high-speed optical communication. Simulation of the iterative HDD shows that these codes are competitive with the best schemes based on HDD. Finally, we suggest a specific design that is compatible with the G.709 framing structure and exhibits a coding gain of >9.35 dB at 7% redundancy under iterative HDD with a latency of approximately 1 million bits.

Convolutional (or spatially-coupled) low-density parity-check (LDPC) codes have now been shown to approach capacity for a variety of problems. Yet, most of these results require sequences of regular LDPC ensembles with increasing variable and check degrees. Previously, Kasai and Sakaniwa showed empirically that, for the BEC, this limitation can be overcome by using spatially-coupled MacKay-Neal (MN) and Hsu-Anastasopoulos (HA) ensembles. In this paper, we prove this analytically for (k, 2, 2)-MN and (2, k, 2)-HA ensembles when k is at least 3. The proof is based on the simple approach to threshold saturation, introduced by Yedla et al., which relies on potential functions. The key step is verifying the non-negativity of a potential function associated with the uncoupled system. Along the way, we derive the potential function general multi-edge type (MET) LDPC ensembles and establish a duality relationship between dual ensembles of MET LDPC codes.

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we analyze a class of spatially-coupled generalized LDPC codes and observe that, in the high-rate regime, they can approach capacity under iterative hard-decision decoding. These codes can be seen as generalized product codes and are closely related to braided block codes.

Convolutional low-density parity-check (LDPC) codes (or spatially-coupled codes) have now been shown to achieve capacity on binary-input memoryless symmetric channels. The principle behind this surprising result is the threshold-saturation phenomenon, which is defined by the belief-propagation threshold of the spatially-coupled ensemble saturating to a fundamental threshold defined by the uncoupled system. Previously, the authors demonstrated that potential functions can be used to provide a simple proof of threshold saturation for coupled scalar recursions. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled vector recursions. The conditions of the theorem are verified for the density-evolution equations of: (i) joint decoding of irregular LDPC codes for a Slepian-Wolf problem with erasures, (ii) joint decoding of irregular LDPC codes on an erasure multiple-access channel, and (iii) admissible protograph codes on the BEC. This proves threshold saturation for these systems.

In this paper, we are interested in performance analyses of a multiple-input multiple-output (MIMO) multiple-access (MA) wireless network where Wyner's linear cellular array model is adopted. Notwithstanding some recent results have shown that, in the Wyner's model, the joint processing of the entire received signal with access point (AP) cooperation can dramatically enhance the system throughput because of the macrodiversity. However, in practice, the channel estimation quality from the providers of the macrodiversity is usually poor. Furthermore, existing literatures do not take channel estimation error into account. The channel estimation error provides us the motive to derive analytical solutions to the large-system throughput (or channel sum-rate) of the MIMO cellular network with imperfect channel estimations. Unlike the most large-system results, our derived results can not only be applied in the scenarios with any given input distributions (not necessarily Gaussian) from the mobile transmitters, but also clarify the performance of the network which was originally involved. Several issues we address including (1) how much of coherence interval should be spent for training and (2) the impact of AP cooperation is highlighted through the analytical results.

The transmitter output of OFDM or DMT systems with a rectangular window is known to have large spectral sidelobes. Windowing and pulse shaping have been proposed to reduce spectral leakage in the literature. If no extra cyclic prefix is available, windowing at the transmitter requires additional post-processing equalization at the receiver. In this paper, we design optimal windows with minimum spectral leakage. Moreover, we show that the post processing affects the SNR at the receiver and the resulting SNR can be given in a closed form. Furthermore, we demonstrate that we can have a good trade-off between SNR and spectral leakage.