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Modern communications have moved away from point-to-point models to increasingly heterogeneous network models. In this article, we propose a novel controller-based architecture to deploy adaptive causal network coding in heterogeneous and highly meshed communication networks. Specifically, we consider using the software-defined network as the main controller. We first present an architecture for highly meshed heterogeneous multi-source multi-destination networks that represent the practical communication networks encountered in the fifth generation of wireless networks and beyond. Next, we present a promising solution to deploy network coding over the new architecture. We also present a new controller-based setting with which network coding modules communicate to attain the required information. Finally, we briefly discuss how the proposed architecture and network coding solution provide a good opportunity for future technologies. [ABSTRACT FROM AUTHOR]

A circulant-permutation-based spatially-coupled (SC) code is constructed by partitioning the circulant permutation matrices (CPMs) in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better cycle properties than their one-dimensional counterparts. In our framework, the multi-dimensional coupling is performed via an informed relocation of problematic CPMs. This work is general in the terms of the number of constituent SC codes that are connected together, the number of neighboring SC codes that each constituent SC code is connected to, and the length of the cycles whose populations we aim to reduce. Finally, we present a decoding algorithm that utilizes the structures of the MD-SC code to achieve lower decoding latency. Compared to the conventional SC codes, our MD-SC codes have a notably lower population of small cycles, and a dramatic BER improvement. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity. [ABSTRACT FROM AUTHOR]

Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention, thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying block code into a number of components and coupling their copies together. In this paper, we first introduce a general approach for the enumeration of detrimental combinatorial objects in the graph of finite-length SC codes. Our approach is general in the sense that it effectively works for SC codes with various partitioning schemes, column weights, and memories. Next, we present a two-stage framework for the construction of high performance binary SC codes optimized for the additive white Gaussian noise channels; we aim at minimizing the number of detrimental combinatorial objects in the error floor region. In the first stage, we deploy a novel partitioning scheme, called the optimal overlap partitioning, to produce the optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental objects in the lifted graph. SC codes constructed by our new framework have up to two orders of magnitude error floor performance improvement and up to 0.6 dB SNR gain compared to prior state-of-the-art SC codes. [ABSTRACT FROM AUTHOR]

In magnetic recording systems, consecutive sections experience different signal-to-noise ratios (SNRs). To perform error correction over these systems, one approach is to use an individual block code for each section. However, the performance over a section affected by a lower SNR is weaker compared to the performance over a section affected by a higher SNR. Spatially-coupled (SC) codes are a family of graph-based codes with capacity approaching performance and low latency decoding. An SC code is constructed by partitioning an underlying block code to several component matrices, and coupling copies of the component matrices together. The contribution of this paper is threefold. First, we present a new partitioning technique to efficiently construct SC codes with column weights 4 and 6. Second, we present an SC code construction for channels with SNR variation. Our SC code construction provides local error correction for each section by means of the underlying codes that cover one section each, and simultaneously, an added level of error correction by means of coupling among the underlying codes. Third, we introduce a low-complexity interleaving scheme specific to SC codes that further improves their performance over channels with SNR variation. Our simulation results show that our SC codes outperform individual block codes by more than one and two orders of magnitudes in the error floor region compared to the block codes with and without regular interleaving, respectively. This improvement is more pronounced by increasing the memory and column weight. [ABSTRACT FROM AUTHOR]

Spatially coupled (SC) codes are a class of sparse graph-based codes known to have capacity-approaching performance. SC codes are constructed based on an underlying low-density parity-check (LDPC) code, by first partitioning the underlying block code and then putting replicas of the components together. Significant recent research efforts have been devoted to the asymptotic, ensemble-averaged study of SC codes, as these coupled variants of the existing LDPC codes offer excellent properties. While the asymptotic analysis is important, due to simplifying assumptions and averaging effects, results from the asymptotic domain are not readily translatable to the practical, finite-length setting. Despite this chasm, the finite-length analysis of SC codes is still largely unexplored. In this paper, we tackle the problem of optimized design of SC codes in the context of magnetic-recording (MR) applications. In particular, we identify combinatorial structures in the graphical representation of the code that are detrimental in the MR setting. An intriguing observation is that for the same SC code, the problematic objects for the MR channels are combinatorially different from the additive white Gaussian noise (AWGN) setting, thus necessitating a careful code design approach for the MR applications. We first demonstrate that the choice of the so-called cutting vector, which guides the code partitioning in the SC code design, directly affects the cardinality of these problematic objects. In particular, we show that the number of problematic objects is the highest—and consequently that the performance is the worst—in the case of the degenerate cutting vector, which precisely corresponds to uncoupled LDPC block codes. We, therefore, show that coupling always improves the performance and that the degree of improvement is dependent on the choice of the cutting vector. We then extend our analysis to different column weights and present SC codes that outperform block codes with unoptimized edge weights by more than 3.5 orders of magnitude and that also outperform both optimized block codes and unoptimized SC codes by more than two orders of magnitude. Through presented examples, we demonstrate high performance of the proposed code design methodology. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the finite-length performance of separable circulant-based spatially-coupled (SCB-SC) LDPC codes for transmission over the additive white Gaussian noise channel. For a general class of finite-length graph-based codes, it is known that the existence of small absorbing sets causes a performance degradation in the error floor regime. We first present the mathematical conditions for the existence of absorbing sets in binary SCB-SC codes. This analysis enables us to find the exact number of absorbing sets as a function of the design parameters. In particular, our results show that the choice of the cutting vector affects the number of absorbing sets and, therefore, the error floor performance of the code. For a fixed column weight, we find provably optimal cutting vectors that result in the least number of absorbing sets. Furthermore, we extend our analysis to nonbinary SCB-SC codes, where we show that the choice of the cutting vector is not as critical as in the binary case. We provide an algorithm which provably removes the problematic nonbinary absorbing sets from nonbinary SCB-SC codes by informed selection of edge labels. Our simulation results show the superior error floor performance of our designed binary and nonbinary SCB-SC codes compared with binary unstructured and nonbinary quasi-cyclic SC codes available in the open literature. [ABSTRACT FROM PUBLISHER]