Recently, several shaping schemes have been proposed for optical and wireless communications. A shaping technique modifies the distribution of transmit symbols to approximate the capacity achieving input distribution, hence resulting in a shaping gain. In this work, probabilistic and geometric shaping techniques for wireless backhaul channel are evaluated based on their frame error rate performance using soft and hard decision decoding with LDPC codes from the WiMAX and DVB-S2 standards. For soft decision decoding, both probabilistic and geometric shaping methods show significant gain compared to transmission with uniformly distributed symbols. However, when low complexity hard decision decoding is employed, only probabilistic shaping schemes exhibit large gains.

In this paper we optimize spatially coupled protographs for window decoding (WD) and arbitrary rate. Previous studies found that the belief propagation (BP) threshold of spatially coupled code ensembles achieves the maximum a posteriori (MAP) threshold of their underlying block code ensemble. This property requires a large coupling length L and thus the window decoder is considered to reduce latency and complexity of the decoding. To approach the BP threshold fast in the size of the window W, it is well known that the code requires a special structure to avoid degree-1 variable nodes inside the window. We further require additional structure to construct a systematic code with low encoding complexity, which unfortunately forces degree-1 variable nodes inside the window. Thus, we formulate an optimization problem to maximize the WD threshold and solve it by applying a differential evolution (DE) based algorithm. Compared to the regular protographs obtained by edge spreading, our optimized irregular protographs show a significant improvement in terms of WD threshold and finite length performance for small window sizes, hence leads to small decoding latency and complexity. Furthermore, for high rates our codes can compete with the highly optimized LDPC block codes from the WiMAX standard.

Spatially coupled low-density parity-check codes can be decoded using a graph-based message passing algorithm applied across the total length of the coupled graph. However, considering practical constraints on decoding latency and complexity, a sliding window decoding approach is normally preferred. In order to reduce decoding complexity compared with standard parallel decoding schedules, serial schedules can be applied within a decoding window. However, uniform serial schedules within a window do not provide the expected reduction in complexity. Hence, we propose non-uniform schedules (parallel and serial) based on measured improvements in the estimated bit error rate (BER). We show that these non-uniform schedules result in a significant reduction in complexity without any loss in performance. Furthermore, based on observations made using density evolution, we propose a non-uniform pragmatic decoding schedule (parallel and serial) that does not require any additional calculations (e.g., BER estimates) within the decoding process.

Spatially-coupled low-density parity-check (SC-LDPC) codes have been shown to be superior in performance than LDPC block codes. In order to comply with the practical constraints on latency, SC-LDPC codes are decoded using a window decoder that reduces the decoder latency and complexity compared to traditional block-wise decoding. However, so far the literature only considers the structural decoding latency of window decoder, ignoring the processing latency. Note that the processing latency directly impacts the decoder's throughput and is an important parameter in any modern communication system. The throughput of an iterative decoder is directly influenced by the number of iterations and hence in this paper we propose a fully parallel window decoder architecture for SC-LDPC codes where the decoding iterations are performed in parallel. This guarantees a high throughout while fulfilling the low latency requirements. The overall decoding latency (structural and processing latency) of the proposed window decoder architecture is compared with the classical window decoder.

Spatially coupled low-density parity-check (SC-LDPC) codes are considered for transmission over the block-fading channel. The diversity order of the SC-LDPC codes is studied using density evolution and simulation results. We demonstrate that the diversity order of the code can be increased, without lowering the code rate, by simply increasing the coupling parameter (memory) of a SC-LDPC code. For a (3,6)-regular SC-LDPC code with rate R = 1=2 and memory mcc= 4 a remarkable diversity of d = 10 is achieved without the need for any specific code structure. The memory of the SC-LDPC codes makes them robust against a non-stationary mobile-radio environment. The decoding of SC-LDPC codes using a latency constrained sliding window decoder is also considered.

Electronic systems of the future require a very high bandwidth communications infrastructure within the system. This way the massive amount of compute power which will be available can be inter-connected to realize future powerful advanced electronic systems. Today, electronic inter-connects between 3D chip-stacks, as well as intra-connects within 3D chip-stacks are approaching data rates of 100 Gbit/s soon. Hence, the question to be answered is how to efficiently design the communications infrastructure which will be within electronic systems. Within this paper approaches and results for building this infrastructure for future electronics are addressed.

Low-density parity-check convolutional (LDPCC) codes, also known as spatially coupled LDPC codes, can be decoded using a message passing algorithm. In order to limit decoding latency and complexity, windowed decoding can be applied. Updates within the window can be performed either in parallel or serially. However, simulation results show that uniform updating schedules do not provide the expected reduction in complexity when applied within the window. Hence we propose non-uniform schedules for updating the nodes based on measured improvements in the bit error rate. Nodes within the window that stop showing any improvement are excluded from the update list for the next iteration. This results in a reduction of up to 50% in complexity compared to uniform window schedules.

Window decoding schedules are very attractive for message passing decoding of spatially coupled LDPC codes. They take advantage of the inherent convolutional code structure and allow continuous transmission with low decoding latency and complexity. In this paper we show that the decoding complexity can be further reduced if suitable message passing schedules are applied within the decoding window. An improvement based schedule is presented that easily adapts to different ensemble structures, window sizes, and channel parameters. Its combination with a serial (on-demand) schedule is also considered. Results from a computer search based schedule are shown for comparison.

Currently, combining turbo or low-density parity-check (LDPC) codes with bit-interleaved coded modulation (BICM) is the most common coding scheme for bandwidth-limited channels. However, in order to be capacity achieving, shaping is necessary, which is difficult in conjunction with iterative processing. An alternative is interleave-division multiplexing (IDM), which can be either treated as a coded modulation scheme or a multiplexing scheme. In IDM, coded data sequences are linearly superimposed, thus avoiding the necessity of active signal shaping. The characteristics of IDM can be controlled by power and phase allocation. With typical parameter settings, IDM is non- bijective. In that case, the main task of channel coding is aiding to resolve the data sequences ("layers") at the receiver side, whereas noise mitigation is a secondary task. In this paper, we demonstrate that classical channel codes (like LDPC and turbo codes) fail when applied with IDM. In fact, repetition coding is quite useful. It is shown by means of an EXIT chart analysis that a concatenation of a high-rate convolutional code with an irregular repetition code matches well with the characteristics of an IDM a posteriori probability (APP) demapper.