Najeeb ul Hassan

Comparison of LDPC block and LDPC convolutional codes based on their decoding latency

We compare LDPC block and LDPC convolutional codes with respect to their decoding performance under low decoding latencies. Protograph based regular LDPC codes are considered with rather small lifting factors. LDPC block and convolutional codes are decoded using belief propagation. For LDPC convolutional codes, a sliding window decoder with different window sizes is applied to continuously decode the input symbols. We show the required Eb/N0 to achieve a bit error rate of 10-5 for the LDPC block and LDPC convolutional codes for the decoding latency of up to approximately 550 information bits. It has been observed that LDPC convolutional codes perform better than the block codes from which they are derived even at low latency. We demonstrate the trade off between complexity and performance in terms of lifting factor and window size for a fixed value of latency. Furthermore, the two codes are also compared in terms of their complexity as a function of Eb/N0. Convolutional codes with Viterbi decoding are also compared with the two above mentioned codes.

Wireless interconnect for board and chip level

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.

Reduced complexity window decoding schedules for coupled LDPC codes

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.

Improving code diversity on block-fading channels by spatial coupling

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.

Challenges and some new directions in channel coding

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, non-binary LDPC codes, and polar coding.

Non-uniform windowed decoding schedules for spatially coupled codes

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.

Protograph design for spatially-coupled codes to attain an arbitrary diversity order

This work focuses on the design of SC-LDPC codes for transmission over non-ergodic, block-fading channels. Our main contribution is an algorithm, allowing to start from a (J,K)-regular, uncoupled LDPC ensemble, from which one can recursively build up a protograph-based SC-LDPC ensemble having any target diversity order d. The diversity order is achieved assuming a low-complexity iterative decoding algorithm. The increase of d comes at the cost of increasing the memory constraint (i.e., the coupling parameter) of the SC-LDPC ensemble.

Energy-Efficient Transceivers for Ultra-Highspeed Computer Board-to-Board Communication

Enabling the vast computational and throughput requirements of future high performance computer systems and data centers requires innovative approaches. In this paper, we will focus on the communication between computer boards. One alternative to the bottleneck presented by copper wire based cable-bound communication is the deployment of wireless links between nodes consisting of processors and memory on different boards in a system. In this paper, we present an interdisciplinary approach that targets an integrated wireless transceiver for short-range ultra-high speed computer board-to-board communication. Based on our achieved results and current developments, we will also estimate energy consumption of such a transceiver.

SC-LDPC codes over the block-fading channel: Robustness to a synchronisation offset

Spatially-Coupled LDPC (SC-LDPC) codes have been recently shown to be very efficient for transmissions over nonergodic channels, in particular over block-fading channels [1]. In fact, it is possible to design a SC-LDPC code with any given code diversity [2]. In this work, we investigate the performance of SC-LDPC codes over block-fading channels, assuming a mismatch (or offset) between the first bit of a transmission packet and a first bit of a codeword. Such a mismatch is called the synchronisation offset, and it has a negative impact on the code diversity. We propose a data-allocation scheme for SC-LDPC codes that allows to obtain a robustness to the synchronisation offset. Combined together with the code design from [2], it allows to design efficient SC-LDPC codes, whose performance degrades only slowly under imperfect transmission conditions.

Non-Uniform Window Decoding Schedules for Spatially Coupled LDPC Codes

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.