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.
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.
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. (Less)
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.
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.
An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the conventional approach, in terms of both complexity and performance, is presented. Conventionally, in each iteration, all symbol nodes and, subsequently, all the check nodes, send messages to their neighbors ("flooding schedule"). In contrast, in the proposed method, the updating of nodes is performed according to a serial schedule which propagates the information twice as fast. A density evolution (DE) algorithm for asymptotic analysis of the new schedule is derived, showing that, when working near the code's capacity, the decoder converges in approximately half the number of iterations. In addition, a concentration theorem is proved, showing that, for a randomly chosen serial schedule, code graph, and decoder input, the decoder's performance approaches its expected one as predicted by the DE algorithm, when the code length increases.
The best known practical algorithm for the decoding of low-density parity-check (LDPC) codes is the iterative sum-product or belief propagation algorithm, operating on a Tanner graph (TG) of the code. Conventionally, in each iteration, all the symbol nodes and subsequently all the check nodes in the TG pass new messages to their neighbors (the so-called "flooding schedule"). We propose a new message-passing schedule, called "probabilistic schedule". Unlike flooding, the probabilistic schedule operation is based on the structure of the TG, and probabilistically balances the frequency at which different symbol nodes update their outgoing messages in accordance with their girths. Our results show that, particularly for short block lengths, the new schedule offers a much better performance/complexity trade-off. For a particular example of a (1268, 456) code, at no cost in complexity, the probabilistic schedule not only decreases both the bit and message error rates by an order of magnitude, but also reduces the number of undetected errors considerably. This work shows the importance of scheduling in the performance of iterative decoding algorithms and suggests that a schedule which matches the structure of the TG can substantially improve the performance/complexity trade-off in the decoding of short LDPC codes.
Abstract — Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation, or message-passing, algorithm over the factor graph of the code. The traditional message-passing schedule consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling raises the problem of finding the best sequence of message updates. This paper presents practical scheduling strategies that use the value of the messages in the graph to find the next message to be updated. Simulation results show that these informed update sequences require significantly fewer iterations than standard sequential schedules. Complexity and implementability issues are also addressed. Index Terms — Belief propagation-algorithm, messagepassing schedule, error-control codes, low-density paritycheck codes. I.