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IEEE Transactions on Communications

Non-Uniform Window Decoding Schedules for Spatially Coupled LDPC Codes

Najeeb ul Hassan, Alí Emre Pusane, Michael Lentmaier, Gerhard Paul Fettweis, Daniel J. Costello

Published Nov 29, 2016• 29 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2016.2633466

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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.
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)
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.
Abstract Spatially coupled low‐density parity‐check (SC‐LDPC) codes generally use a window decoding scheme, which is known to yield a near‐optimal decoding, compared to full block decoding. Recently, a non‐uniform schedule has been proposed to eliminate unnecessary updates of variable nodes within a window: this schedule is generated based on the behaviour of variable node updates analysed by density evolution. Here, the authors present a new non‐uniform schedule based on integer programming, whereby the objective functions and constraints are derived from a protograph‐based extrinsic information transfer chart. Our design is more flexible than the previous design, because the integer programming‐based design allows reduction of update numbers and performance losses through the constraints function, whereas the previous design requires observation of variable node update behaviour. The authors report the performance of their designs of non‐uniform schedules in additive white Gaussian noise (AWGN) and inter‐symbol interference (ISI) channels. Particularly, in the ISI channel, the authors’ non‐uniform schedules are designed with cooperative decoding between a Bahl‐Cocke‐Jelinek‐Raviv (BCJR) detector and an SC‐LDPC decoder.
Spatially coupled low-density parity-check (SC-LDPC) codes can achieve capacity approaching performance with a small message recovery latency due to the sliding window decoding (SWD). Using a partial Tanner graph, the SWD performs iterative message passing until the average error probability Peof the target symbols falls below a threshold or the maximum iteration number is reached. However, Pedoes not decrease monotonically as iteration progresses. This implies the symbol likelihoods that were yielded when the decoding terminates may not be optimal for making decisions. Therefore, this paper proposes an improved SWD (ISWD) for SC-LDPC codes. The proposal monitors the achievable minimum of Peand stores its associated likelihoods, so that when the decoding terminates the target symbols will be estimated based on the stored likelihoods. Our research shows the ISWD is able to enhance the decoding performance, especially in the waterfall region. It exhibits an asymptotic convergence to the SWD performance. A complexity reducing variant of the ISWD is also proposed to facilitate the decoding but at the cost of error-correction performance.
In this paper, we compare the finite-length performance of non-binary spatially coupled low-density parity-check (NB SC-LDPC) codes constructed from protographs to non-binary LDPC block codes (NB LDPC-BCs). A sliding window decoding architecture with a stopping rule based on a soft bit-error-rate (BER) estimate for the NB SC-LDPC codes is considered. It is demonstrated that NB SC-LDPC codes with sliding window decoding outperform NB LDPC-BCs with no increase in decoding complexity when the decoding latency of the SC-LDPC codes equals the block length of the LDPC-BCs. We also investigate the relationship between the protograph lifting factor, the decoding window size, and the decoding performance of NB SC-LDPC codes when the decoding latency is fixed. Simulation results for several (3,6)-regular NB code examples confirm that NB SC-LDPC codes can significantly outperform both binary LDPC-BCs and binary SC-LDPC codes with the same decoding latency.