Iteratively decodable sliding codes on graphs

Gilles Zémor

Shiyuan Mo, Li Chen

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.

Patrick Guy Farrell, Seyed H. Razavi

Jiayi Sun, Xiurong Ma, Yunlong Shan

This study investigates the Layered Sliding Window Decoding (LSWD) algorithm for Spatially Coupled Low-Density Parity-Check (SC LDPC) codes and proposes an enhanced decoding approach, the Improved Sliding Window Layered Decoding (ILSWD). While the LSWD algorithm reduces decoding latency and iteration counts compared to traditional Sliding Window Decoding (SWD), it does not significantly improve decoding performance. To address this, the ILSWD algorithm incorporates dynamic sliding window techniques, reorganizes decoding layers, and intro-duces suppression factors when errors enter the extended sliding window. Simulation results for 5G SC LDPC codes with single-sided coupling demonstrate that ILSWD achieves a 0.25 dB gain over LSWD at a specific bit error rate, alongside a notable improvement in decoding iteration rate. These findings highlight that ILSWD overcome the limitations of LSWD, offering a more efficient decoding solution with enhanced performance for SC LDPC codes in 5G applications.

Roman Sokolovskii, Alexandre Graell i Amat, Fredrik Brännström

We propose four finite-length scaling laws to predict the frame error rate (FER) performance in the waterfall region of spatially-coupled low-density parity-check code ensembles under full belief propagation (BP) decoding with a limit on the number of decoding iterations and a scaling law for sliding window decoding, also with limited iterations. The laws for full BP decoding provide a choice between accuracy and computational complexity; a good balance between them is achieved by the law that models the number of decoded bits after a certain number of BP iterations by a time-integrated Ornstein-Uhlenbeck process. This framework is developed further to model sliding window decoding as a race between the integrated Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the left boundary of the sliding window. The proposed scaling laws yield accurate FER predictions for the semi-structured code ensembles proposed by Olmos and Urbanke.

G. David Forney