Reduced Complexity Window Decoding of Spatially Coupled LDPC Codes for Magnetic Recording Systems

Abstract

In channel coding theory, the performance of error correcting codes (ECCs) approaching the Shannon limit can be achieved through increasing code lengths. Unfortunately, the complexity of ECCs will be increased as the code length increases. Nowadays, the magnetic recording (MR) system takes advantage of powerful ECCs by using 4 Kbytes sector. Among the advanced ECCs, the spatially coupled LDPC (SC-LDPC) codes (also known as a LDPC convolutional code) [1]are shown to have the decoding latency and complexity lower than those of the underlying LDPC block codes (LDPC-BC). Moreover, the SC-LDPC codes with threshold decoding outperform the LDPC-BC codes [2]. Hence, the SC-LDPC codes are the strong candidate for the future MR systems, when the sector size is increased beyond 4 Kbytes. An SC-LDPC decoder can use sliding window decoding [3]whereby the received signals are decoded by sliding window along the bit sequence. The window decoder is called “uniform window decoding (U-WD),” when all variable nodes (VNs) within a window are updated. In order to reduce the complexity of window decoding, some researchers proposed the non-uniform window decoding (N-WD) [4], which do not update the VNs with no improvement in the bit error rate (BER). This approach provides about 35-50% reduction in complexity compared to U-WD. In this work, we consider the application of SC-LDPC codes in MR systems, whereby SC-LDPC decoder cooperates with BCJR detector to encounter inter-symbol interference (ISI). We propose the dynamic shifting of window decoding (DS-WD) to reduce the complexity of SC-LDPC codes. Herein, the number of shifted bits is defined according to their soft BERs which are estimated at each decoding position. In addition, we modify the N-WD [4]to reinforce our proposed algorithm called “dynamic-shifting non-uniform window decoding (DS-N-WD).” The DS-WD and DS-N-WD achieve the complexity reduction of 7% and 25% without any loss in performance compared to the N-WD algorithms.