Continuous Transmission of Spatially Coupled LDPC Code Chains

Abstract

We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using spatially-coupled low-density parity-check (SC-LDPC) codes. In CC transmission, instead of transmitting a sequence of independent codewords from a terminated SC-LDPC code chain, we connect multiple chains in a layered format, where encoding, transmission, and decoding are performed in a continuous fashion. The connections between chains are created at specific points, chosen to improve the finite-length performance of the code structure under iterative decoding. We describe the design of CC schemes for different SC-LDPC code ensembles constructed from protographs: a (J, K)-regular SC-LDPC code chain, a spatially-coupled repeat-accumulate (SC-RA) code, and a spatially-coupled accumulate-repeat-jagged-accumulate (SC-ARJA) code. In all cases, significant performance improvements are reported and it is shown that using CC transmission only requires a small increase in decoding complexity and decoding delay with respect to a system employing a single SC-LDPC code chain for transmission.

Finite-Length Analysis for Spatially Coupled LDPC Codes Based on Base Matrix

“…This effect is more severe for smaller values M. However, since SC-LDPC code ensemble has a linear growth of minimum distance with block length nM, the codes with small cycles or low-weight stopping sets can hardly be found for sufficiently large M. Therefore, when M increases to a few thousands, the effects on the prediction accuracy will be small enough to be ignored. Next, we extended the analysis to the case of connecting three different chains and considered the ensemble P (3,6,3,9,3,12,15). The mean value r1 (τ) with M = 200 and different is plotted in Figure 6.…”

“…Similar results can be observed that, when approaching the threshold * = 0.3114, the r1 (τ * ) values gradually decrease to approximately zero. In Table 2, the δ 1 (τ * ) values are calculated for the codes generated from the ensemble P (3,6,3,9,3,12,15). The predicted error probabilities and the simulated ones for these codes are shown in Figure 7.…”

“…In addition, most of the literature focused on applying the concept of spatial coupling on other error correction codes to improve the decoding thresholds, such as spatially coupled repeataccumulate (SC-RA) codes, spatially coupled turbo codes (SC-TCs), spatially coupled precoded rateless codes and so on [5][6][7]. Moreover, spatial coupling need not be limited to forming a single chain, and more general structures formed by connecting multiple coupled chains were presented to improve the decoding thresholds [8][9][10]. Different from connecting multiple identical coupled chains, the SC-LDPC codes constructed by parallelly connecting multiple different chains (PC-MSC-LDPC) were proposed in [11], which showed that the thresholds of the PC-MSC-LDPC code ensembles with flexible rates are very close to Shannon limits over the BEC.…”

“…Figure 7. Simulated error probabilities (solid lines) and predicted error probabilities (dash lines) for the codes C(3,6,3,9,3,12,15, 200) and C(3,6,3,9,3,12,15, 500). The rate is 0.6222 and the codelengths are 27,000 and 67,500 respectively.…”