A Unified Ensemble of Concatenated Convolutional Codes

We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles

Spatially Coupled Turbo Codes: Principles and Finite Length Performance

In this paper, we give an overview of spatially coupled turbo codes (SC-TCs), the spatial coupling of parallel and serially concatenated convolutional codes, recently introduced by the authors. For presentation purposes, we focus on spatially coupled serially concatenated codes (SC-SCCs). We review the main principles of SC-TCs and discuss their exact density evolution (DE) analysis on the binary erasure channel. We also consider the construction of a family of rate-compatible SC-SCCs with simple 4-state component encoders. For all considered code rates, threshold saturation of the belief propagation (BP) to the maximum a posteriori threshold of the uncoupled ensemble is demonstrated, and it is shown that the BP threshold approaches the Shannon limit as the coupling memory increases. Finally we give some simulation results for finite lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems (ISWCS), Aug. 201

Spatially Coupled Turbo Codes

In this paper, we introduce the concept of spatially coupled turbo codes (SC-TCs), as the turbo codes counterpart of spatially coupled low-density parity-check codes. We describe spatial coupling for both Berrou et al. and Benedetto et al. parallel and serially concatenated codes. For the binary erasure channel, we derive the exact density evolution (DE) equations of SC-TCs by using the method proposed by Kurkoski et al. to compute the decoding erasure probability of convolutional encoders. Using DE, we then analyze the asymptotic behavior of SC-TCs. We observe that the belief propagation (BP) threshold of SC-TCs improves with respect to that of the uncoupled ensemble and approaches its maximum a posteriori threshold. This phenomenon is especially significant for serially concatenated codes, whose uncoupled ensemble suffers from a poor BP threshold.Comment: in Proc. 8th International Symposium on Turbo Codes & Iterative Information Processing 2014, Bremen, Germany, August 2014. To appear. (The PCC ensemble is changed with respect to the one in the previous version of the paper. However, it gives identical thresholds

Combating Error Propagation in Window Decoding of Braided Convolutional Codes

In this paper, we study sliding window decoding of braided convolutional codes (BCCs) in the context of a streaming application, where decoder error propagation can be a serious problem. A window extension algorithm and a resynchronization mechanism are introduced to mitigate the effect of error propagation. In addition, we introduce a soft bit-error-rate stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm and resynchronization mechanism, the error performance of BCCs can be improved by up to three orders of magnitude with reduced computational complexity.Comment: 6 pages, 10 figures, submitted for IEEE ISIT201