Partially information coupled turbo codes (PIC-TCs) is a class of spatially coupled turbo codes (SC-TCs) that can approach the BEC capacity while keeping the encoding and decoding architectures of the underlying component codes unchanged. However, due to the coupling, PIC-TCs have significant rate loss compared to its component rate-1/3 turbo code, and the rate loss increases with the coupling ratio. To absorb the rate loss, in this paper, we propose the partially information coupled duo-binary turbo codes (PIC-dTCs). Given a rate-1/3 turbo code as the benchmark, we construct a duo-binary turbo code by introducing one extra input to the benchmark code. Then, some of the information bits from the original input are coupled to the extra input of the next code block. By looking into the graph model of PIC-dTC ensembles, we derive the exact density evolution equations of the PIC-dTC ensembles and compute their belief propagation decoding thresholds on the binary erasure channel. Simulation results verify the correctness of our theoretical analysis, and also shows significant error performance improvement over the uncoupled rate-1/3 turbo codes and existing designs of spatially coupled turbo codes.
SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using the entire code block, for increased data reliability. In this paper, we pursue the analysis and design of such codes from both finite-length and asymptotic lenses. This mixed approach has rarely been applied in designing SC codes, but it is beneficial for optimizing code graphs for local and global performance simultaneously. Our proposed framework consists of two steps: 1) designing the local code for both threshold and cycle counts, and 2) designing the coupling of local codes for the best cycle count in the global design.
We introduce a novel design of spatially coupled low density parity check codes in order to reduce the effects of error propagation in low-latency sliding window decoding for large frame lengths or streaming applications. Speciﬁcally, we employ reduced-degree check nodes spaced throughout the coupling chain, which have the effect of allowing the decoder to recover from error bursts. A simpliﬁed analysis of the block error rate (BLER) of the proposed codes is presented that allows us to predict the effect of different placements of reduced-degree checks in the coupling chain. Simulation results supporting the beneﬁcial effect of the new code design on the overall BLER performance are included.
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a (2,3)-regular compact graph. In this paper, we introduce a family of (dv, dc)-regular GLDPC codes with convolutional code constraints (CC-GLDPC codes), which form an extension of classical BCCs to arbitrary regular graphs. In order to characterize the performance in the waterfall and error floor regions, we perform an analysis of the density evolution thresholds as well as the finite-length ensemble weight enumerators and minimum distances of the ensembles. In particular, we consider various ensembles of overall rate R= 1/3 and R= 1/2 and study the trade-off between variable node degree and strength of the component codes. We also compare the results to corresponding classical LDPC codes with equal degrees and rates. It is observed that for the considered LDPC codes with variable node degree dv>2, we can find a CC-GLDPC code with smaller dv that offers similar or better performance in terms of BP and MAP thresholds at the expense of a negligible loss in the minimum distance.
In this paper, we propose a non-uniform windowed decoder for multi-dimensional spatially-coupled LDPC (MD-SC-LDPC) codes over the binary erasure channel. An MD-SC-LDPC code is constructed by connecting together several SC-LDPC codes into one larger code that provides major benefits over a variety of channel models. In general, SC codes allow for low-latency windowed decoding. While a standard windowed decoder can be naively applied, such an approach does not fully utilize the unique structure of MD-SC-LDPC codes. In this paper, we propose and analyze a novel non-uniform decoder to provide more flexibility between latency and reliability. Our theoretical derivations and empirical results show that our non-uniform decoder greatly improves upon the standard windowed decoder in terms of design flexibility, latency, and complexity.