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Register a new userThresholds of Braided Convolutional Codes on the AWGN Channel
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Added by
Muhammad Umar Farooq Mr.
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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In this paper, we perform a threshold analysis of braided convolutional codes (BCCs) on the additive white Gaussian noise (AWGN) channel. The decoding thresholds are estimated by Monte-Carlo density evolution (MC-DE) techniques and compared with approximate thresholds from an erasure channel prediction. The results show that, with spatial coupling, the predicted thresholds are very accurate and quickly approach capacity if the coupling memory is increased. For uncoupled ensembles with random puncturing, the prediction can be improved with help of the AWGN threshold of the unpunctured ensemble.
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In this paper, we study systematic Luby Transform (SLT) codes over additive white Gaussian noise (AWGN) channel. We introduce the encoding scheme of SLT codes and give the bipartite graph for iterative belief propagation (BP) decoding algorithm. Similar to low-density parity-check codes, Gaussian approximation (GA) is applied to yield asymptotic performance of SLT codes. Recent work about SLT codes has been focused on providing better encoding and decoding algorithms and design of degree distributions. In our work, we propose a novel linear programming method to optimize the degree distribution. Simulation results show that the proposed distributions can provide better bit-error-ratio (BER) performance. Moreover, we analyze the lower bound of SLT codes and offer closed form expressions.
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.
We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER) performance at small to moderate frame length. Here, we consider a sliding window decoder in the context of large frame length or one that continuously outputs blocks in a streaming fashion. In this case, decoder error propagation, due to the feedback inherent in BCCs, can be a serious problem.In order to mitigate the effects of error propagation, we propose several schemes: a emph{window extension algorithm} where the decoder window size can be extended adaptively, a resynchronization mechanism where we reset the encoder to the initial state, and a retransmission strategy where erroneously decoded blocks are retransmitted. In addition, we introduce a soft BER 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, resynchronization mechanism, and retransmission strategy, the BER performance of BCCs can be improved by up to four orders of magnitude in the signal-to-noise ratio operating range of interest, and in addition the soft BER stopping rule can be employed to reduce computational complexity.
This work proposes a tractable estimation of the maximum a posteriori (MAP) threshold of various families of sparse-graph code ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) function, first proposed by Measson et al. We consider the transmission over non-binary complex-input additive white Gaussian noise channel and extend the existing results to obtain an expression for the GEXIT function. We estimate the MAP threshold by applying the Maxwell construction to the obtained approximate EBP-GEXIT charts for various families of low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC, and serially concatenated turbo codes (SC-TC). When codewords of SC-TC are modulated using Gray mapping, we also explore where the spatially-coupled belief propagation (BP) threshold is located with respect to the previously computed MAP threshold. Numerical results indicate that the BP threshold of the spatially-coupled SC-TC does saturate to the MAP threshold obtained via EBP-GEXIT chart.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.
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