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Register a new userDeep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes
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Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.
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Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for identifying the distance-spectrum-optimal (DSO) CRC polynomial for a given tail-biting convolutional code (TBCC) when the target undetected error rate (UER) is small. Lou et al. found that the DSO CRC design for a given zero-terminated convolutional code under low UER is equivalent to maximizing the undetected minimum distance (the minimum distance of the concatenated code). This paper applies the same principle to design the DSO CRC for a given TBCC under low target UER. Our algorithm is based on partitioning the tail-biting trellis into several disjoint sets of tail-biting paths that are closed under cyclic shifts. This paper shows that the tail-biting path in each set can be constructed by concatenating the irreducible error events (IEEs) and circularly shifting the resultant path. This motivates an efficient collection algorithm that aims at gathering IEEs, and a search algorithm that reconstructs the full list of error events with bounded distance of interest, which can be used to find the DSO CRC. Simulation results show that DSO CRCs can significantly outperform suboptimal CRCs in the low UER regime.
Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than $0.1$dB. Code available at https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders
As a typical example of bandwidth-efficient techniques, bit-interleaved coded modulation with iterative decoding (BICM-ID) provides desirable spectral efficiencies in various wireless communication scenarios. In this paper, we carry out a comprehensive investigation on tail-biting (TB) spatially coupled protograph (SCP) low-density parity-check (LDPC) codes in BICM-ID systems. Specifically, we first develop a two-step design method to formulate a novel type of constellation mappers, referred to as labeling-bit-partial-match (LBPM) constellation mappers, for SC-P-based BICM-ID systems. The LBPM constellation mappers can be seamlessly combined with high-order modulations, such as M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM). Furthermore, we conceive a new bit-level interleaving scheme, referred to as variable node matched mapping (VNMM) scheme, which can substantially exploit the structure feature of SC-P codes and the unequal protection-degree property of labeling bits to trigger the wave-like convergence for TB-SC-P codes. In addition, we propose a hierarchical extrinsic information transfer (EXIT) algorithm to predict the convergence performance (i.e., decoding thresholds) of the proposed SC-P-based BICM-ID systems. Theoretical analyses and simulation results illustrate that the LBPM-mapped SC-P-based BICM-ID systems are remarkably superior to the state-of-the-art mapped counterparts. Moreover, the proposed SC-P-based BICM-ID systems can achieve even better error performance with the aid of the VNMM scheme. As a consequence, the proposed LBPM constellation mappers and VNMM scheme make the SC-P-based BICM-ID systems a favorable choice for the future-generation wireless communication systems.
Deep neural networks (DNNs) based digital receivers can potentially operate in complex environments. However, the dynamic nature of communication channels implies that in some scenarios, DNN-based receivers should be periodically retrained in order to track temporal variations in the channel conditions. To this aim, frequent transmissions of lengthy pilot sequences are generally required, at the cost of substantial overhead. In this work we propose a DNN-aided symbol detector, Meta-ViterbiNet, that tracks channel variations with reduced overhead by integrating three complementary techniques: 1) We leverage domain knowledge to implement a model-based/data-driven equalizer, ViterbiNet, that operates with a relatively small number of trainable parameters; 2) We tailor a meta-learning procedure to the symbol detection problem, optimizing the hyperparameters of the learning algorithm to facilitate rapid online adaptation; and 3) We adopt a decision-directed approach based on coded communications to enable online training with short-length pilot blocks. Numerical results demonstrate that Meta-ViterbiNet operates accurately in rapidly-varying channels, outperforming the previous best approach, based on ViterbiNet or conventional recurrent neural networks without meta-learning, by a margin of up to 0.6dB in bit error rate in various challenging scenarios.
We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the PCC encoding. GSC-PCCs can be seen as a generalization of the original spatially coupled parallel concatenated convolutional codes (SC-PCCs) proposed by Moloudi et al. [1]. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. We show that the proposed codes have some nice properties such as threshold saturation and that their decoding thresholds improve with the repetition factor $q$. Most notably, our analysis suggests that the proposed codes asymptotically approach the capacity as $q$ tends to infinity with any given constituent convolutional code.
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