In this letter, we investigate the application of the subgradient method to design efficient algorithm for linear programming (LP) decoding of binary linear codes. A major drawback of the original formulation of LP decoding is that the description complexity of the feasible region is exponential in the check node degrees of the code. In order to tackle the problem, we propose a processing technique for LP decoding with the subgradient method, whose complexity is linear in the check node degrees. Consequently, a message-passing type decoding algorithm can be obtained, whose per-iteration complexity is extremely low. Moreover, if the algorithm converges to a valid codeword, it is guaranteed to be a maximum likelihood codeword. Simulation results on several binary linear codes with short lengths suggest that the performances of LP decoding based on the subgradient method and the state-of-art LP decoding implementation approach are comparable.

This paper proposes a novel differential active self-interference canceller (DASIC) algorithm for asynchronous in-band full-duplex (IBFD) Gaussian filtered frequency shift keying (GFSK), which is designed for wireless Internet of Things (IoT). In IBFD communications, where two terminals simultaneously transmit and receive signals in the same frequency band, there is an extremely strong self-interference (SI). The SI can be mitigated by an active SI canceller (ASIC), which subtracts an interference replica based on channel state information (CSI) from the received signal. The challenging problem is the realization of asynchronous IBFD for wireless IoT in indoor environments. In the asynchronous mode, pilot contamination is induced by the non-orthogonality between asynchronous pilot sequences. In addition, the transceiver suffers from analog front-end (AFE) impairments, such as phase noise. Due to these impairments, the SI cannot be canceled entirely at the receiver, resulting in residual interference. To address the above issue, the DASIC incorporates the principle of the differential codec, which enables to suppress SI without the CSI estimation of SI owing to the differential structure. Also, on the premise of using an error correction technique, iterative detection and decoding (IDD) is applied to improve the detection capability while exchanging the extrinsic log-likelihood ratio (LLR) between the maximum a-posteriori probability (MAP) detector and the channel decoder. Finally, the validity of using the DASIC algorithm is evaluated by computer simulations in terms of the packet error rate (PER). The results clearly demonstrate the possibility of realizing asynchronous IBFD.

In this letter, a deep neural network (DNN) aided joint source-channel (JSCC) decoding scheme is proposed for polar codes. In the proposed scheme, an integrated factor graph with an unfolded structure is first designed. Then a DNN aided flooding belief propagation decoding (FBP) algorithm is proposed based on the integrated factor, in which both source and channel scaling parameters in the BP decoding are optimized for better performance. Experimental results show that, with the proposed DNN aided FBP decoder, the polar coded JSCC scheme can have about 2-2.5 dB gain over different source statistics p with source message length NSC = 128 and 0.2-1 dB gain over different source statistics p with source message length NSC = 512 over the polar coded JSCC system with existing BP decoder.

This paper proposes a non-linear overloaded MIMO detector that outperforms the conventional soft-input maximum likelihood detector (MLD) with less computational complexity. We propose iterative log-likelihood ratio (LLR) estimation and multi stage LLR estimation for the proposed detector to achieve such superior performance. While the iterative LLR estimation achieves better BER performance, the multi stage LLR estimation makes the detector less complex than the conventional soft-input maximum likelihood detector (MLD). The computer simulation reveals that the proposed detector achieves about 0.6dB better BER performance than the soft-input MLD with about half of the soft-input MLD's complexity in a 6×3 overloaded MIMO OFDM system.

The class of k-bit delay decodable codes, source codes allowing decoding delay of at most k bits for k≥0, can attain a shorter average codeword length than Huffman codes. This paper discusses the general properties of the class of k-bit delay decodable codes with a finite number of code tables and proves two theorems which enable us to limit the scope of codes to be considered when discussing optimal k-bit delay decodable codes.

This letter introduces a prime-factor Galois field Fourier transform (PF-GFFT) architecture to frequency domain decoding (FDD) of cyclic codes. Firstly, a fast FDD scheme is designed which converts the original single longer Fourier transform to a multi-dimensional smaller transform. Furthermore, a ladder-shift architecture for PF-GFFT is explored to solve the rearrangement problem of input and output data. In this regard, PF-GFFT is considered as a lower order spectral calculation scheme, which has sufficient preponderance in reducing the computational complexity. Simulation results show that PF-GFFT compares favorably with the current general GFFT, simplified-GFFT (S-GFFT), and circular shifts-GFFT (CS-GFFT) algorithms in time-consuming cost, and is nearly an order of magnitude or smaller than them. The superiority is a benefit to improving the decoding speed and has potential application value in decoding cyclic codes with longer code lengths.

The decoders, which improve the error-correction performance by finding and correcting the error bits caused by channel noise, are a hotspot for polar codes. In this paper, we present a threshold based D-SCFlip (TD-SCFlip) decoder with two improvements based on the D-SCFlip decoder. First, we propose the LLR fidelity criterion to define the LLR threshold and investigate confidence probability to calculate the LLR threshold indirectly. The information bits whose LLR values are smaller than the LLR threshold will be excluded from the range of candidate bits, which reduces the complexity of constructing the flip-bits list without the loss of error-correction performance. Second, we improve the calculation method for flip-bits metric with two perturbation parameters, which locates the channel-induced error bits faster, thus improving the error-correction performance. Then, TD-SCFlip-ω decoder is also proposed, which is limited to correcting up to ω bits in each extra decoding attempt. Simulation results show that the TD-SCFlip decoding is slightly better than the D-SCFlip decoding in terms of error-correction performance and decoding complexity, while the error-correction performance of TD-SCFlip-ω decoding is comparable to that of D-SCFlip-ω decoding but with lower decoding complexity.

In recent years, physical layer security (PLS), which is based on information theory and whose strength does not depend on the eavesdropper's computing capability, has attracted much attention. We have proposed a chaos modulation method as one PLS method that offers channel coding gain. One alternative is based on polar codes. They are robust error-correcting codes, have a nested structure in the encoder, and the application of this mechanism to PLS encryption (PLS-polar) has been actively studied. However, most conventional studies assume the application of conventional linear modulation such as BPSK, do not use encryption modulation, and the channel coding gain in the modulation is not achieved. In this paper, we propose a PLS-polar method that can realize high-quality transmission and encryption of a modulated signal by applying chaos modulation to a polar-coding system. Numerical results show that the proposed method improves the performance compared to the conventional PLS-polar method by 0.7dB at a block error rate of 10-5. In addition, we show that the proposed method is superior to conventional chaos modulation concatenated with low-density parity-check codes, indicating that the polar code is more suitable for chaos modulation. Finally, it is demonstrated that the proposed method is secure in terms of information theoretical and computational security.

The hardness of the syndrome decoding problem (SDP) is the primary evidence for the security of code-based cryptosystems, which are one of the finalists in a project to standardize post-quantum cryptography conducted by the U.S. National Institute of Standards and Technology (NIST-PQC). Information set decoding (ISD) is a general term for algorithms that solve SDP efficiently. In this paper, we conducted a concrete analysis of the time complexity of the latest ISD algorithms under the limitation of memory using the syndrome decoding estimator proposed by Esser et al. As a result, we present that theoretically nonoptimal ISDs, such as May-Meurer-Thomae (MMT) and May-Ozerov, have lower time complexity than other ISDs in some actual SDP instances. Based on these facts, we further studied the possibility of multiple parallelization for these ISDs and proposed the first GPU algorithm for MMT, the multiparallel MMT algorithm. In the experiments, we show that the multiparallel MMT algorithm is faster than existing ISD algorithms. In addition, we report the first successful attempts to solve the 510-, 530-, 540- and 550-dimensional SDP instances in the Decoding Challenge contest using the multiparallel MMT.

This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.

This paper proposes an efficient scheduling algorithm for the layered decoding of block low-density parity-check (LDPC) codes. To efficiently configure check node-based scheduling groups, the proposed algorithm utilizes the base matrix of the block LDPC code for a block-by-block scheduling group configuration; i.e., the proposed algorithm generates a scheduling group of check nodes, satisfying the weight condition of the layered decoding, which is performed in block units (including several check nodes). Therefore, unlike the conventional scheduling algorithms performed in node units, the proposed algorithm can efficiently generate scheduling groups for layered decoding at low computational complexity and memory requirements. In addition, to accelerate the decoding convergence speed, check nodes are allocated in each scheduling group such that messages from check nodes up to the current group are delivered as evenly as possible to bit nodes. Simulation results confirm that the proposed algorithm can accelerate decoding convergence compared to other block-based scheduling algorithms for layered decoding of block LDPC codes.

In channel decoding, a decoder with suboptimal metrics may be used because of the uncertainty of the channel statistics or the limitations of the decoder. In this case, the decoding metric is different from the actual channel metric, and thus it is called mismatched decoding. In this paper, applying the technique of the DS2 bound, we derive an upper bound on the error probability of mismatched decoding over a regular channel for the ensemble of linear block codes, which was defined by Hof, Sason and Shamai. Assuming the ensemble of random linear block codes defined by Gallager, we show that the obtained bound is not looser than the conventional bound. We also give a numerical example for the ensemble of LDPC codes also introduced by Gallager, which shows that our proposed bound is tighter than the conventional bound. Furthermore, we obtain a single letter error exponent for linear block codes.

In the source coding problem with cost constraint, a cost function is defined over the code alphabet. This can be regarded as a noiseless channel coding problem with cost constraint. In this case, we will not distinguish between the input alphabet and the output alphabet of the channel. However, we must distinguish them for a noisy channel. In the channel coding problem with cost constraint so far, the cost function is defined over the input alphabet of the noisy channel. In this paper, we define the cost function over the output alphabet of the channel. And, the cost is paid only after the received word is observed. Note that the cost is a random variable even if the codeword is fixed. We show the channel capacity with cost constraint defined over the output alphabet. Moreover, we generalize it to tolerate some decoding error and some cost overrun. Finally, we show that the cost constraint can be described on a subset of arbitrary set which may have no structure.

Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating synchronization errors. This paper investigates the maximum run-length limited single insertion/deletion correcting (RLL-SIDC) codes. More precisely, we construct efficiently encodable and decodable RLL-SIDC codes. Moreover, we present its encoding and decoding algorithms and show the redundancy of the code.

A properly designed stopping criterion for iterative decoding algorithms can save a number of iterations and lead to a considerable reduction of system latency. The symbol flipping decoding algorithms based on prediction (SFDP) have been proposed recently for efficient decoding of non-binary low-density parity-check (LDPC) codes. To detect the decoding frames with slow convergence or even non-convergence, we track the number of oscillations on the value of objective function during the iterations. Based on this tracking number, we design a simple stopping criterion for the SFDP algorithms. Simulation results show that the proposed stopping criterion can significantly reduce the number of iterations at low signal-to-noise ratio regions with slight error performance degradation.

One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

This paper proposes out-of-bound signal demapping for lattice reduction-aided iterative linear receivers in overloaded MIMO channels. While lattice reduction aided linear receivers sometimes output hard-decision signals that are not contained in the modulation constellation, the proposed demapping converts those hard-decision signals into binary digits that can be mapped onto the modulation constellation. Even though the proposed demapping can be implemented with almost no additional complexity, the proposed demapping achieves more gain as the linear reception is iterated. Furthermore, we show that the transmission performance depends on bit mapping in modulations such as the Gray mapping and the natural mapping. The transmission performance is confirmed by computer simulation in a 6 × 2 MIMO system, i.e., the overloading ratio of 3. One of the proposed demapping called “modulo demapping” attains a gain of about 2 dB at the packet error rate (PER) of 10-1 when the 64QAM is applied.

This paper proposes coded modulation for physical layer network coding in multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) bi-directional wireless relay systems where precoding is applied. The proposed coded modulation enables the relays to decode the received signals, which improves the transmission performance. Soft input decoding for the proposed coded modulation is proposed. Furthermore, we propose two precoder weight optimization techniques, called “per subcarrier weight optimization” and “total weight optimization”. This paper shows a precoder configuration based on the optimization with the lattice reduction or the sorted QR-decomposition. The performance of the proposed network coding is evaluated by computer simulation in a MIMO-OFDM two-hop wireless relay system with the 16 quadrature amplitude modulation (QAM) or the 256QAM. The proposed coded modulation attains a coding gain of about 2dB at the BER of 10-4. The total weight optimization achieves about 1dB better BER performance than the other at the BER of 10-4.

For low-density parity-check (LDPC) codes, the penalized decoding method based on the alternating direction method of multipliers (ADMM) can improve the decoding performance at low signal-to-noise ratios and also has low decoding complexity. There are three effective methods that could increase the ADMM penalized decoding speed, which are reducing the number of Euclidean projections in ADMM penalized decoding, designing an effective penalty function and selecting an appropriate layered scheduling strategy for message transmission. In order to further increase the ADMM penalized decoding speed, through reducing the number of Euclidean projections and using the vertical layered scheduling strategy, this paper designs a fast converging ADMM penalized decoding method based on the improved penalty function. Simulation results show that the proposed method not only improves the decoding performance but also reduces the average number of iterations and the average decoding time.

This paper proposes a low complexity soft input decoding in an iterative linear receiver for overloaded MIMO. The proposed soft input decoding applies two types of lattice reduction-aided linear filters to estimate log-likelihood ratio (LLR) in order to reduce the computational complexity. A lattice reduction-aided linear with whitening filter is introduced for the LLR estimation in the proposed decoding. The equivalent noise caused by the linear filter is mitigated with the decoder output stream and the LLR is re-estimated after the equivalent noise mitigation. Furthermore, LLR clipping is introduced in the proposed decoding to avoid the performance degradation due to the incorrect LLRs. The performance of the proposed decoding is evaluated by computer simulation. The proposed decoding achieves about 2dB better BER performance than soft decoding with the exhaustive search algorithm, so called the MLD, at the BER of 10-4, even though the complexity of the proposed decoding is 1/10 as small as that of soft decoding with the exhaustive search.