This paper proposes a method to design low-density parity-check (LDPC) codes for delayed bit-interleaved coded modulation (DBICM). In the method, the code variable node (VN) degree distributions and the assignments of VNs with different degrees to DBICM subchannels are optimized via two cascaded differential evolution (DE) steps. In each step, to optimize VN degree distribution or channel assignment, a parity-check matrix is constructed, and the associated decoding threshold is calculated for each element in a generation. In constructing a parity-check matrix for each channel assignment, we propose a constraint PEGlike code construction method. Protograph-EXIT is employed to calculate the decoding threshold for each parity-check matrix. We apply the proposed method to construct irregular binary LDPC codes for both 16-QAM DBICM and BICM schemes. Simulation results demonstrate that the optimized LDPC codes are within 1 dB from the associated capacity limit at a bit error rate (BER) of 10-6. Besides, the LDPC coded DBICM achieves an SNR gain of 0.5 dB to 0.1 dB over BICM counterparts at a code rate ranges from 0.25 to 0.5.

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. The information sequence is partitioned equally into blocks and transmitted directly, while their replicas are interleaved and transmitted in a block Markov superposition manner. By taking into account that the codes are systematic, we derive both upper and lower bounds on the bit-error-rate (BER) under maximum a posteriori decoding. The derived lower bound reveals connections among BER, encoding memory and code rate, which provides a way to design good systematic BMST-R codes and also allows us to make trade-offs among efficiency, performance, and complexity. Numerical results show that: 1) the proposed bounds are tight in the high signal-to-noise ratio region; 2) systematic BMST-R codes perform well in a wide range of code rates; and 3) rate 1/2 systematic BMST-R codes outperform the considered (3,6)- and (4,8)-regular spatially coupled low-density parity-check codes under an equal decoding latency constraint.

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional (RCPC) codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. By taking into account that the codes are systematic, the performance of systematic BMST-R codes under maximum a posteriori (MAP) decoding can be analyzed with a simple lower bound and an upper bound with the help of partial input-redundancy weight enumerating function (IRWEF). Numerical results verify our analysis and show that systematic BMST-R codes perform well in a wide range of code rates.

In this paper, we consider the asymptotic and finite-length performance of block Markov superposition transmission (BMST) of short codes, which can be viewed as a new class of spatially coupled (SC) codes where the generator matrices of short codes (referred to as basic codes) are coupled. A modified extrinsic information transfer (EXIT) chart analysis that takes into account the relation between mutual information (MI) and bit-error-rate (BER) is presented to study the convergence behavior of BMST codes. Using the modified EXIT chart analysis, we investigate the impact of various parameters on BMST code performance, thereby providing theoretical guidance for designing and implementing practical BMST codes suitable for window decoding. Then, we present a performance comparison of BMST codes and SC low-density parity-check (SC-LDPC) codes on the basis of equal decoding latency. Also presented is a comparison of computational complexity. Simulation results show that, under the equal decoding latency constraint, BMST codes using the repetition code as the basic code can outperform both (3,6)-regular SC-LDPC codes and (4,8)-regular SC-LDPC codes in the waterfall region but have a higher computational complexity.

In this paper, a modified extrinsic information transfer (EXIT) chart analysis that takes into account the relation between mutual information (MI) and bit-error-rate (BER) is presented to study the convergence behavior of block Markov superposition transmission (BMST) of short codes (referred to as basic codes). We show that the threshold curve of BMST codes using an iterative sliding window decoding algorithm with a fixed decoding delay achieves a lower bound in the high signal-to-noise ratio (SNR) region, while in the low SNR region, due to error propagation, the thresholds of BMST codes become slightly worse as the encoding memory increases. We also demonstrate that the threshold results are consistent with finite-length performance simulations.

In this paper, asymptotic methods are used to form lower and upper bounds on the typical free distance growth rate of ensembles of periodically time-varying protograph-based spatially coupled low-density parity-check (SC-LDPC) codes over GF(q). By evaluating and comparing these bounds, we find that the typical free distance of q-ary SC-LDPC codes increases linearly with constraint length and that the bounds coincide for a sufficiently large period. In particular, we show that the free distance to constraint length ratio of (3, 6)-regular q-ary SC-LDPC code ensembles exceeds the minimum distance to block length ratio of an underlying q-ary LDPC block code (LDPC-BC) ensemble. We also show that, similar to the minimum distance growth rate of the (3, 6)-regular q-ary LDPC-BC ensemble, the free distance growth rate of (3, 6)-regular q-ary SC-LDPC code ensembles increases with the field size q up to a certain point, and then it decreases as q increases further.

In this paper, we compare the finite-length performance of protograph-based spatially coupled low-density paritycheck (SC-LDPC) codes and LDPC block codes (LDPC-BCs) over GF(q). To reduce computational complexity and latency, a sliding window decoder with a stopping rule based on a soft belief propagation (BP) estimate is used for the q-ary SC-LDPC codes. Two regimes are considered: one when the constraint length of q-ary SC-LDPC codes is equal to the block length of q-ary LDPC-BCs and the other when the two decoding latencies are equal. Simulation results confirm that, in both regimes, (3,6)-, (3,9)-, and (3,12)-regular non-binary SC-LDPC codes can significantly outperform both binary and non-binary LDPC-BCs and binary SC-LDPC codes. Finally, we present a computational complexity comparison of q-ary SC-LDPC codes and q-ary LDPC-BCs under equal decoding latency and equal decoding performance assumptions.

A construction of big convolutional codes from short codes called block Markov superposition transmission (BMST) is proposed. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. The BMST codes can also be viewed as a class of spatially coupled codes, where the generator matrices of the involved short codes (referred to as basic codes) are coupled. The encoding process of BMST can be as fast as that of the basic code, while the decoding process can be implemented as an iterative sliding-window decoding algorithm with a tunable delay. More importantly, the performance of BMST can be simply lower bounded in terms of the transmission memory given that the performance of the short code is available. Numerical results show that: 1) the lower bounds can be matched with a moderate decoding delay in the low bit-error-rate (BER) region, implying that the iterative sliding-window decoding algorithm is near optimal; 2) BMST with repetition codes and single parity-check codes can approach the Shannon limit within 0.5 dB at the BER of 10-5for a wide range of code rates; and 3) BMST can also be applied to nonlinear codes.

In this paper, we compare the finite-length performance of non-binary spatially coupled low-density parity-check (NB SC-LDPC) codes constructed from protographs to non-binary LDPC block codes (NB LDPC-BCs). A sliding window decoding architecture with a stopping rule based on a soft bit-error-rate (BER) estimate for the NB SC-LDPC codes is considered. It is demonstrated that NB SC-LDPC codes with sliding window decoding outperform NB LDPC-BCs with no increase in decoding complexity when the decoding latency of the SC-LDPC codes equals the block length of the LDPC-BCs. We also investigate the relationship between the protograph lifting factor, the decoding window size, and the decoding performance of NB SC-LDPC codes when the decoding latency is fixed. Simulation results for several (3,6)-regular NB code examples confirm that NB SC-LDPC codes can significantly outperform both binary LDPC-BCs and binary SC-LDPC codes with the same decoding latency.

In this study, the authors consider designing low‐density parity‐check (LDPC) coded modulation systems to achieve unequal error protection (UEP). They propose a new UEP approach by partial superposition transmission (PST) called UEP‐by‐PST. In the UEP‐by‐PST system, the information sequence is distinguished as two parts, the more important data (MID) and the less important data (LID), both of which are coded with LDPC codes. The codeword that corresponds to the MID is superimposed on the codeword that corresponds to the LID. The system performance can be analysed by using discretised density evolution. Also proposed in this study is a criterion from a practical point of view to compare the efficiencies of different UEP approaches. Numerical results show that, over both additive white Gaussian noise channels and uncorrelated Rayleigh fading channels, (i) UEP‐by‐PST provides higher coding gain for the MID compared with the traditional equal error protection approach, but with negligible performance loss for the LID; and (ii) UEP‐by‐PST is more efficient with the proposed practical criterion than the UEP approach in the digital video broadcasting system.

In this paper, we present a new approach, called block Markov superposition transmission (BMST), to construct from short codes a class of convolutional codes with large constraint length. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. We also present an iterative sliding-window decoding algorithm for the proposed transmission scheme. The extra coding gain obtained by BMST can be bounded in terms of the Markov order and with the help of the input-output weight enumerating function (IOWEF) of the BMST system, which can be computed from that of the short code by performing a trellis-based algorithm. Numerical results verify our analysis and show that an extra coding gain of 6.4 dB at bit-error rate (BER) 10-5can be obtained by BMST of the [7, 4] Hamming code.