Age of information (AoI) is a fundamentally important metric to characterize the freshness of information in real-time Internet of Things (IoT) monitoring systems. Another important metric is the energy cost for information sensing and transmission. In this paper, we investigate the average AoI and energy cost for low-density parity-check coded status update with and without automatic repeat request (ARQ), where the fixed redundancy scheme is employed. The non-ARQ, classical ARQ, truncated ARQ, and truncated hybrid ARQ with Chase combining (HARQ-CC) schemes are analyzed and compared. By using the renewal processes theory, the expressions for the average AoI as well as the average energy cost of each considered scheme are derived. Both the lower bound of age and the upper bound of energy are provided. It is shown through simulation results that the average AoI and energy cost are mainly influenced by network parameters in the low signal-to-noise ratio (SNR) region. With short code, the smaller average AoI can be obtained at the cost of more energy consumption. Compared with other schemes, the truncated HARQ-CC achieves the best average AoI and the moderate average energy cost, which is a compromise between the age and energy.

This paper proposes a new class of spatially coupled codes, which are constructed by sending codewords of a low-density parity-check block code (LDPC-BC) in a block Markov superposition transmission (BMST) manner, resulting in the BMST-LDPC codes. Different from the conventional spatially coupled LDPC (SC-LDPC) codes, the proposed BMST-LDPC codes can have encoder/decoder implemented using the structure of the corresponding LDPC-BCs. The proposed construction is universal, which is applicable to any existing LDPC-BCs including the 5 G New Radio (5G-NR) LDPC-BCs to obtain extra coding gains. The proposed BMST-LDPC codes are also a special class of BMST codes, which have lower error floors even with an encoding memory of one, inheriting a low decoding latency. Moreover, partial superposition, where a fraction of the coded bits are superimposed onto the following codewords, is introduced to alleviate the decoding error propagation. The construction can be optimized, for random long codes, by a protograph-based extrinsic information transfer (EXIT) chart analysis, or by a one-dimensional search for structured block codes. Furthermore, the BMST-LDPC scheme is integrated with the hybrid automatic retransmission request (HARQ) over the block fading channel, improving the throughput performance. Numerical results are presented to validate our analysis and demonstrate the performance advantage of the BMST-LDPC codes over the LDPC-BCs. They also show that the proposed HARQ scheme can yield a throughput improvement of up to 10% over the conventional HARQ scheme.

We propose a class of codes, referred to as staircase matrix codes (SMCs), which have staircase-like generator matrices or parity-check matrices. We illustrate that polar codes and Reed-Muller (RM) codes are (equivalent to) two instances of SMCs. The most distinguished feature of the SMCs is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE). Then we propose a representative ordered statistics decoding (ROSD) algorithm for the SMCs. Different from the conventional OSD, which forms the most reliable basis (MRB) by selecting reliable bits globally, the proposed ROSD forms an extended basis by selecting relatively reliable bits locally at least one from each staircase. We demonstrate by simulation that the ROSD has a similar performance to the OSD with local constraints (LC-OSD) and that the proposed random SMCs can outperform the RM codes and the polar codes. To further reduce the decoding delay and improve the performance, we propose a heuristic construction of staircase generator matrix codes (SGMCs) and analyze the ensemble weight spectrum (related to performance) and the quality of MRB (related to average number of test error patterns (TEPs)) for the heuristic construction. The simulation results show that, the proposed heuristic construction can reduce the average number of TEPs of the ROSD and provide a potential reduction in average decoding delay in the high signal-to-noise ratio (SNR) region. Furthermore, the proposed heuristic construction can approach the RCU bounds in a wide range of code rates.

In this letter, we propose partial superposition for 5G hybrid automatic retransmission request (HARQ), resulting in a throughput-enhanced HARQ scheme for the 5G system. The novelty of the proposed scheme is to retransmit an erroneous packet by superimposing (XORing) its partial bits onto a fresh packet, costing no extra bandwidth and transmission power. The proposed HARQ schemes can be implemented with the basis of the hardware components of the 5G standard. Numerical results show that the proposed HARQ schemes can yield a throughput improvement up to 10% over the original 5G HARQ scheme.

In this paper, we present a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving over binary-input output-symmetric (BIOS) channels. In the finite-length region, we propose the generalized representative ordered statistics decoding with local constraints (LC-ROSD) algorithm for the SGMCs. The most distinguished feature of the SGMCs with LC-ROSD is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE), avoiding the serial GE of conventional OSD and supporting a potential low decoding latency, as implied from simulations. To analyze the performance of random SGMCs in the finite-length region, we derive the ensemble weight spectrum and invoke the conventional union bound. We also derive a partially random coding union (RCU) bound, which is tighter than the conventional one and is used as a criterion to design the SGMCs. Staircase-like generator matrices allow us to derive a series of (tighter and tighter) lower bounds based on the second-order Bonferroni inequality with the incremental number of codewords. The numerical results show that the decoding performance can match well with the proposed partially RCU bound for different code rates and different profiles. The numerical results also show that the tailored SGMCs with the LC-ROSD algorithm can approach the finite-length performance bound, outperforming the 5G low-density parity-check (LDPC) codes, 5G polar codes, and Reed-Muller (RM) codes.

Free-ride coding, as an approach that admits transmission of a few extra bits over a low-density parity-check (LDPC) coded link without bandwidth expansion, is applied in this paper to construct coupled LDPC codes. Firstly, we present a syndrome channel model and derive the lower and upper bounds on its capacity (referred to as accessible capacity), indicating the feasibility of the reliable transmission of extra bits. Secondly, we present the performance evaluation on both the word error rate (WER) and the bit error rate (BER) for the free-ride codes with simple lower and upper bounds. Then we propose three applications of free-ride coding to construct coupled LDPC codes, including implicit globally-coupled LDPC (GC-LDPC) codes, partial product-LDPC codes, and terminated spatially-coupled LDPC (SC-LDPC) codes, all of which have the figure of merits that they share the same code rates with the basic component LDPC codes. Simulation results show that: 1) the proposed GC-LDPC codes can outperform the component LDPC codes, yielding a coding gain of up to 0.8 dB; 2) the proposed product codes with (3, 6)-regular LDPC component codes of length 1024 can lower the WER from 10 ^-2 down to 10 ^-6 at the SNR around 2 dB; 3) the proposed terminated SC-LDPC codes can perform as well as the conventional terminated SC-LDPC codes but without any rate loss.