Successive cancellation list (SCL) decoding enables polar codes to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL (PSCL) decoding algorithm, implemented over a PSCL decoding tree, can be utilized. In this work, we aim to lower down the complexity of the PSCL decoding, resulting in an efficient decoding algorithm with low latency and complexity for polar codes. To achieve this, we define two metrics at each level of the PSCL decoding tree. One is for evaluating the reliability of a path and the other is for evaluating the reliability of a list of paths. Then, we propose a double-threshold strategy in the PSCL decoding process where unreliable valid paths are pruned based on the first metric, and then the smallest reliable list of paths is selected to continue based on the second metric. Simulation results demonstrate that when polar codes are decoded using the proposed low-complexity PSCL decoder, both the sorting complexity and the computational complexity are reduced and significantly decrease as the signal-to-noise ratio (SNR) increases.

Successive cancellation list (SCL) decoding enables polar codes and their generalizations to deliver satisfactory performance in finite-length scenarios but it comes with high latency and complexity. To reduce latency, a partitioned SCL (PSCL) decoding algorithm, implemented over a PSCL decoding tree, can be utilized. In this work, we aim to lower down the complexity of the PSCL decoding, resulting in an efficient decoding algorithm with low latency and complexity for polar-like codes. To achieve this, we define two metrics at each level of the PSCL decoding tree. One is for evaluating the reliability of a path and the other is for evaluating the reliability of a list of paths. Then, we propose a double-threshold strategy in the PSCL decoding process where unreliable valid paths are pruned based on the first metric, and then the smallest reliable list of paths is selected to continue based on the second metric. Simulation results demonstrate that when polar/CRC-polar/PAC codes are decoded using the proposed low-complexity PSCL decoder, both the sorting complexity and the computational complexity are reduced and significantly decrease as the signal-to-noise ratio (SNR) increases.

In this paper, we propose an approach to construction of polar codes for successive cancellation list (SCL) decoding with a preset list size. For a given code length, we construct a trellis through which a path corresponds to a polar code. Then, we employ a sequential search algorithm to find an expected path based on four path metrics and five path selection rules. Additionally, for polarization-adjusted convolutional (PAC) construction, we optimize the convolutional generator polynomial based on our constructed polar code. Numerical results show that our polar/PAC codes can achieve satisfactory performance.

A ring-based constant composition distribution matcher (R-CCDM) is designed for shaping rotationally symmetrical two-dimensional (RS-2D) constellations. The procedure of distribution matching can be divided into two steps. First, nonuniformly distributed rings are generated by CCDM to approach a probability distribution calculated from that of modulation symbols. Second, a uniform mapping is performed to select one amplitude signal point from each ring. Compared with CCDM, the proposed DM contains multiple amplitude compositions, and hence achieves less rate loss. Numerical results show that, at moderate spectral efficiency, probabilistic shaping with R-CCDM outperforms that with CCDM by about $0.2 \sim 0.3 \mathrm{~dB}$ for different modulation formats.

We propose a length-flexible coding scheme by defining a balanced tree. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either active bits or frozen bits, and a parent node is related to its child nodes by a length-adaptive$(U+V\mid V)$operation. Both the encoding and the successive cancellation (SC)-based decoding can be implemented over the constructed coding tree. For code construction, we propose a signal-to-noise ratio (SNR)-dependent method and two SNR-independent methods, all of which evaluate the reliabilities of leaf nodes and then select the most reliable leaf nodes as the active nodes. Numerical results demonstrate that our proposed codes can have comparable performance to the 5G polar codes. To reduce the decoding latency, we propose a partitioned successive cancellation (PSC)-based decoding algorithm, which can be implemented over a sub-tree obtained by pruning the coding tree. Numerical results show that the PSC-based decoding can achieve similar performance to the conventional SC-based decoding.

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.