Block Orthogonal Sparse Superposition (BOSS) codes are a promising class of joint coded modulation techniques that can closely approach the finite-blocklength capacity with low-complexity decoding at low code rates under Gaussian channels. However, in fading channels, the performance of BOSS codes degrades considerably due to varying channel fading effects on coded symbols. This paper presents a unified approach to extending BOSS codes to practical fading scenarios and introduces novel joint demodulation and decoding solutions. For fast-fading channels, we propose a minimum mean square error approximation maximum a posteriori (MMSE-A-MAP) algorithm that integrates demodulation and decoding when channel state information is available at the receiver (CSIR). Additionally, for block-fading channels without CSIR, we introduce a joint demodulation and decoding method, referred to as the non-coherent sphere decoding (NSD) algorithm. Simulation results demonstrate that BOSS codes with MMSE-A-MAP decoding outperform 5G polar codes, while the NSD algorithm achieves performance comparable to quasi-maximum likelihood decoding but with significantly reduced complexity. Both decoding methods can be implemented for parallel processing, allowing them to meet low-latency requirements. Furthermore, real-time simulations on a software-defined radio testbed validate the feasibility of using BOSS codes for low-power transmission.

We address the suboptimality of successive cancellation (SC) decoding for polar codes, which is caused by treating as random variables all the future bits to be estimated later. For a target information bit, we define the frozen and parity bits located behind it as its future constraints (FCs). To incorporate FCs into the sequential decoding of the target bit, we propose two elementary techniques: an SC check (SCC) algorithm and an FC conversion rule enabling belief propagation (BP). Focusing on the binary erasure channel (BEC), we also present a tree search technique based on stack-based backjumping (SBJ) to efficiently solve dynamic constraint satisfaction problems (CSP) formulated by FCs. Numerical results show that the combination of BP and SCC decoding algorithms accompanied with the SBJ technique achieves excellent erasure recovery performance over the BEC, which is close to the dependence testing (DT) achievability bound.

This paper presents an analytically designed layered decoding algorithm for quasi-cyclic low-density parity-check (QC-LDPC) codes in the 5th Generation (5G) New Radio (NR) mobile communication system. First, a layered density evolution (DE) based on reciprocal channel approximation (RCA) is newly developed to accurately reflect the layered decoding operation in the decoder design. Using this technique, a single nested sequence is optimized in a greedy way to configure the processing order for any given number of layers. The error-correction performance is improved by up to 0.15 dB, while the number of iterations is reduced by about one simultaneously.

This paper presents density evolution (DE) techniques based on reciprocal channel approximation (RCA) for general bit-interleaved coded modulation (BICM) systems. The original RCA-based DE (RCA-DE) technique is implemented under the assumption of binary-input additive white Gaussian noise channels (BI-AWGNCs). In BICM systems, however,$M$-ary modulation schemes are generally used, and they can be regarded as to be a parallel transmission of$\log _{2} M$bits. Thus,$\log _{2} M$separate bit-level channels, which are not Gaussian equivalent, need to be considered. In order to extend the conventional RCA-DE technique to BICM systems, we first establish a model of protograph BICM ensembles. Two methods are developed based on the bit error rate (BER) and the BICM capacity in order to find a corresponding BI-AWGNC that models each of the bit-level channels. Using these methods, we implement the protograph RCA-DE technique for BICM systems and show that it achieves an accurate estimation. As a practical application of the proposed RCA-DE method, we design bit interleavers in order to achieve better BICM performance in the 3GPP New Radio (NR) LDPC coding system. Numerical results show that performance gain of up to 0.3 dB is consistently achieved over a wide range of parameter values.

In this paper, we introduce a structural extension method of polar codes as a new code modification method. Structural extension is a systematic method of generating additional codeword bits from the mother code by selecting intermediate bits obtained in the middle of the polar encoding. We start by studying simplex-extension from a 2×2 local polarization kernel, and then, we generalize this method to construct polar codes of arbitrary lengths. This extension method does not change the original polar code structure, and thus, the conventional encoder and decoder can be employed with a slight modification. We present a code construction tool by modifying density evolution to design punctured, shortened, and extended polar codes. By analysis and numerical experiments, we show that the proposed structural extension method enables to achieve an excellent tradeoff between performance and implementation complexity.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made incapable (by puncturing) or to be shortened are governed by binary domination. In particular, we show that binary domination completely determines incapable or shortened bit patterns for polar codes, and that all the possible incapable or shortened bit patterns can be identified. We then present the patterns of the corresponding encoder output bits to be punctured or fixed, when the incapable or shortened bits are given.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination. For punctured and shortened polar codes, we prove that the partial order by binary domination completely determines both incapable bit patterns (by puncturing) and fixed bit patterns (by shortening). In particular, we give a necessary and sufficient condition for an encoder output bit to be fixed by additionally shortening a single encoder input bit, as well as a necessary and sufficient condition for an encoder input bit to be made incapable by additionally puncturing a single encoder output bit. We also identify all the puncturing bit patterns yielding a given incapable bit pattern. These results provide a guidance to design a practical rate-matching scheme for polar codes. As an example, we present a rate-matching scheme based on our analytical observations. Numerical results show that it performs well over a wide range of code lengths and rates, compared with conventional rate-matching schemes.

In this paper we present a class of structured low-density parity-check (LDPC) codes from affine permutation matrices, called the APM-LDPC codes, which are a generalization of quasi-cyclic LDPC codes. We give a necessary and sufficient condition under which an APM-LDPC code has a cycle and introduce a simple method to construct APM-LDPC codes of large length by combining those of small length based on the Chinese remainder theorem. In particular, we show that the girth of APM-LDPC codes obtained in this method is always larger than or equal to those of given APM-LDPC codes

In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.