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In order to achieve rate-compatible RM codes, two most effective ways are puncturing and shortening. In this paper, puncturing schemes are studied. Different from the existing spherical puncturing, puncturing schemes which do no change the Plotkin structure of RM codes are proposed, enabling existing decoding techniques be readily accessible. The proposed puncturing schemes are based on Hamming weights of column indices of the generator matrix of RM codes. When Hamming weights of column indices (also determining the column weights, CW) are the same, different strategies are proposed, producing four different puncturing strategies, called CW-IV, CW-LSB, CW-MSB, and CW-MSB-Sym, respectively. Analysis is performed to show the union bound on error performance of RM codes with puncturing. Theoretically, it also shows that the punctured first 1st-order subcode can have potentially better performance than the non-puncturing case if puncturing is properly designed. Simulation results show that the proposed puncturing strategies outperform random and quasi-uniform puncturing (QUP) schemes in terms of block error rate (BLER). Union bound results also confirm that the first 1st-order subcode shows better performance than the original non-puncturing case. This fact indicates a more efficient transmission scheme of RM codes: transmitting part of the original codeword to increase the spectrum efficiency while achieving a better BLER performance under recursive list decoding.

Decoding via sequentially guessing the error pattern in a received noisy sequence has received attention recently, and ORBGRAND has been proposed as one such decoding algorithm that is capable of utilizing the soft information embedded in the received noisy sequence. An information theoretic study is conducted for ORBGRAND, and it is shown that the achievable rate of ORBGRAND using independent and identically distributed random codebooks almost coincides with the channel capacity, for an additive white Gaussian noise channel under antipodal input. For finite-length codes, improved guessing schemes motivated by the information theoretic study are proposed that attain lower error rates than ORBGRAND, especially in the high signal-to-noise ratio regime.

In this paper, we propose an enhanced quasi-maximum likelihood (EQML) decoder for short LDPC codes. The proposed EQML decoder selects unreliable variable nodes (VNs) and performs the reprocessing if the first belief propagation (BP) decoding attempt fails. To improve the decoding error rate performance, we propose a novel node selection method based on the sign fluctuation of VNs' extrinsic messages. We also present a partial pruning stopping (PPS) rule to reduce the decoding complexity by deactivating part of the decoding tests once a valid codeword is found. Simulation results show that the proposed PPS rule achieves 20% lower decoding complexity compared to the full list decoding without sacrificing the error rate performance. In addition, the proposed EQML decoder outperforms the augmented BP decoder for short LDPC codes and approaches the performance of the ML decoder within 0.3 dB in terms of the frame error rate.

Probabilistic shaping (PS) combined with bipolar amplitude shift keying modulation is a promising transmission scheme to increase spectral efficiency. Different from the existing design of the point to point communications, we propose a PS-based uplink nonorthogonal multiple access (NOMA) scheme for fading channels to support multiple connections simultaneously, where successive interference cancellation (SIC)-based maximum a posterior (MAP) detection is implemented at the receiver. To exploit the shaping gain for each user, we first theoretically analyze the ergodic channel capacity and the constellation constrained (CC) capacity with discrete-constellation inputs, respectively. And then, a multi-step optimization scheme for maximizing the ergodic CC capacity is proposed to obtain the optimal probability mass function (PMF) of these input signals. The order of optimization is inverse to the SIC decoding order so that for each specific user, the remaining multiuser interference is calculated based on the optimal PMF of the later decoded users. Furthermore, based on this non-equiprobable transmission scheme, the closed-form pairwise error probability expressions for each user are obtained for the first time. Finally, compared with the uniform scheme, the simulations show that the proposed PS NOMA strategies achieve more than 1 dB gain in terms of the error performance.

The super codes of the first order Reed-Muller code are widely used in the practical wireless communication systems, such as WCDMA and LTE. However, the super codes are usually obtained by exhaustive computer search, which involves huge computational cost. Therefore a systematic algorithm to construct the super codes beyond exhaustive computer search has been expected for long time. In this paper, we propose a systematic algorithm for the super codes construction base on the m-sequence pairs, which only involves some item permutation within the m-sequence. In addition, the constructed super codes outperform the conventional codes in terms of decoding error rate. Meanwhile, the super codes share the same characteristics as the conventional ones, such as being of arbitrary length and rate, and being efficiently decodable with Fast Hadamard Transform (FHT).

A novel algorithm, named Improved Protograph-based Extrinsic Information Transfer (IP-EXIT), is proposed in this paper. With the proposed algorithm, quite accurate performance evaluations of Quasi-Cyclic LDPC (QC-LDPC) codes with arbitrary puncturing can be provided. LDPC codes combined with IR-HARQ technique have been a hot topic at present and puncturing is definitely one of the most efficient ways to achieve LDPC combined with HARQ. Unlike Turbo codes, different puncturing patterns for the same LDPC code may result in huge performance gap, so researchers are trying to design the puncturing pattern with better performance for LDPC codes. Inevitably, a large number of puncturing pattern with different performance should be compared in order to choose the best one from them, and usually this work is done by simulations with computer. In this paper, a novel algorithm is proposed to replace the work of simulation. It has been proved that the proposed algorithm can accurately evaluate the performance of arbitrary puncturing pattern, with very low complexity and very little time.