A high-rate coding scheme that polar codes are concatenated with low density generator matrix (LDGM) codes is proposed in this paper. The scheme, referred to as polar-LDGM (PLG) codes, can boost the convergence speed of polar codes and eliminate the error floor behavior of LDGM codes significantly, while retaining the low encoding and decoding complexity. With a sensibly designed Gaussian approximation (GA), we can accurately predict the theoretical performance of PLG codes. The numerical results show that PLG codes have the potential to approach the capacity limit and avoid error floors effectively. Moreover, the encoding complexity is lower than the existing LDPC coded system. This motives the application of powerful PLG codes to satellite communications in which message transmission must be extremely reliable. Therefore, an adaptive relaying protocol (ARP) based on PLG codes for the relay satellite system is proposed. In ARP, the relay transmission is selectively switched to match the channel conditions, which are determined by an error detector. If no errors are detected, the relay satellite in cooperation with the source satellite only needs to forward a portion of the decoded message to the destination satellite. It is proved that the proposed scheme can remarkably improve the error probability performance. Simulation results illustrate the advantages of the proposed scheme

In this article, we investigate the depth distribution and the depth spectra of linear codes over the ring R=F2+uF2+u2F2, where u3=1. By using homomorphism of abelian groups from R to F2 and the generator matrices of linear codes over R, the depth spectra of linear codes of type 8k14k22k3 are obtained. We also give the depth distribution of a linear code C over R. Finally, some examples are presented to illustrate our obtained results.

In this paper, we derive a simple formula to generate a wide-sense systematic generator matrix(we call it quasi-systematic) B for a Reed-Solomon code. This formula can be utilized to construct an efficient interpolation based erasure-only decoder with time complexity O(n2) and space complexity O(n). Specifically, the decoding algorithm requires 3kr + r2 - 2r field additions, kr + r2 + r field negations, 2kr + r2 - r + k field multiplications and kr + r field inversions. Compared to another interpolation based erasure-only decoding algorithm derived by D.J.J. Versfeld et al., our algorithm is much more efficient for high-rate Reed-Solomon codes.

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the proposed encoding-aware LDPC codes is comparable to that of the progressive-edge-growth (PEG) constructed nonbinary LDPC cycle codes.

This paper considers the optimal generator matrices of a given binary cyclic code over a binary symmetric channel with crossover probability p→0 when the goal is to minimize the probability of an information bit error. A given code has many encoder realizations and the information bit error probability is a function of this realization. Our goal here is to seek the optimal realization of encoding functions by taking advantage of the structure of the codes, and to derive the probability of information bit error when possible. We derive some sufficient conditions for a binary cyclic code to have systematic optimal generator matrices under bounded distance decoding and determine many cyclic codes with such properties. We also present some binary cyclic codes whose optimal generator matrices are non-systematic under complete decoding.

This paper presents the generator polynomial matrices and the upper bound on the constraint length of punctured convolutional codes (PCCs), respectively. By virtue of these properties, we provide the puncturing realizations of the good known nonsystematic and systematic high rate CCs.