On gap rigidity problems for compact Hermitian symmetric spaces

We prove a gap rigidity theorem for diagonal curves in maximal polyspheres of irreducible compact Hermitian symmetric spaces of tube type, which is a dual analog to a theorem obtained by Mok. Motivated by the proof we show that the Chow space of certain totally geodesic submanifolds is affine algebraic, which gives a weaker version of gap rigidity for a class of higher dimensional submanifolds.     

Multiple decoding for polar-coded chase combining HARQ

The polar-coded hybrid automatic repeat request (HARQ) scheme with chase combining (CC) has very low complexity and is easy to combine with other techniques such as the coded-modulation and space–time coding, etc. However, the CC-HARQ scheme usually suffers from error and throughput performance degradation. A multiple decoding CC-HARQ (MDCC-HARQ) scheme is proposed in this paper by providing extra decoding chances when the joint decoding fails. Specifically, new LLR-sequences are constructed from the received signals, which can be utilized for the extra decoding attempts. Simulation results show that the proposed MDCC-HARQ scheme can achieve better error-performance and higher throughput efficiency, while requires less retransmission when compared with the CC-HARQ scheme.     

Performance analysis and design of quasi-cyclic LDPC codes for underwater magnetic induction communications

Magnetic induction (MI) communication is an effective scheme for underwater wireless communication. In this paper, we aim to design an underwater MI communication system based on Quasi-cyclic LDPC (QC-LDPC) codes. Firstly, for a given QC-LDPC code used in underwater MI communication, we propose a novel algorithm to evaluate its performance, which is named as underwater magnetic induction protograph (UWMIP) extrinsic information transfer algorithm. Furthermore, we present a differential evolution UWMIP (DE-UWMIP) algorithm, which incorporates the differential evolution method and the UWMIP algorithm. By this algorithm, we search the optimized QC-LDPC codes with best distance threshold. Simulation results show that the proposed algorithm is effective and provide a good guidance to design the underwater MI communication system.     

Constacyclic codes over finite commutative semi-simple rings

Finite commutative semi-simple rings are direct sum of finite fields. In this study, we investigate the algebraic structure of λ-constacyclic codes over such finite semi-simple rings. Among others, necessary and sufficient conditions for the existence of self-dual, LCD, and Hermitian dual-containing λ-constacyclic codes over finite semi-simple rings are provided. Using the CSS and Hermitian constructions, quantum MDS codes over finite semi-simple rings are constructed.     

A q-polynomial approach to constacyclic codes

As a generalization of cyclic codes, constacyclic codes is an important and interesting class of codes due to their nice algebraic structures and various applications in engineering. This paper is devoted to the study of the q-polynomial approach to constacyclic codes. Fundamental theory of this approach will be developed, and will be employed to construct some families of optimal and almost optimal codes in this paper.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.