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The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
In this paper, we investigate the error performance of the protograph (LDPC) codes over Nakagami-$m$ fading relay channels. We first calculate the decoding thresholds of the protograph codes over such channels with different fading depths…
The sixth generation (6G) wireless communication system will improve the key technical indicators by one to two orders of magnitude, and come with some new features. As a crucial technique to enhance the reliability and efficiency of data…
LDPC lattices were the first family of lattices which have an efficient decoding algorithm in high dimensions over an AWGN channel. Considering Construction D' of lattices with one binary LDPC code as underlying code gives the well known…
Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an…
Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding…
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the…
In this paper, we analyze the finite-length performance of codes on graphs constructed by connecting spatially coupled low-density parity-check (SC-LDPC) code chains. Successive (peeling) decoding is considered for the binary erasure…
We face the following dilemma for designing low-density parity-check codes (LDPC) for quantum error correction. 1) The row weights of parity-check should be large: The minimum distances are bounded above by the minimum row weights of…
A three terminal relay system with binary erasure channel (BEC) was considered, in which a source forwarded information to a destination with a relay's "assistance". The nested LDGM (Low-density generator-matrix) -LDPC (low-density…
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…
There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them are focused on protographs with single edges and little research has been done for the…
Quantum error correction (QEC) is critical for practical realization of fault-tolerant quantum computing, and recently proposed families of quantum low-density parity-check (QLDPC) code are prime candidates for advanced QEC hardware…
An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the…
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which…
In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is derived to design non-binary LDPC codes…
In this paper, we develop a new channel model, which we name the $q$-ary partial erasure channel (QPEC). QPEC has a $q$-ary input, and its output is either one symbol or a set of $M$ possible values. This channel mimics situations when…
In streaming applications, doping improves the performance of spatially-coupled low-density parity-check (SC-LDPC) codes by creating reduced-degree check nodes in the coupled chain. We formulate a scaling law to predict the bit and block…
This paper studies coding schemes for the $q$-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size $q=2^m$, $m\in\mathbb{N}$, thus complementing some recently proposed packet-based…