Irregular low-density parity check (LDPC) codes are particularly well-suited for transmission schemes that require unequal error protection (UEP) of the transmitted data due to the different connection degrees of its variable nodes. However, this UEP capability is strongly dependent on the connection profile among the protection classes. This paper applies a multi-edge type analysis of LDPC cod...

Coded modulation systems based on low density parity check (LDPC) codes of finite lengths are considered. The union bounds on the bit error probabilities of the maximum likelihood (ML) decoding are presented for both additive white Gaussian noise (AWGN) and flat Rayleigh fading channels. The tightness of the derived bound is verified by simulating the ML decoding of a very short LDPC code. For ...

This paper considers the application of low-density parity check (LDPC) error correcting codes to code division multiple access (CDMA) systems over satellite links. The adapted LDPC codes are selected from a special class of semi-random (SR) constructions characterized by low encoder complexity, and their performance is optimized by removing short cycles from the code bipartite graphs. Relative...

In this paper, the cycles of Tanner’s (3, 5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner’s (3, 5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15-th root of unity of the prime field Fp. By checking the existence of solutio...

Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of codes called low-density parity-check (LDPC) codes. The are alternatives to the surface code, which currently leading candidate implement fault-tolerance. We introduce zoo LDPC and their potential making computers robust against noise. particular, explain ...

Multi-Edge Low-Density Parity-Check Coded Modulation Lei Zhang Master of Applied Science Graduate Department of Edward Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 2011 A method for designing low-density parity-check (LDPC) codes for bandwidth-efficient high-order coded modulation is proposed. Code structure utilizes the multi-edge-type LDPC code ensemble t...

The finite-length performance of multi-edge spatially coupled low-density parity-check (SC-LDPC) codes is analyzed over the binary erasure channel (BEC). Existing scaling laws are extended to arbitrary protograph base matrices including puncturing patterns and multiple edges between nodes. Compared to more involved rate-1/2 structures proposed to improve the threshold to minimum distance trade-...

This paper investigates the Triangle Single Parity Check (T/SPC) code, a novel class of high-rate low-complexity LDPC codes. T/SPC is a regular, soft decodable, linear-time encodable/decodable code. Compared to previous high-rate and low-complexity LDPC codes, such as the well-known Turbo Product Code / Single Parity Check (TPC/SPC), T/SPC provides higher code rates, shorter code words, and low...

A constant challenge in Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes lies on flexible code lengths and rates, conditioned by good error performance. This paper presents an optimal construction method of QC-LDPC Codes on the basis of graphical model and search algorithm. Utilizing the proposed scheme, we can construct adaptable QC-LDPC codes whose girths are no less than 12, and column ...