We consider Gallager’s soft-decoding (belief propagation) algorithm for decoding low-density parity-check (LDPC) codes, when applied to an arbitrary binary-input symmetric-output channel. By considering the expected values of the messages, we derive both lower and upper bounds on the performance of the algorithm. We also derive various properties of the decoding algorithm, such as a certain rob...

1.1. Point 1: Cited Papers. Gunnam et al. claim that we did not cite correctly their work [2] and refer to other four publications of their own to provide further explanation. Actually the introductory section of our work [3] aims at providing an overview of the state-of-the-art architectures on the subject. The five works by Gunnam et al. basically propose the same LDPC architecture where the ...

A specific LDPC check matrix structure is used to form multi-channel alternative signal to solve the problem that traditional block codes inhibiting PAPR scheme is not suitable for a large number of sub-carriers and LDPC code is applied to the field of optimization of peak-to-average ratio. A rapid construction method of LDPC check matrix and fast encoding process using matrix are analyzed in d...

A simple design method using dynamic programming is proposed for good LDPC codes with relatively low code-rate. By applying a dynamic programming optimization to the construction of the portion fixed for easy encoding in the parity-check matrix, we can maximize the girth associated with columns contained in that portion of the matrix. Simulation results show performance improvement over the con...

We present a technique for designing low-density parity-check (LDPC) code matrices for the MCS-1 to MCS-4 coding schemes of GSM. We demonstrate that these codes have significant performance gains over randomly constructed LDPC codes in the GSM setup. The new codes also show significant gains in performance over the conventional MCS-1 to MCS-4 GSM coding schemes when compared in terms of the bit...

An explicit construction of a family of binary LDPC codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.

In this paper, we analyze the robustness for low-density parity-check (LDPC) codes over the Gilbert-Elliott (GE) channel. For this purpose we propose a density evolution method for the case where LDPC decoder uses the mismatched parameters for the GE channel. Using this method, we derive the region of tuples of true parameters and mismatched decoding parameters for the GE channel, where the dec...

In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over the binary erasure channel (BEC). The main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of LDPC codes when decoded iteratively. We also give expressions for upper bounds on the average bit and block erasure probab...

Low-density parity-check (LDPC) 부호는 다양한 통신 시스템에서 중요한 오류 정정 기법으로 채택되었다. 특히 block-type LDPC (B-LDPC) 부호는 광대역 무선 접속 시스템에 관한 IEEE 802.16e 표준 [1]에 포함되었으며, 또한 무선랜 (wireless LAN)의 데이터 전송률에 대한 제한을 극복하기 위한 IEEE 802.11n 표준 [2]으로 제안되었다. B-LDPC 부호는 선형 시간 부호화와 효율적인 복호를 실제 시스템에서 적은 수의 하드웨어 메모리를 사용하여 쉽게 구현할 수 있게 해준다. Belief propagation (BP) 복호 [3]는 LDPC 부호의 복호 방법으로 잘 알려져 있다. 하지만 신뢰도 높은 정보를 복원하기 위하여 많은 반복 횟수를 ...

Simple cycles are the easiest cycles to reveal in Low-Density Parity Check (LDPC) codes. All minimum matrices of simple cycles with the same length will be equivalent after row or column permutations .In this paper,we analysis the structure of simple cycles and show all figures of minimal matrices of simple cycles. Firstly, we introduce a more general definition of cycle and investigate simple ...