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IEEE Wireless Communications Letters

Iterative Low Complexity Algorithm for LDPC Systems in the Presence of Phase Noise

Seare H. Rezenom, Fambirai Takawira

Published Aug 22, 2017• 2 citations
Publisher

Abstract

In this letter, we propose a low-complexity graph-based iterative receiver for low-density parity-check (LDPC) coded systems in the presence of strong phase noise. The proposed receiver exploits the inherent circular characteristics of phase noise and uses complex Gaussian density functions to construct the messages. We show the proposed method achieves similar bit-error rate performance as the existing lowest complexity algorithm, and has lower complexity for higher modulation.

DOI
10.1109/lwc.2017.2742998

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In this letter, we propose a low-complexity graph-based iterative receiver for low-density parity-check (LDPC) coded systems in the presence of strong phase noise. The proposed receiver exploits the inherent circular characteristics of phase noise and uses complex Gaussian density functions to construct the messages. We show the proposed method achieves similar bit-error rate performance as the existing lowest complexity algorithm, and has lower complexity for higher modulation.
We present two new iterative decoding algorithms for channels affected by strong phase noise and compare them with the best existing algorithms proposed in the literature. The proposed algorithms are obtained as an application of the sum-product algorithm to the factor graph representing the joint a posteriori probability mass function of the information bits given the channel output. In order to overcome the problems due to the presence in the factor graph of continuous random variables, we apply the method of canonical distributions . Several choices of canonical distributions have been considered in the literature. Well-known approaches consist of discretizing continuous variables or treating them as jointly Gaussian, thus obtaining a Kalman estimator. Our first new approach, based on the Fourier series expansion of the phase probability density function, yields better complexity/performance tradeoff with respect to the usual discretized-phase method. Our second new approach, based on the Tikhonov canonical distribution, yields near-optimal performance at very low complexity and is shown to be much more robust than the Kalman method to the placement of pilot symbols in the coded frame. We present numerical results for binary LDPC codes and LDPC-coded modulation, with particular reference to some phase-noise models and coded-modulation formats standardized in the next-generation satellite Digital Video Broadcasting (DVB-S2). These results show that our algorithms achieve near-coherent performance at very low complexity without requiring any change to the existing DVB-S2 standard.
Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These Quasi-Cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature.
Low-density Parity check codes (LDPC) are gaining interest for high data rate application in both terrestrial and spatial communications which requires low bit error rate. This paper proposes an algorithm through which the best parity check matrix is obtained for irregular low density parity check codes, which reduces the Bit Error Rate ,Frame Error Rate and computational complexity. Tanner graph also called a bipartite graph format in an Low Density Parity Check (LDPC) code design contains many short cycles; it will produce a computational complexity in a code design process and it degrades the code performance. To overcome this effect, we proposed an new algorithm which obtains a best final parity check matrix. Throughout the paper we will give the detailed description of an efficient algorithm proposed. The complexity is studied graphically and analytically. Using proposed algorithm, cycles of length four observed in corresponding matrix are removed. Each matrix is evaluated over a noisy Additive White Gaussian Noise (AWGN) channel. Bit Error rate and Frame error rate is calculated. The results are compared with randomly generated best parity check matrix. Simulation results shows that proposed method successfully overcomes the computational complexity and meets the near Shannon limit.
We develop a new low complexity algorithm for decoding low-density parity-check (LDPC) codes. The developments are oriented specifically toward the low cost-yet effective-decoding of (high rate) finite geometry LDPC codes. The decoding procedure updates the hard-decision received vector iteratively in search of a valid codeword in the vector space. Only one bit is changed in each iteration and the bit selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optimal mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing performance versus complexity trade-off for finite geometry LDPC codes.
We develop a new low-complexity algorithm to decode low-density parity-check (LDPC) codes. The developments are oriented specifically toward low cost, yet effective, decoding of (high-rate) finite-geometry LDPC codes. The decoding procedure iteratively updates the hard-decision received vector in search of a valid codeword in the vector space. Only one bit is changed in each iteration, and the bit-selection criterion combines the number of failed checks and the reliability of the received bits. Prior knowledge of the signal amplitude and noise power is not required. An optional mechanism to avoid infinite loops in the search is also proposed. Our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for finite-geometry LDPC codes.
In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can achieve performance as close as 1.3 dB and 0.7 dB to that of belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.