Performance analysis of protograph-based low-density parity-check codes with spatial diversity

Abstract

In wireless communications, spatial diversity techniques, such as space-time block code and single-input multipleoutput (SIMO), are employed to strengthen the robustness of the transmitted signal against channel fading. This article studies the performance of protograph-based low-density parity-check (LDPC) codes with receive antenna diversity. The authors first propose a modified version of the protograph extrinsic information transfer algorithm and use it for deriving the threshold of the protograph codes in a SIMO system. The authors then calculate the decoding threshold and simulate the biterror rate (BER) of two protograph codes (accumulate-repeat-by-3-accumulate (AR3A) code and accumulate-repeat-by-4-jagged-accumulate (AR4JA) code), a regular (3,6) LDPC code and two optimised irregular LDPC codes. The results reveal that the irregular codes achieve the best error performance in the low signal-to-noise-ratio (SNR) region and the AR3A code outperforms all other codes in the high-SNR region. Utilising the theoretical analyses and the simulated results, the authors further discuss the effect of the diversity order on the performance of the protograph codes. Accordingly, the AR3A code stands out as a good candidate for wireless communication systems with multiple receive antennas.

Protograph LDPC codes for STBC Rayleigh fading channels

“…In [14], we have proposed a novel PEXIT algorithm over Rayleigh fading channels. In the following, we will extend this algorithm for our system with minor modifications and demonstrate that the output extrinsic LLR messages in such a system satisfy the aforementioned condition.…”

“…Adopting the formula (12), the modified PEXIT algorithm is easily obtained based on [14], which is applicable for our system so as to derive the decoding threshold of the protograph codes.…”

“…Later, the accumulate repeat accumulate (ARA) code and accumulated repeat by-4-jagged accumulate (AR4JA) code, which possess simple protograph structures to realize linear encoding and decoding, have been proposed by Jet Propulsion Laboratory (JPL) [12], [13]. Based on the aforementioned advantages, the protograph codes have been analyzed and optimized over ergodic and quasi-static fading channels by utilizing the protograph EXIT (PEXIT) algorithms [14]- [16]. Nevertheless, thus far, there is no literature analyzing the concatenated framework of the protograph codes and STBC.…”

Performance of Joint Source-Channel Coding Based on Protograph LDPC Codes over Rayleigh Fading Channels

“…Moreover, if a fixed channel vector h j is given for the jth coded bit, the associated initial channel log-likelihood ratio (LLR) with MRC method has been proved to follow a symmetric complex Gaussian distribution, and it can be expressed as [7] L ch,j = ln…”

“…Although protograph extrinsic information transfer (PEXIT) algorithms [6] have been further tailored to predict the decoding thresholds of protograph-based codes over single-input multiple-output (SIMO) fading channels [7], to the best of our knowledge, little is known on the analytical performance for DP LDPC codes considering both source statistics and multiple receive antennas under fading conditions.…”