Lower Computation and Storage Complexity of QC-LDPC Codes in Rayleigh Fading Channel

Abstract

Abstract-This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes and a new multicarrier frequency hopping spread spectrum (MCFH-SS) system. The performance of newly obtained codes is evaluated by comparing with Reed Solomon (RS) codes. The computer simulation results show that the two girth-twelve QC-LDPC codes significantly outperform conventional RS codes with a gain of 2.1 dB at Index Terms-Bit error rate, DPSK, Girth, QC-LDPC, Rayleigh fading I. INTRODUCTIONA thought-provoking mission for wireless channels to communicate authentic data postulates many unusual problems. Low-density parity-check codes [1] have acquired considerable attention due to its near-capacity error execution and powerful channel coding technique with an adequately long codeword length. The performance of LDPC codes has been investigated in [2,3], and are encountered to outperform turbo codes.The potency of LDPC codes is outclass over the additive White Gaussian noise (AWGN) channel [4], where coherent detection employing phase shift keying (PSK) [5] can be carried out with carrier phase estimation. Precise phase tracking and high-quality estimation of channel state information (CSI) is required for the appropriate execution of coherent detection.The coherent detection of PSK often experiences problems while performing on Rayleigh fading channels. The reason is inaccurate CSI, due to complex channel gains variation with a passage of time, specified that LDPC codes characteristically function at a very low signal-to-noise ratio (SNR).In order to acquire accurate CSI, the authors in [6], have derived the estimates of the complex channel gain and variance of the additive noise from known pilot symbols and an estimation filter. In their work the authors have employed Turbo codes which have been detected coherently over for No channel estimation or equalization is expected if DPSK modulation is employed. Accordingly, the receiver can be more elementary and pilot symbols can be neglected at the cost of higher SNR.In [9,10], the authors have prevailed over the CSI by employing differential PSK modulation over Rayleigh fading channels with regular LDPC codes. However, the metric, which has been derived in [9], requires accurate estimates of the amplitudes of the complex channel gains, which can degrade the performance of the system if estimation falls erroneous.In [10], authors have emphasized the operation of differential detection relatively to codes themselves. They have employed LDPC codes with column weights 3 and 4, which have high computation and storage complexity. While LDPC codes with column weight j = 2, have respective advantage, since they have lower computation and storage complexity and their encoders and decoders are merer to employ. In work [9,10], authors have used differential PSK modulation but with regular LDPC codes.In this work, large girth QC-LDPC codes have been developed by deriving the basic idea from Bit-Filling (BF) and Progressive Edge-Growth algorithms proposed by C...