Research On ADMM Decoding Algorithms For LDPC Codes Over ISI Channels

The low-density parity-check(LDPC)codes with good error-correcting performance approaching the channel capacity and low decoding complexity are concerned by scholars.And LDPC codes have been adopted by many communication standards,such as ITU-T G.9960,Wi-Fi,CCSDS,DTMB and CMMB.Particularly,in October 2016 3GPP agreed to use LDPC codes as the data channel coding scheme of enhanced mobile broadband(eMBB)scenario in 5G.The alternating direction method of multipliers(ADMM)decoding algorithm for LDPC codes has a better performance over memoryless channels,while the current studies on ADMM decoding for LDPC codes over channels with memory are still little.The ADMM decoding methods for LDPC codes over ISI channels are investigated,and the inter symbol interference(ISI)channel is a common channel model with memory in the digital storage system.The main works of ADMM decoding research are summarized as follows: 1.LDPC codes and linear block codes are outlined.The performances of Sum-Product(SP)decoding algorithm based on turbo equalization and interior point decoding algorithm for LDPC codes over ISI channels are analyzed in detail.And three typical decoding algorithms of LDPC codes are simulated over memoryless channel,including Sum-Product(SP)decoding,Min-Sum(MS)decoding and ADMM decoding.The performances of LDPC codes with these three decoding algorithms are analyzed.2.The SP decoding algorithm is usually used to decode LDPC codes based on turbo equalization over ISI channels.And the ADMM penalized decoding algorithm of LDPC codes exhibits better performances at error floor region comparable to that of the SP decoding algorithm over memoryless channel.In this thesis,the ADMM penalized decoding algorithm based on turbo equalization is proposed for LDPC codes over ISI channels.Simulation results of some LDPC codes show that the proposed decoding algorithm over ISI channels performs better than the existing SP decoding method at high signal-to-noise ratio.3.The decoding problem of LDPC codes over ISI channels can be seen as a quadratic programming.By making a detailed analysis of the ADMM that is a classic method for solving the convex optimization problem,the ADMM penalized decoding algorithm for LDPC codes over ISI channels is proposed.The simulation results indicate that the presented ADMM penalized decoding algorithm can significantly improve the performance of LDPC codes over ISI channels,compared with the interior point decoding algorithm.