A Research On The Decoding Algorithm Of LDPC Codes On Graphical Models

Low Density Parity Check Codes are a class of linear block error-correcting codes that can be defined by the very sparse parity-check matrix. Their error performance approach Shannon limits. Message-passing schedule is an important factor which affects the performance of decoding. An significative question is whether different schedules could improve decoding performance.This paper mainly contains the following aspects:(1) First, simply introduce the development of error-correcting codes; analyse the capacity of channels; and introduce the background of LDPC Codes, point out that researching on LDPC Codes will help us get to the Shannon limit.(2) Introduce the graph theory of LDPC Codes; analyse the impact of cycle; and research how to construct the parity check matrix. These are the basic theory for following research.(3) Combined with probability statistic knowledge, introduce the basic theory of Message Passing Algorithm; analyse the classical decoding algorithm of LDPC Codes, including Sum Product Algorithm which based on probability and LLR, and Min Sum Algorithm. (4) Research message passing process on the tree; according SPA, turn the flooding schedule to serial schedule based on C-nodes and V-nodes, namely serial algorithmâ… andâ…¡, analyse DE and complexity; simulations show that the both serial algorithms could improve decoding performance, improve convergence property, reduce complexity. Serial algorithmâ…¡improves decoding performance greatly; serial algorithmâ… finds the better trade-off between performance and complexity, it is a good decoding algorithm with high application value.(5) Introduce the background of quantized decoding and basic theory. Analyse effect of quantized decoding, research the impact of limited quantized to serial decodingâ… , and present feasible project for quantized decoding.