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 algorithmⅠandⅡ, analyse DE and complexity; simulations show that the both serial algorithms could improve decoding performance, improve convergence property, reduce complexity. Serial algorithmⅡimproves decoding performance greatly; serial algorithmⅠfinds 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 decodingⅠ, and present feasible project for quantized decoding.