Low-Density Parity-Check Codes Speaker : 詹承洲 Advisor : Prof. Andy Wu Date : 2007/03/07

Outline Introduction to LDPC Codes Problem Statement What You Will Learn Expected Results Reference

Communication Channel Noise

Digital Communication System rb rc JPEG, MPEG LDPC codes BPSK, QPSK, 16-QAM, 64-QAM Transmitter Modulator Channel Encoder Source Information rs Channel Demodu- lator Channel Decoder Source Data Sink Receiver

Motivation LDPC codes were first introduced by Gallager in 1962 LDPC codes was rediscovered by MacKay in 1993: Excellent error-correcting performance near the Shannon limit BER LDPC codes Only 0.045dB gap SNR(dB)

Applications WiMAX system IEEE 802.11n NSC 3C IT Project NTU/MTK Project

Introduction to LDPC Codes Parity check matrix : sparse matrix Bipartite graph B1 B2 B3 B4 B5 B6 B7 B8 B9 C1 C2 C3 C4 C5 C6 Bit nodes (columns) B1 B2 B3 B4 B5 B6 B7 B8 B9 Check nodes (rows) C1 C2 C3 C4 C5 C6

Our Achievement JSSC’02–(1024, 512)--52.5mm2 Our chip for WiMAX system

Problem Statement Algorithm domain: Architecture domain : Complex operation of VNU and CNU Low hardware utilization efficiency Inefficient termination scheme Architecture domain : Large area cost Need some high throughput approaches High power consumption

What You Will Learn Concept of channel coding The most powerful channel coding till now – LDPC Fixed-point analysis Evaluation of the performance of a channel coding

Expected Results Paper survey and acquaintance with LDPC codes C model of LDPC codes Advanced schedule Algorithm domain Operation function Termination Scheme Architecture domain Critical path shortening

Background Needed Linear algebra C programming Matlab (Optional) DSP or Communication Systems (Optional)

Reference [1] Xiao-Yu Hu, Eleftheriou E.; Arnold D.-M., Dholakia A., “Efficient Implementations of the Sum-Product Algorithm for Decoding LDPC Codes,” Global Telecommunications Conference, Vol. 2, pp.1036 – 1036E, Nov. 2001