Improving BER Performance of LDPC Codes Based on Intermediate Decoding Results

1. Improving BER Performance of LDPC Codes Based on Intermediate Decoding Results Esa Alghonaim, M. Adnan Landolsi, Aiman El-Maleh King Fahd University of Petroleum & Minerals Saudi Arabia

2. Outline • Motivation • Overview of LDPC codes • Belief Propagation (BP) Algorithm • LDPC Decoding Error Patterns Types • Proposed Improvement on BP Algorithm • Experimental Results • Conclusions

3. Motivation • LDPC codes belong to a family of error correction systems with performance close to information-theoretic limits. • Selected for next-generation digital satellite broadcasting standard (DVB-S2), ultra high-speed Local Area Networks (10Gbps Ethernet LANs). • Amenable to efficient parallel hardware implementation. • Built-in Error Checking. • At high SNR, uncorrected error patterns dominated by oscillating patterns • Number of bits in error varies considerably between iterations

4. LDPC Codes Overview • LDPC codes: linear block codes decoded by efficient iterative decoding. • An LDPC parity check matrix H represents the parity equations in a linear form • codeword c satisfies the set of parity equations H . c = 0. • each column in the matrix represents a codeword bit • each row represents a parity check equation c0 c1 c3 = 0 c1 c2 c4 = 0 c2 c3 c5 = 0 c3 c4 c6 = 0

5. 0 1 2 3 4 5 6 0 1 2 3 LDPC Codes Overview • Code Rate ratio of information bits to total number of bits in codeword. • LDPC codes represented by Tanner Graphs • two types of vertices: Bit Vertices and Check Vertices • Performance of LDPC code affected by presence of cycles in Tanner graph.

6. BP LDPC Decoding Algorithm • Iterative algorithm • Produces optimum performance in cycle-free graphs

7. BP LDPC Decoding Algorithm Check to variable Information Variable to Check Information Information check node j sends to bit node i about P(xi=b) Information bit node i sends to check node j about P(xi=b)

8. LDPC Decoding Error Patterns Types • Frame errors can be classified intro three main categories: • Oscillation error pattern: with nearly periodic change between maximum & minimum number of bits in errors. • High variation in bit error count as a function of iteration number. • Nearly-constant error pattern:bit error count becomes constant after few decoding iterations • Mainly due small size trapping sets • Random-like error pattern: error count evolution follows a random shape characterized by low variation range.

9. LDPC Decoding Error Patterns Types

10. Percentage of Error Patterns Types • Progressive-Edge-Growth (PEG) LDPC code minimizes girth (cycle length) and achieves good performance. • (1024, 512) PEG LDPC code

11. Correlation Between Uncorrected Codeword Bits & Failed Parity Check Equations

12. = Proposed Improvement on BP Algorithm

13. Experimental Results • Parallel computing simulation platform developed to run LDPC decoding simulations on 130 nodes LAN network. • Simulated LDPC codes • PEG (1024, 512) • IEEE 802.16e (960,480) • Randomly constructed LDPC codes (free of 4- and 6-cycles)

14. BER Improvement for (1024, 512) PEG LDPC Code

15. BER Improvement for IEEE802.16e(960,480)

16. Conclusions • A method to improve residual BER level in BP decoding of LDPC codes. • Oscillating error pattern dominant at high SNR for well designed LDPC codes. • Minimized BER using number of failed check equations as an indicator for the number of bits in error. • At SNR=3 dB, BER reduction of 40% achieved.