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On Construction of Rate-Compatible Low-Density Parity-Check (RC-LDPC) Codes

On Construction of Rate-Compatible Low-Density Parity-Check (RC-LDPC) Codes. by Mohammadreza Yazdani and Amir H. Banihashemi Department of Systems and Computer Engineering Carleton University Ottawa, Ontario, Canada. Outline. Introduction and Motivation

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On Construction of Rate-Compatible Low-Density Parity-Check (RC-LDPC) Codes

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  1. On Construction of Rate-Compatible Low-Density Parity-Check (RC-LDPC) Codes by Mohammadreza Yazdani and Amir H. Banihashemi Department of Systems and Computer Engineering Carleton University Ottawa, Ontario, Canada

  2. Outline • Introduction and Motivation • Design Guidelines for Irregular RC-LDPC Codes • Construction of RC-LDPC Codes • Performance of Constructed Codes in Type-II Hybrid-ARQ Schemes • Concluding Remarks

  3. Introduction and Motivation • Rate-Compatible Codes: • Different quality of service and protection requirements in packet data communications • Adaptive coding and/or unequal error protection • Type-II Hybrid-ARQ Protocols • Single encoder/decoder pair

  4. Background • RC convolutional and block codes (since 1970’s) • RC punctured turbo codes (Barbulescu and Pietrobon, 1995; Mantha and Kschischang, 1999; Rowitch and Milstein, 2000; Kim and Struber, 2000; Abou-El-Azm, El-Fishawy, Mohammed, 2000;Chundi, Yonghui and Yuezu, 2002; Babich, Montorsi and Vatta, 2002; Chan and Modestino, 2003) • RC-LDPC codes (Li and Narayanan, 2002; Ha and McLaughlin, 2003)

  5. Irregular RC-LDPC Codes • Finite block lengths • Puncturing and extending • New structure for extensions (modular and deterministic) • Puncturing starts from lower degree nodes • Linear-time encodable • Progressive-Edge-Growth (PEG) Algorithm with optimized symbol degree distribution

  6. Overview of Results • Type-II hybrid ARQ: • K=1024; R=8/19,8/18, …, 8/10 • Throughput is only about 0.7 dB away from Shannon Limit • Outperforms similar schemes by up to 0.5 dB

  7. Design Guidelines • Finding the proper rate for the mother code • Properly extending and puncturing the mother code (to preserve both performance and linear-time encodability) • Construct a good linear-time encodable mother code

  8. p3 LDPC mother code Zero Zero Zero p1 Rate=k / (n+p1+p2+p3) p2 Sparse area p3 RC Codes Obtained by Extending p1 p2 • Extended codes perform better than punctured codes • At higher rates, extended codes perform poorly

  9. An Example • Characteristics of the family of RC-LDPC codes • k=1024 • Highest rate=8/10 • Lowest rate=8/19 • Rate of mother code=8/13 • Puncturing and extending profile: 8/10, 8/11, 8/12 8/13 8/14, 8/15, 8/16, 8/17, 8/18, 8/19 • Both the mother code and the extension matrix are constructed by linear-PEG with • Puncturing is performed on lower degree nodes Puncturing Extending

  10. Performance of Constructed Codes in Type-II Hybrid ARQ Protocols • Throughput: • Ni= The total number of bits transmitted after the ith transmission • pi= Probability that decoder accepts the packet after ith transmission • Fi = Frame error rate after the ith transmission. • To increase the throughput, we need to decrease the frame error rates of RC-LDPC codes.

  11. Throughput Curves

  12. Concluding Remarks • Guidelines for construction of irregular RC-LDPC codes with linear-time encoding were given. • Using PEG construction and a modular structure for the extended codes, RC-LDPC codes with very good performance and linear-time encoding were constructed. • In a type-II hybrid ARQ scheme, the constructed codes achieve a throughput which is only about 0.7dB away from Shannon Limit (k=1024, R=8/19,…,8/10).

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