September 2004 doc IEEE 802 11 04992 r
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Irregular Structured LDPC Codes and Structured Puncturing Victor Stolpman, Nico van Waes, Tejas Bhatt, Charlie Zhang, and Amitabh Dixit This presentation accompanies submission IEEE 802. 11 -04/948 r 1 Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Parity-Check “Seed” Matrix • Small binary matrix low storage costs. • Acts as a blueprint to the structure of the expanded LDPC code. • Constructed from an ensemble with good asymptotic properties for the desired channel (e. g. AWGN, BEC, Fading, MIMO, etc. ). • Expanded using permutation matrices (e. g. single circular-shift) to construct the LDPC matrix used in the error control system. • After expansion, final LDPC matrix will be of the same ensemble. • Storage is smaller than the storage of exponents. • For example purposes only, a seed matrix: Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Permutation “Spread” Matrices • Finite set of matrices consisting of circular-shift matrices, the identity matrix, and the all zeros matrix. • Indexed via their exponent values. Submission Victor Stolpman et. al
September, 2004 Expanded LDPC Matrix doc. : IEEE 802. 11 -04/992 r 1 • “Expanded” LDPC matrix whose sub-matrices belong to the finite set of permutation matrices • In matrix notation, we write • Thus, the final exponents are of the finite set: Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Universal Exponential Matrix • Exponential matrix definition used for all LDPC code constructions despite the ensemble and seed construction dimension. • Because it is “rule-based” and not tied to a particular “seed” matrix construction, it offers forward-compatibility and hardware reuse for different products and standards. • Adapts for multiple block sizes and code rates without additional storage for exponent values. • Applicable to different ensembles designed for different channels. Submission Victor Stolpman et. al
September, 2004 Final Exponential Matrix doc. : IEEE 802. 11 -04/992 r 1 • Constructed via masking the “seed” matrix with the “universal” exponent matrix (Note: operations can be reduced to just the ones locations in the seed parity-check matrix). • Using the following mapping: Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Small Construction Example Parity Submission Systematic Victor Stolpman et. al
September, 2004 Simulations doc. : IEEE 802. 11 -04/992 r 1 • Simulated Block Sizes: – {576, 720, 768, 864, 960, 1008, 1152, 1296, 1344, 1440, 1536, 1584, 1728, 1872, 1920, 2016, 2112, 2160, 2304} • Permutation sub-matrix dimensions: – {12, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 33, 36, 39, 40, 42, 44, 45, 48} • Rate 1/2 Seed Matrices of dimension (24 x 48) – 3 seed matrices (designed for AWGN – all 3 from the same ensemble) • Rate 2/3 Seed Matrices of dimension (16 x 48) – 4 seed matrices (designed for AWGN – all 4 from the same ensemble) • Rate 3/4 Seed Matrices of dimension (12 x 48) – 4 Seed matrices (designed for AWGN – all 3 from the same ensemble) • 50 iterations of conventional belief propagation • In the pipeline … – Rate 7/8 Seed Matrices – Additional block sizes (forward-compatibility and hardware reuse) – Additional Layered Belief-Propagation decoding Submission Victor Stolpman et. al
September, 2004 Submission doc. : IEEE 802. 11 -04/992 r 1 Rate 1/2 BLER – AWGN BPSK Victor Stolpman et. al
September, 2004 Submission doc. : IEEE 802. 11 -04/992 r 1 Rate 2/3 BLER – AWGN BPSK Victor Stolpman et. al
September, 2004 Submission doc. : IEEE 802. 11 -04/992 r 1 Rate 3/4 BLER – AWGN BPSK Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Layered v/s Conventional BP (Rate 1/2) Layered BP (15 iterations) Conventional BP (50 iterations) Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 LDPC, N=1920, Different Code-Rates Submission Victor Stolpman et. al
September, 2004 Submission LDPC, N=1920, R-1/2 doc. : IEEE 802. 11 -04/992 r 1 Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Channel B 2 x 2 Simulation Results (to be revised before meeting) Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Channel D 1 x 1 Simulation Results (to be revised before meeting) Submission Victor Stolpman et. al
September, 2004 doc. : IEEE 802. 11 -04/992 r 1 Channel E 1 x 1 Simulation Results (to be revised before meeting) Submission Victor Stolpman et. al
September, 2004 Features doc. : IEEE 802. 11 -04/992 r 1 • Supports a wide range of block sizes without shortening – Shortening causes some inefficiencies with hardware: • Must shorten a longer codeword in decoding than needed • Power consumption and/or performance may vary with block size • Shortening rules continue to propagate in future systems • • Upper triangular seed matrices linear time encoder Wide range of block sizes reduces zero-padding inefficiencies Supports ensembles designed for different channel models Future compatibility and hardware reuse going forward – Additional block sizes are easily added for advancements in silicon – Additional ensembles are easily added for difference channel models • Layered Belief-Propagation decoding can be done to speed up convergence and reduce decoding latency Submission Victor Stolpman et. al
September, 2004 Summary doc. : IEEE 802. 11 -04/992 r 1 • Irregular Structure LDPC Codes – Applicable to seed matrices designed for different channels and antenna configurations (i. e. AWGN, BEC, fading, SISO, MIMO, etc. ). – “Rule-based” exponent reduces storage requirements because only seed matrices need to be stored and not exponents. – Reusable hardware for different channel models and product lines. – Performance is in line with other structured approaches customized for specific channels. • Structured Puncturing of LDPC Codes – A change in code rate does not require a change of connective nets in either the encoder or decoder. – Can work with different ensembles of different rates. – Allows for simple link adaptation and can easily support different code rates for separate spatial streams in MIMO antenna configurations. – Can reuse hardware for different error control applications. – Can coexist with other code rate adaptation approaches (e. g. nested matrices, shortening, etc. ). Submission Victor Stolpman et. al
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