Recent Advances in Stochastic Decoding

1
Recent Advances in Stochastic Decoding

• Gord Harling
• Prof. Warren Gross, Prof. Shie Mannor
• McGill University
• Montreal, Quebec, Canada

2
LDPC Codes are the next wave

• They provide the best error correction
  performance of all known codes
• Standards
• DVB-S2
• IEEE 802.3an (10GBASE-T)?
• IEEE 802.16e (WiMAX)?
• IEEE 802.11n (WiFI)?

3
(No Transcript)
4
Belief Propagation (Sum-Product Algorithm)?
5
Belief Propagation (Sum-Product Algorithm)?

6
Architectures

• Fully parallel
• - bit serial,
• - analog
• - stochastic
• (big, fast)?

• Partially parallel
• (small, slow, flexible but limited to only
  certain codes)?

7
Stochastic representation
P 0.76 ( 19/25)? 0111111110011011011111011

• Encode probabilities as streams of random bits
• Common fallacy low precision
• 0.001 (10 bits in fixed-point vs. 1000 bits in
  stoc)?
• Robust applications
• Care about flow of changes of statistics of bits
  rather than on the precise value in a discrete
  frame of bits

8
multiplication
division
9
Stochastic decoding

• Stochastic decoding is a digital relaxation
  process
• Belief propagation, not message passing
• Very efficient parallel HW implementation
• lay out the graph in silicon
• Bit-serial
• Reduces routing congestion
• 75/83 fewer wires than 4/6 bit sum-product
  algorithm
• Fully digital easy to design, scale, and port

10
Stochastic Parity-Check Node Gaudet and Rapley,
Elec. Letters 2003
Soft XOR
11
Stochastic Variable Node Gaudet and Rapley,
Elec. Letters 2003
12
Variable Nodes

• Significant sharing of random numbers
• Share between comparators / EMs

13
Stochastic Decorrelators

• Decorrelation on the cheap!
• Break lock-up cycles
• Output stream has same stats
• Keep a flow of good (regenerative) bits
• Remember/use only the regenerative bits

Agreement
Disagreement

old outcomes
14
Applications 10 Gigabit Ethernet

• A single, low-overhead, high-performance LDPC
  code.
• IEEE 802.3an (10 GbE)
• 1723/2048 code
• No error floor to 1e-12
• 4 twisted pairs running at a raw bit rate of 2.5
  Gbps (PAM encoded for a symbol rate of 800 Mbaud)

15
Francois Leduc-Primeau, Warren Gross, Shie
Mannor, 2008
16
Applications WiFi and WiMAX

• Modern wireless standards define LDPC codes with
  multiple operating modes.
• IEEE 802.11n (WiFi)
• 648, 1296, and 1944 bit codewords
• 1/2, 2/3, 3/4, and 5/6 code rates
• IEEE 802.16e (WiMAX)
• 576, 672, ... , 2208, 2304 bit codewords (19
  sizes!)?
• 1/2, 2/3a, 2/3b, 3/4a, 3/4b, 5/6 code rates

17
FPGA Implementation

• Avg. clocks (10-8 BER ) 141
• Max clocks 700 (740 w/ I/O)?
• Latency 3.3 ?s _at_ 222 MHz
• (trade-off is possible)?
• T/P gt 1 Gbps for SNR gt 3 dB
• 1.66 Gbps at SNR 4.25 dB

18
(No Transcript)
19
Conclusions

• Stochastic decoding a new approach to LDPC
  decoders
• Fully-parallel LDPC decoder
• Fast (gt 1 Gbps) and area-efficient
• Bit-serial interleaver and simple node HW
• ? efficient ASICs
• Easy, scalable and portable design
• Potential for very low-power

20
Acknowledgements

• Saeed Sharifi Tehrani
• Kevin Cushon
• Francois Leduc-Primeau
• Prof. Shie Mannor
• Prof. Warren Gross