Recitation: Rehearsing Wireless Packet
Reception in Software
Zhenjiang Li, Yaxiong Xie, Mo Li,
Nanyang Technological University
Kyle Jamieson
University College London
Wireless transmissions is going wider-band
Up to
160 MHz
Up to 40 MHz
802.11 ac
(2013)
802.11 n
Up to 22 MHz
(2009)
802.11 a/b/g
(1999)
Selective fading in wideband channels
SNR
Channel
Subcarriers
Selective fading in wideband channels
Channel
Heterogeneous BERs
Can we predict the bit destiny before
transmitting the packet?
Can we predict the bit destiny before
transmitting the packet?
• Narrow band SNR-BER theory cannot apply
• Approximation with effective SNR inaccurate
• Work with commodity WiFi NICs
Rehearsing before transmissions
Packet error rate (PER)
CSI
(Input)
Rehearse
transmissions
(Output)
Error-prone bit positions
To this end, we need?
Complex but predictable
Channel
CSI (as input)
Interleaving
Channel
Interleaving
CSI (as input)
Deterministic
Interleaving
• Block interleaver
interleaver
𝐗𝟏
𝐗𝟐
𝐗𝟑
𝐗 𝟏 𝐗 𝟐 𝐗 𝟑 𝐗 𝟒 𝐗 𝟓 …𝐗 𝟏𝟐
𝐗𝟒
𝐗𝟓
𝐗𝟔
write in row
𝐗𝟕
𝐗𝟖
𝐗𝟗
𝐗 𝟏𝟎
𝐗 𝟏𝟏
𝐗 𝟏𝟐
read in column
Interleaving
• Block interleaver
𝑩
𝒋=
× 𝒊 𝒎𝒐𝒅 𝟏𝟑 + 𝒊/𝟏𝟑
𝟏𝟑
interleaver
𝐗 𝟏 𝐗 𝟐 𝐗 𝟑 𝐗 𝟒 𝐗 𝟓 …𝐗 𝟏𝟐
write in row
read in column
𝐗 𝟏 𝐗 𝟒 𝐗 𝟕 𝐗 𝟏𝟎 𝐗 𝟐 …𝐗 𝟏𝟐
BER
So far
Coded Bits
Packet Bits
Coding
Channel
Interleaving
CSI (as input)
Deterministic
Predictable
Coding
Convolutional coding
• Simple encoder
– Coding rate of ½
– 3 registers (4 finite states)
Convolutional Coding
+
Output
Input
+
Convolutional coding
• Decoding
– Path with the minimal Hamming distance
• Failure
– Faulty path is chosen
– Error event
Convolutional coding
• Error event probability (EVP)
– Probability that a faulty path will be selected
• EVPi
– Any faulty path that diverges at state i
Convolutional coding
• EVPi varies
– Indicate the error-prone bit positions
Convolutional coding
Convolutional coding
Convolutional coding
∞
lim
𝒌→∞
𝒏𝒌 ∗ 𝑷𝒌
Viterbi theory
𝒌
Andrew James Viterbi
 𝑷𝒌 is the probability that one path with Hamming distance 𝑘 will be
chosen as the decoding result
𝒌
𝑷𝒌 =
𝒎=(𝒌+𝟏)/𝟐
𝒌 𝒎
𝒑𝒆 (𝟏 − 𝒑𝒆 )𝒌−𝒎 ,
𝒆
𝟏 𝒌
𝒌/𝟐
𝒑𝒆 (𝟏 − 𝒑𝒆 )𝒌/𝟐 +
𝟐 𝒌/𝟐
𝒌
𝒌
𝒎= +𝟏
𝟐
𝒌 𝒊𝒔 𝒐𝒅𝒅
𝒌 𝒎
𝒑 (𝟏 − 𝒑𝒆 )𝒌−𝒎 , 𝒌 𝒊𝒔 𝒆𝒗𝒆𝒏
𝒆 𝒆
 𝒏𝒌 = 2k is the number of paths with Hamming distance 𝑘
Convolutional coding
∞
lim
𝒌→∞
𝒏𝒌 ∗ 𝑷𝒌
Viterbi theory
𝒌
Andrew James Viterbi
BER
Assumption Each coded bit has the same error probability 𝑝𝑒
Coded Bits
BER
However …
Coded Bits
Output 1
+
𝑿𝒏
𝑿𝒏−𝟏
𝑿𝒏−𝟐
𝑿𝒏−𝟑
𝑿𝒏−𝟒
𝑿𝒏−𝟓
𝑿𝒏−𝟔
Input
+
Output 2
EVP calculation in 802.11
• Diverging segments of faulty paths
– Cannot be directly measured
– Use error burst length to approximate
• All possible error combinations
EVP calculation in 802.11
(1) Short divergent segments
(2) Small number of error bits
Reducing computations
Sort
𝛌
𝑬𝑽𝑷 +=
𝒑𝒊 ×
𝒊∈𝑭
(𝟏 − 𝒑𝒊 ) × 𝒘𝒆,𝒍
𝒊∉𝑭
LDPC (Low Density Parity Check)
• Block code
Packet bits
Coded bits
LDPC (Low Density Parity Check)
• Block code
Packet bits
Coded bits
Decoding Error
𝑬𝑽𝑷𝒊 =
𝒏𝒊
𝒍=𝑬𝑪𝑪
𝓕∈𝑭𝒍
𝒑𝒋 ∙
𝒋∈𝓕
(𝟏 − 𝒑𝒋 )
𝒋∈𝓕
Finally
CSI (as input)
Experiment evaluation
• TP-Link TL-WDR7500 Wi-Fi router
– Atheros 9580 NIC (802.11n)
– SoC QCA9558
• Data collected
–
–
–
–
50 locations (U-shape route)
93,000+ UDP packets with 1000 byte random payloads
Iterating all 8 data rates (6.5, 13, 19.5, 26, 39, 52, 58.5, 65 Mbps)
CSIs and transmitted packets (correct and corrupted)
Benchmark tests
• Packet Error Rate (PER) prediction
Convolutional Code
LDPC Code
Benchmark tests
• Computational overhead
Average delay < 0.2 ms
Application -- #1 Rate selection
Rect-Rate: PER by Recitation < 0.1
ESNR: ESNR rate selection approach
OPT: Oracle selection based on actual
transmissions
• Throughput improvement
– Average: 25.6%
Application -- #2 Unequal protection
• Error-prone positions
Periodical pattern
(in OFDM symbols)
EVP accurately
describes the BER
Application -- #2 Unequal protection
Video streaming
• Rect-Video
•
•
I-frames at more reliable
positions
P-, B- frames at other positions
• Stan-Video
• Average 6dB improvement on PSNR (peak SNR), a standard
metric to measure video quality
More evaluations
• System parameters
• Partial packet recovery
• MIMO settings
• Mobility
Takeaways
1. Frequency selective fading in wideband channels
2. Narrow band experience unsuitable
3. Complicated but predictable 802.11 PHY operations