polar codes for practical applicationsindividual.utoronto.ca/z_li/others/zl_proposal.pdf ·...

Polar Codes for Practical ApplicationsM.A.Sc. Thesis Proposal Presentation

Zhipeng Li

Department of Electrical and Computer EngineeringUniversity of Toronto

Supervisor: Elvino S. Sousa

May 26, 2017

Zhipeng Li (Universities of Toronto) Polar Codes for Practical Applications May 26, 2017 1 / 15

Outline

1 Polar CodesIntroductionDecoders and Adoption

2 Research Directions

Primary Concepts of Polar Codes

Invented by Arikan in 2009 [1].

First constructive codes that are mathematically proven to achievechannel capacities.

Apply an elegant effect: channel polarization.

Send pre-shared bits through low capacity channels.- called frozen bits, usually set to all zeros

Send information through high capacity channels.- called information bits

Primary Concepts of Polar Codes

Invented by Arikan in 2009 [1].

First constructive codes that are mathematically proven to achievechannel capacities.

Apply an elegant effect: channel polarization.

Send pre-shared bits through low capacity channels.- called frozen bits, usually set to all zeros

Send information through high capacity channels.- called information bits

Decoders and Recent Updates

Decoding alorithms

Successive cancellation (SC) decoder: O(NlogN).

- Greedy algorithm: picking most likely bits locally.

SC list (SCL) decoder: O(LNlogN).

- Selecting the most likely sequence from L candidates.

Cyclic redundancy check aided SCL (CA-SCL) decoder: O(LNlogN).

- Selecting the one passed CRC check.

Adoption

In November, 2016, polar codes were selected for control channel inthe enhanced mobile broadband (eMBB) scenario for 5G by 3GPP [2].

Standards for the other two major scenarios in 5G are still in debate.

- Almost equal supports for polar and LDPC codes.

Decoders and Recent Updates

Decoding alorithms

Successive cancellation (SC) decoder: O(NlogN).

- Greedy algorithm: picking most likely bits locally.

SC list (SCL) decoder: O(LNlogN).

- Selecting the most likely sequence from L candidates.

Cyclic redundancy check aided SCL (CA-SCL) decoder: O(LNlogN).

- Selecting the one passed CRC check.

Adoption

In November, 2016, polar codes were selected for control channel inthe enhanced mobile broadband (eMBB) scenario for 5G by 3GPP [2].

Standards for the other two major scenarios in 5G are still in debate.

- Almost equal supports for polar and LDPC codes.

Research Directions: Making Polar Codes Practical

Increase the throughput of SC-based decoders.- SC is a highly sequential algorithm.- Throughput of SC decoder is low, although it has low complexity.- Parallel segmentation polar codes is a possible solution.

Improve reliability by inner coding.- With the help of CRC, CA-SCL outperforms SCL.- CRC can be viewed as inner coding before polar coding.- It is possible to decrease the error rate further by using other channel

coding methods as inner coding.

Reduce memory usage of SCL decoder.- SCL decoder suffers from high memory consumption.- Around six times higher than turbo/LDPC codes [3].- Serial segmentation polar codes is a possible solution.

Find common components of LDPC and polar codes decoders- 5G standard adopts both LDPC and polar codes.- Having two decoders increases chip size.- Investigate the similarities between them may ease this problem.

Reference I

E. Arikan, “Channel polarization: A method for constructingcapacity-achieving codes for symmetric binary-input memorylesschannels,” IEEE Transactions on Information Theory, vol. 55,pp. 3051–3073, July 2009.

Z. Ye, “Chinese firms gain ground in 5G battle,” 2016.

R1-164360, “Analysis of candidate code types for long block length,”3GPP TSG RAN WG1 Meeting 85, 2016.

K. Niu, K. Chen, J. Lin, and Q. T. Zhang, “Polar codes: Primaryconcepts and practical decoding algorithms,” IEEE CommunicationsMagazine, vol. 52, pp. 192–203, July 2014.

Some Details: Performance Comparison

Figure: Block error rate (BLER) comparison [4]. Turbocodes use Log-MAP algorithm with Imax = 8. LDPCcodes use standard BP algorithm with Imax = 200.

Blocklength:210, except forLDPC whereN = 1056

Code rate: 0.5

Around 0.4 dBperformancegain to LDPCcodes when useCA-SCL withL = 32 and 24bits CRC

Some DetailsUnderstanding Channel Polarization

(X1,X2) = (U1 ⊕ U2,U2)

P(Y = y |X = x) = W (y |x)

C = I (X ;Y ) = I (W )

Sum-capacity preservation

Since the mapping (U1,U2)→ (X1,X2) is invertible, we have:

I (U1,U2;Y1,Y2) = I (X1,X2;Y1,Y2) = I (X1;Y1)+I (X1;Y2) = 2I (W )

The chain rule decomposition:

I (U1,U2;Y1,Y2) = I (U1;Y1,Y2) + I (U2;Y1,Y2|U1) = 2I (W )

tells us to first decode u1 by observing y1 and y2, then decode u1 byobserving y1 and y2, along with the side information of u1.

Some DetailsUnderstanding Channel Polarization

(X1,X2) = (U1 ⊕ U2,U2)

P(Y = y |X = x) = W (y |x)

C = I (X ;Y ) = I (W )

Capacity polarization - binary erasure channel (BEC) case

u1 is an erasure unless both y1 and y2 are received correctly. Thus,W (1) = BEC (1− (1− ε)2) = BEC (2ε− ε2).

Given knowledge u1, y1 and y2 act as two independent observation ofu2, so u2 is an erasure if both y1 and y2 are missed. W (2) = BEC (ε2).

W (1) ≤ W (2) since 0 ≤ ε ≤ 1

Some DetailsHigh Order Polarization

Some DetailsEncoder and SC Decoder Structure

Figure: Encoder of polar codes

Figure: SC decoder of polar codes

Some DetailsPolar Codes Properties

Low encoding and decoding complexity.

Encoders/decoders share universal structures.

Code constructions are channel dependent and generally hard.

- It is equivalent to finding those virtual channels with higher reliability.- Some low complexity construction methods are proposed.

Code rates can be tuned with 1-bit granularity.

Decoding performance is not sensitive to SNR estimation.

No error flooring found so far.

Segmentation Polar Codes I

Figure: Non-Segmented Polar Code

Segmentation Polar Codes II

Figure: Parallel Segmented Polar Code

Segmentation Polar Codes III

Figure: Serial Segmented Polar Code

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