5G/NR Channel Codes Evolution and Recommendation on Polar Codes
In order to meet higher data rates and more diverse requirements of typical NR scenarios including eMBB, mMTC, and URLLC, a powerful and flexible channel coding scheme is one of the fundamental components of the NR access technology. In the recent RAN1# discussion, various channel coding schemes were discussed and 3GPP considered convolutional codes, turbo codes, polar codes and LDPC codes for evaluation.
3GPP has adopted Polar Coding for 5G/NR Uplink/Downlink control channel for eMBB. To improve the performance of polar coding, concatenated coding and combined decoding schemes are proposed.
What is Polar Codes?
Polar codes can asymptotically (for code length going to infinity) achieve the capacity of any binary input symmetric memoryless channel with encoding and decoding complexity of the order O(N log N), where N is the code length. At present they are the only class of channel codes that are provably capacity achieving with an explicit construction.
Types of Polar Codes for 5G/NR
To improve the performance of Polar codes, some concatenated coding and combined decoding schemes are proposed.
 CRCconcatenated Polar codes (CAPolar Code) with singleparitycheck code concatenation and multi CRCconcatenation
 Paritycheck concatenated Polar code (PCPolar Code)
How Polar Codes Constructed?
A Polar code is constructed by recursively applying a linear polarization transform to the binary input symmetric and memoryless channel W, expressed as the 2by2 matrix. Repeated use of the transform, n = log_{2}(N) times, results in an NbyN matrix, denoting the nfold Kronecker product. Polar codes leverage a phenomenon known as channel polarization. Above transform together with a successive cancellation decoder structure turns the N available channels (N channel uses) in to another set of N bitchannels, referred to as synthesised channels, such that the capacities of these bit channels tend to 0 (fully unreliable) or to 1 (fully reliable) when N goes to infinity.
In fact, the proportion of reliable channels, K, tends to the capacity of the original communication channel. Data is communicated by placing information bits on the K reliable channels and placing fixed bits, usually zeros, on the NK unreliable channels. These bits on the unreliable channels are referred to as frozen bits, and the set of their positions is referred to as the frozen set F of size NK. Frozen bits and the frozen set is known by both the encoder and the decoder. In this way, a polar code of code length N, information word length K, and code rate R=K/N is constructed.
 Polar code construction allows for different rates by the choice of the size of the frozen set F.
 It allows only for lengths that are powers of two, i.e., N = 2^{n}.
 Polar codes of other lengths may be constructed by puncturing or shortening. In puncturing, some code bits are not transmitted, while in shortening, some systematic bits are set to zero and not transmitted.
Evolution Consideration of Different Channel Coding Schemes:
An advantage of the class of Polar Codes is that different types of decoders are possible for the same encoder. Therefore Polar codes are suitable to be used in a wide range of scenarios with diverse requirements. In contrast, other candidate schemes, such as Turbo codes, LDPC codes, and (TB)CCs cannot provide such flexibility. The power and area efficiency of Turbo decoders deteriorates very fast when increasing the block size. LDPC codes perform typically well for large blocks and high rates, however, performance is poor for rates below ½. It is noted that such code rate range can be the most common scenario in eMBB case. Table 1 summarizes the suitability of the different channel coding schemes. The gray squares indicate that the channel coding scheme cannot meet the requirements for that application.
Polar Codes  Turbo Codes  LDPC  (TB)CC  
eMBB:Large Block >8K 

Low power/area efficiency;


Not considered 
eMBB:
1K~8K blocks Fine granularity of code rates and code lengths 



Not considered 
URLLC/ControlCH/MTCUL:
Small block Highreliability 




MTCDL:
Small block Low Power 
Smalllist decoder or SC decoder for lowpower realization

Poor Performance with small block à not considered  Poor Performance with small block à not considered 

Furthermore, the performance of Polar Codes keeps improving along with increasing list size of the SCL decoder. According to our simulation with list sizes up to 2048, we have not observed any performance saturation so far. In contrast, we observe that the performance of turbo codes and LDPC codes saturates with the number of decoding iterations. As a result, the operators can keep improving the system capacity with newer ASIC technology. For example, when the list size is increased from 32 to 128 (the decoding complexity increases about by a factor of four), the BLER performance will gain another 0.5 ~0.7dB for some control channels. Therefore the system capacity can simply be increased with the availability of new Polar decoding chips.
Reference: R1164039 and R11700979
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