Abstract
In this paper, we propose a rate-compatible (RC) parallel concatenated punctured polar (PCPP) codes for incremental redundancy hybrid automatic repeat request (IR-HARQ) transmission schemes, which can transmit multiple data blocks over a time-varying channel. The PCPP coding scheme can provide RC polar coding blocks in order to adapt to channel variations. First, we investigate an improved random puncturing (IRP) pattern for the PCPP coding scheme due to the code-rate and block length limitations of conventional polar codes. The proposed IRP algorithm only select puncturing bits from the frozen bits set and keep the information bits unchanged during puncturing, which can improve 0.2–1 dB decoding performance more than the existing random puncturing (RP) algorithm. Then, we develop a RC IR-HARQ transmission scheme based on PCPP codes. By analyzing the overhead of the previous successful decoded PCPP coding block in our IR-HARQ scheme, the optimal initial code-rate can be determined for each new PCPP coding block over time-varying channels. Simulation results show that the average number of transmissions is about 1.8 times for each PCPP coding block in our RC IR-HARQ scheme with a 2-level PCPP encoding construction, which can reduce half of the average number of transmissions than the existing RC polar coding schemes.
Highlights
Polar codes, proposed by Arikan [1], are the first class of structured channel codes that can provably achieve the capacity of the binary-input discrete memoryless symmetric channels via a low-complexity successive cancellation (SC) decoder [2,3,4,5,6]
We investigate an improved random puncturing (IRP) pattern for the parallel concatenated punctured polar (PCPP) coding scheme to obtain a sequence of nested encoding functions in a PCPP coding block transmission, for which the set of parity bits of a higher code-rate polar code is a subset of the set of parity bits of a lower code-rate polar code for a PCPP coding block incremental redundancy hybrid automatic repeat request (IR-HARQ) transmission
Coding block in our IR-HARQ scheme, the optimal initial code-rate can be determined for each new PCPP coding block over time-varying channels
Summary
Polar codes, proposed by Arikan [1], are the first class of structured channel codes that can provably achieve the capacity of the binary-input discrete memoryless symmetric channels via a low-complexity successive cancellation (SC) decoder [2,3,4,5,6]. A popular solution to compensate for channel state variations is incremental redundancy hybrid automatic repeat request (IR-HARQ) [20,21,22], where the parity bits are sent in an incremental fashion depending on the quality of the time-varying channel In this way, the rate-compatible (RC) codes are well-suited for the IR-HARQ scheme to address the scalable code-rate requirement, which can be implemented with a single encoder/decoder pair. Due to the block length and code-rate limitation of polar codes, both constructions of RC polar codes can achieve the capacity only for a sequence of rates that satisfy a certain relationship These RC coding schemes can be used only when the family of channels over which the transmission takes place is ordered by degradation; otherwise, the nested property does not hold.
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