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Register a new userOn Systematic Polarization-Adjusted Convolutional (PAC) Codes
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Added by
Thibaud Tonnellier
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose systematic PAC codes. Thanks to the systematic property, improvement in the bit-error rate of up to 0.2 dB is observed, while preserving the frame-error rate performance. Moreover, a genetic-algorithm based construction method targeted to approach the theoretical bound is provided. It is then shown that using the proposed construction method systematic and non-systematic PAC codes can approach the theoretical bound even for higher code sizes such as (256,128).
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Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS and PAC codes has more than $0.25$ dB coding gain over the NASA standard concatenation scheme, which uses RS and convolutional codes.
This paper proposes a rate-profile construction method for polarization-adjusted convolutional (PAC) codes of any code length and rate, which is capable of maintaining trade-off between the error-correction performance and decoding complexity of PAC code. The proposed method can improve the error-correction performance of PAC codes while guaranteeing a low mean sequential decoding complexity for signal-to-noise ratio (SNR) values beyond a target SNR value.
This brief proposes a hardware implementation architecture for Fano decoding of polarization-adjusted convolutional (PAC) codes. This architecture uses a novel branch metric unit specific to PAC codes. The proposed decoder is tested on FPGA, and its performance is evaluated on ASIC using TSMC 28 nm 0.72 V library. The decoder can be clocked at 500 MHz and reach an average information throughput of 38 Mb/s at 3.5 dB signal-to-noise ratio for a block length of 128 and a code rate of 1/2.
In this paper, we present an optimal metric function on average, which leads to a significantly low decoding computation while maintaining the superiority of the polarization-adjusted convolutional (PAC) codes error-correction performance. With our proposed metric function, the PAC codes decoding computation is comparable to the conventional convolutional codes (CC) sequential decoding. Moreover, simulation results show an improvement in the low-rate PAC codes error-correction performance when using our proposed metric function. We prove that choosing the polarized cutoff rate as the metric functions bias value reduces the probability of the sequential decoder advancing in the wrong path exponentially with respect to the wrong path depth. We also prove that the upper bound of the PAC codes computation has a Pareto distribution; our simulation results also verify this. Furthermore, we present a scaling-bias procedure and a method of choosing threshold spacing for the search-limited sequential decoding that substantially improves the decoders average computation. Our results show that for some codes with a length of 128, the search-limited PAC codes can achieve an error-correction performance close to the error-correction performance of the polar codes under successive cancellation list decoding with a list size of 64 and CRC length of 11 with a considerably lower computation.
Performance and complexity of sequential decoding of polarization-adjusted convolutional (PAC) codes is studied. In particular, a performance and computational complexity comparison of PAC codes with 5G polar codes and convolutional codes is given. A method for bounding the complexity of sequential decoding of PAC codes is proposed.
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