Performance of short polar codes under ML decoding (original) (raw)

From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance

IEEE Transactions on Communications, 2014

We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that "interpolates" between RM and polar codes, call this family Cinter = {Cα : α ∈ [0, 1]}, where Cα α=1 is the original polar code, and Cα α=0 is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of α. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family Cinter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel.

Towards Optimal Decoding for Polar Codes

arXiv (Cornell University), 2022

In the conventional successive cancellation (SC) decoder for polar codes, all the future bits to be estimated later are treated as random variables. However, polar codes inevitably involve frozen bits, and their concatenated coding schemes also include parity bits (or dynamic frozen bits) causally generated from the past bits estimated earlier. We refer to the frozen and parity bits located behind a target decoding bit as its future constraints (FCs). Although the values of FCs are deterministic given the past estimates, they have not been exploited in the conventional SC-based decoders, not leading to optimality. In this paper, with a primary focus on the binary erasure channel (BEC), we propose SC-check (SCC) and belief propagation SCC (BP-SCC) decoding algorithms in order to leverage FCs in decoding. We further devise an improved tree search technique based on stack-based backjumping (SBJ) to solve dynamic constraint satisfaction problems (CSPs) formulated by FCs. Over the BEC, numerical results show that a combination of the BP-SCC algorithm and the SBJ tree search technique achieves the erasure recovery performance close to the dependence testing (DT) bound, a bound of achievable finite-length performance.

Generalized Fast Decoding of Polar Codes

2018 IEEE Global Communications Conference (GLOBECOM), 2018

Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have been selected as one of the coding schemes in the 5 th generation wireless standard (5G). Over the years various polar code decoding algorithms, like SC-list (SCL), have been proposed to improve the mediocre performance of the successive cancellation (SC) decoding algorithm for finite code lengths; however, like SC, they suffer from long decoding latency. Fast decoding of polar codes tries to overcome this problem by identifying particular subcodes in the polar code and decoding them with efficient decoders. In this work, we introduce a generalized approach to fast decoding of polar codes to further reduce SC-based decoding latency. We propose three multi-node polar code subcodes whose identification patterns include most of the existing subcodes, extending them to SCL decoding, and allow to apply fast decoding to larger subsets of bits. Without any error-correction performance degradation, the proposed technique shows up to 23.6% and 29.2% decoding latency gain with respect to fast SC and SCL decoding algorithms, respectively, and up to 63.6% and 49.8% if a performance loss is accepted, whose amount depends on code and decoding algorithm parameters, along with the desired speedup.

Performance Analysis of Belief Propagation Polar Code Decoder

IOP Conference Series: Materials Science and Engineering, 2019

Attributable to their ability accomplishing execution and low encoding and interpreting intricacy, polar codes have gotten noteworthy consideration as of late. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two mainstream approaches for disentangling polar codes. SCD, in spite of having less computational intricacy when contrasted and BPD, experiences long inertness because of the serial idea of the SC calculation. BPD, then again, is parallel in nature and is more alluring for low-dormancy applications. Nonetheless, because of the iterative idea of BPD, the required inertness and vitality dispersal increment straightly with the quantity of emphasis. In this paper, we propose a novel plan in light of sub-factor diagram solidifying to lessen the normal number addition the normal number of cycles required by BPD, which specifically converts into bring down inactivity and vitality dissemination. Besides, the equipment design for the proposed plot is cr...

Serially concatenated scheme of polar codes and the improved belief propagation decoding algorithm

IET Communications, 2020

In this study, a serially concatenated scheme of polar codes with convolutional codes is proposed to improve the error correction performance. The novel belief propagation (BP) decoding algorithm addresses two issues that are present in the currently available BP decoding algorithms. The first issue is the poor performance of the BP decoding algorithms, in particular the introduction of an error floor. The second is the component codes can only use systematic codes in the traditional concatenated scheme of polar codes with convolutional codes, which inhibits the effective update of the prior information of the redundant check bits. The proposed BP decoding algorithm is based on right-directed message processing, which effectively improves the decoding performance. In addition, the proposed concatenated scheme extends the selection of component codes from the systematic polar codes to the non-systematic polar codes. Hence, the areas of applications and the prior information of information bits for polar codes are expanded and more effectively updated, respectively. The simulation results show that the proposed scheme is much better than the traditional concatenated scheme, and the error floor is no longer introduced in terms of the block error rate, while the storage and computational complexities have not increased obviously.

Performance of polar codes for channel and source coding

2009

Polar codes, introduced recently by Arıkan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation, are optimal in this respect, their finite-length performance is not record breaking. We discuss several techniques through which their finite-length performance can be improved. We also study the performance of these codes in the context of source coding, both lossless and lossy, in the single-user context as well as for distributed applications.

On the construction and decoding of concatenated polar codes

2013 IEEE International Symposium on Information Theory, 2013

A scheme for concatenating the recently invented polar codes with interleaved block codes is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation scheme captures the capacity-achieving property of polar codes, while having a significantly better error-decay rate. We show that for any > 0, and total frame length N , the parameters of the scheme can be set such that the frame error probability is less than 2 −N 1− , while the scheme is still capacity achieving. This improves upon 2 −N 0.5− , the frame error probability of Arikan's polar codes. We also propose decoding algorithms for concatenated polar codes, which significantly improve the error-rate performance at finite block lengths while preserving the low decoding complexity.

An Improved Belief Propagation Decoding of Concatenated Polar Codes with Bit Mapping

—Bit-channels of finite-length polar codes are not fully polarized, and the negative influences from semi-polarized channels are not negligible. In this paper, we consider the concatenated system of an inner polar code and an outer low-density parity-check (LDPC) code to improve the error correction performance of finite length polar code with belief propagation (BP) decoding. We propose a bit mapping method between LDPC coded bits and polarized channels, aiming to match coding protection of LDPC codes with polarization of polar codes. Simulation results show that, concatenated polar codes with bit mapping outperform pure polar codes with BP decoding and concatenated polar codes with traditional consecutive bit mapping.

Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes

The capacity-achieving property of polar codes has garnered much recent research attention resulting in low-complexity and high-throughput hardware and software decoders. It would be desirable to implement flexible hardware for polar encoders and decoders that can implement polar codes of different lengths and rates, however this topic has not been studied in depth yet. Flexibility is of significant importance as it enables the communications system to adapt to varying channel conditions and is mandated in most communication standards. In this work, we describe a low-complexity and flexible systematic-encoding algorithm, prove its correctness, and use it as basis for encoder implementations capable of encoding any polar code up to a maximum length. We also investigate hardware and software implementations of decoders, describing how to implement flexible decoders that can decode any polar code up to a given length with little overhead and minor impact on decoding latency compared to...

A Novel Flip-List-Enabled Belief Propagation Decoder for Polar Codes

Electronics, 2021

Due to the design principle of parallel processing, belief propagation (BP) decoding is attractive, and it provides good error-correction performance compared with successive cancellation (SC) decoding. However, its error-correction performance is still inferior to that of successive cancellation list (SCL) decoding. Consequently, this paper proposes a novel flip-list- (FL)-enabled belief propagation (BP) method to improve the error-correction performance of BP decoding for polar codes with low computational complexity. The proposed technique identifies the vulnerable channel log-likelihood ratio (LLR) that deteriorates the BP decoding result. The FL is utilized to efficiently identify the erroneous channel LLRs and correct them for the next BP decoding attempt. The preprocessed channel LLR through FL improves the error-correction performance with minimal flipping attempts and reduces the computational complexity. The proposed technique was compared with the state-of-the-art BP, i.e...