Fast Successive-Cancellation-Based Decoders of Polar Codes (original) (raw)

A low-complexity improved successive cancellation decoder for polar codes

2014 48th Asilomar Conference on Signals, Systems and Computers, 2014

Under successive cancellation (SC) decoding, polar codes are inferior to other codes of similar blocklength in terms of frame error rate. While more sophisticated decoding algorithms such as list-or stack-decoding partially mitigate this performance loss, they suffer from an increase in complexity. In this paper, we describe a new flavor of the SC decoder, called the SC flip decoder. Our algorithm preserves the low memory requirements of the basic SC decoder and adjusts the required decoding effort to the signal quality. In the waterfall region, its average computational complexity is almost as low as that of the SC decoder.

Fast List Decoders for Polar Codes

IEEE Journal on Selected Areas in Communications, 2016

Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern codes such as low-density parity-check (LDPC) codes. Of the many methods to improve the error-correction performance of polar codes, list decoding yields the best results, especially when the polar code is concatenated with a cyclic redundancy check (CRC). List decoding involves exploring several decoding paths with SC decoding, and therefore tends to be slower than SC decoding itself, by an order of magnitude in practical implementations. In this paper, we present a new algorithm based on unrolling the decoding tree of the code that improves the speed of list decoding by an order of magnitude when implemented in software. Furthermore, we show that for software-defined radio applications, our proposed algorithm is faster than the fastest software implementations of LDPC decoders in the literature while offering comparable error-correction performance at similar or shorter code lengths.

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.

A method to enhance the performance of successive cancellation decoding in polar codes

2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), 2016

Polar codes are regarded as a major breakthrough in modern channel coding since they are capacity-achieving using simple successive cancellation (SC) decoding. However, this is only possible with significantly large code lengths which may not be applicable for many systems. In this paper, we focus on short length polar codes and present a method which can enhance the performance of the successive cancellation decoder. For the purpose of analysis, we discuss the SC code tree and show how the proposed method can improve the performance by increasing the computational nodes in the code tree. The results quantify the achieved performance improvement over the conventional SC decoder.

Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes

2021 IEEE International Symposium on Information Theory (ISIT)

This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements P that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is O N 1−1/µ + N P log 2 log 2 N P , where N is the block length of the code and µ is the scaling exponent of the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where P = N 2 , the latency of SSC decoding is O N 1−1/µ , which is sublinear in the block length. This recovers a result from our earlier work. Second, in a fully-serial implementation where P = 1, the latency of SSC decoding scales as O (N log 2 log 2 N). The multiplicative constant is also calculated: we show that the latency of SSC decoding when P = 1 is given by (2 + o(1)) N log 2 log 2 N. Third, in a semi-parallel implementation, the smallest P that gives the same latency as that of the fully-parallel implementation is P = N 1/µ. The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.

Hardware Implementation of Successive Cancellation Decoders for Polar Codes

Journal of Signal Processing Systems

The recently-discovered polar codes are seen as a major breakthrough in coding theory; they provably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm. Motivated by recent developments in polar coding theory, we propose a family of efficient hardware implementations for SC polar decoders. We show that such decoders can be implemented with O(n) processing elements, O(n) memory elements, and can provide a constant throughput for a given target clock frequency. Furthermore, we show that SC decoding can be implemented in the logarithm domain, thereby eliminating costly multiplication and division operations and reducing the complexity of each processing element greatly. We also present a detailed architecture for an SC decoder and provide logic synthesis results confirming the linear growth in complexity of the decoder as the code length increases.

Fast and Flexible Software Polar List Decoders

Journal of Signal Processing Systems, 2019

Flexibility is one mandatory aspect of channel coding in modern wireless communication systems. Among other things, the channel decoder has to support several code lengths and code rates. This need for flexibility applies to polar codes that are considered for control channels in the future 5G standard. This paper presents a new generic and flexible implementation of a software Successive Cancellation List (SCL) decoder. A large set of parameters can be fine-tuned dynamically without re-compiling the software source code: the code length, the code rate, the frozen bits set, the puncturing patterns, the cyclic redundancy check, the list size, the type of decoding algorithm, the tree-pruning strategy and the data quantization. This generic and flexible SCL decoder enables to explore tradeoffs between throughput, latency and decoding performance. Several optimizations are proposed to achieve a competitive decoding speed despite the constraints induced by the genericity and the flexibility. The resulting polar list decoder is about 4 times faster than a generic software decoder and only 2 times slower than a nonflexible unrolled decoder. Thanks to the flexibility of the decoder, the fully adaptive SCL algorithm can be easily

Successive-Cancellation Flip Decoding of Polar Codes with a Simplified Restart Mechanism

2023 IEEE Wireless Communications and Networking Conference (WCNC)

Polar codes are a class of error-correcting codes that provably achieve the capacity of practical channels. The successive-cancellation flip (SCF) decoder is a low-complexity decoder that was proposed to improve the performance of the successive-cancellation (SC) decoder as an alternative to the highcomplexity successive-cancellation list (SCL) decoder. The SCF decoder improves the error-correction performance of the SC decoder, but the variable execution time and the high worst-case execution time pose a challenge for the realization of receivers with fixed-time algorithms. The dynamic SCF (DSCF) variation of the SCF decoder further improves the error-correction performance but the challenge of decoding delay remains. In this work, we propose a simplified restart mechanism (SRM) that reduces the execution time of SCF and DSCF decoders through conditional restart of the additional trials from the second half of the codeword. We show that the proposed mechanism is able to improve the execution time characteristics of SCF and DSCF decoders while providing identical error-correction performance. For a DSCF decoder that can flip up to 3 simultaneous bits per decoding trial, the average execution time, the average additional execution time and the execution-time variance are reduced by approximately 31%, 37% and 57%, respectively. For this setup, the mechanism requires approximately 3.9% additional memory.

LLR-Based Successive Cancellation List Decoding of Polar Codes

IEEE Transactions on Signal Processing, 2015

We present an LLR-based implementation of the successive cancellation list (SCL) decoder. To this end, we associate each decoding path with a metric which (i) is a monotone function of the path's likelihood and (ii) can be computed efficiently from the channel LLRs. The LLR-based formulation leads to a more efficient hardware implementation of the decoder compared to the known log-likelihood based implementation. Synthesis results for an SCL decoder with block-length of N = 1024 and list sizes of L = 2 and L = 4 confirm that the LLR-based decoder has considerable area and operating frequency advantages in the orders of 50% and 30%, respectively.

Unrolled Polar Decoders, Part II: Fast List Decoders

Polar codes asymptotically achieve the symmetric capacity of memoryless channels, yet their error-correcting performance under successive-cancellation (SC) decoding for short and moderate length codes is worse than that of other modern codes such as low-density parity-check (LDPC) codes. Of the many methods to improve the error-correction performance of polar codes, list decoding yields the best results, especially when the polar code is concatenated with a cyclic redundancy check (CRC). List decoding involves exploring several decoding paths with SC decoding, and therefore tends to be slower than SC decoding itself, by an order of magnitude in practical implementations. This is the second in a two-part series of papers on unrolled polar decoders. Part I focuses on hardware SC polar decoders. In this paper (Part II), we present a new algorithm based on unrolling the decoding tree of the code that improves the speed of list decoding by an order of magnitude when implemented in softwa...