Polar codes for non-identically distributed channels

Kim, Jangseob; Lee, Jung Woo

doi:10.1186/s13638-016-0782-2

Cited by 6 publications

(8 citation statements)

References 12 publications

(53 reference statements)

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“…This feature provides the extendibility of the decoder for various code rates [17]. Polar codes are extended to nonidentically distributed channels and they were found to be capacity achieving but the latency and complexity were sacrificed [18].…”

Section: Introductionmentioning

confidence: 99%

Successive cancellation decoding of polar codes using new hybrid processing element

James

Lakshminarayanan²

2022

IJRES

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Polar codes are one of the best linear block codes that are capacity achieving and incorporating along with it a simplified encoding and decoding routines. Successive cancellation (SC) algorithm is one of the predominantly used decoding algorithms due to its low complexity. It has broad scopes for hardware architecture design and reformulation. For polar code, the trade-off among the long latency and the silicon area of the SC algorithm is a bottleneck for the design of a high throughput polar decoder. The available prior SC polar decoder designs have higher area requirements for higher block length. This paper introduces a unique reformulation of the processing element (PE) block of SC decoding. The proposed reformulation leads to two benefits: firstly, critical path and hardware complexity of the PE are meaningfully reduced by using a unified adder block. Secondly, the silicon area requirement and the power consumption were also reduced considerably without any loss in performance. The proposed PE is used to build the decoder for various block lengths. Moreover, a Gate-level analysis of the proposed decoder has revealed that the design attains an 18% area reduction and 38% reduction in power consumption over the conventional one with similar performance.

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Section: Introductionmentioning

confidence: 99%

Successive cancellation decoding of polar codes using new hybrid processing element

James

Lakshminarayanan²

2022

IJRES

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“…We have expanded the conference article mentioned above by including further details in the description of the shortening algorithm proposed, another algorithm that performs extension, an analysis of the approach and extra simulation results of several application scenarios. In the works of [48] and [49] methods are proposed to generalize the channel polarization in scenarios of parallel transmission or when the channel parameter is unknown. In [48], a technique for PC construction for multichannel polar codes has been reported, including a scheme for modulation and bit interleaving, resulting in rate-matching compatibility.…”

Section: Introdutionmentioning

confidence: 99%

“…In [48], a technique for PC construction for multichannel polar codes has been reported, including a scheme for modulation and bit interleaving, resulting in rate-matching compatibility. The PC construction scheme proposed in [49] deals with scenarios with parallel channels and random channel parameters.…”

Section: Introdutionmentioning

confidence: 99%

Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Oliveira

Lamare²

2021

IEEE Access

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In this paper we propose a technique for polar codes (PC) construction for any code length. By default, PC construction is limited to code length proportional to the power of two. To construction the code length arbitrary, puncturing, shortening and extension techniques must be applied. However, performance is degraded with the use of these techniques. Other ways to design polar codes with arbitrary code length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for belief propagation (BP) or successive cancellation list (SCL) decoding. The polarization theory [1] is generalized for non-uniform channels (NUC) and with this approach we can construction rate-compatible PC and variable code length. We developed an implementation algorithm based on the of PC construction by Gaussian approximation (NUPGA). In a scenario where the transmission is over an additive white Gaussian noise (AWGN) channel and under successive cancellation (SC) decoding, the PC construction of arbitrary code length can be implemented with NUPGA. With NUPGA we repolarize the projected synthetic channels by choosing more efficiently the positions of the information bits. In addition, we present a generalization of the Gaussian approximation (GA) for the polarization and repolarization processes and an extension technique for PC. The PC construction based on NUPGA present better performance than the existing techniques as shown in the simulations of this work.

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“…In this paper, we present the concept of non-uniform polarization, which allows the construction of rate-compatible polar codes considering the polarization of channels with an arbitrary distribution of the Bhattacharyya parameter. Generalized channel polarization schemes have been proposed in [49] and [50]. In [49] the authors present a rate-matching scheme for multi-channel polar codes, which can be directly applied to bitinterleaved coded modulation schemes.…”

Section: Introdutionmentioning

confidence: 99%

“…In [49] the authors present a rate-matching scheme for multi-channel polar codes, which can be directly applied to bitinterleaved coded modulation schemes. Moreover, in [50] polar coding schemes are introduced for independent parallel channels in which the channel parameters are no longer fixed but exhibit some random behaviors.…”

Section: Introdutionmentioning

confidence: 99%

Study of Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Oliveira,

de Lamare

2021

Preprint

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We propose a novel scheme for rate-compatible arbitrarylength polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of nonuniform channel polarization. The original polar codes can only be designed with code lengths that are powers of two. Puncturing, shortening and extension are three strategies to obtain arbitrary code lengths and code rates for polar codes. There are other ways to design codes with arbitrary length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for Belief propagation (BP) or Successive Cancellation (SC) decoding. In general, the quality of the projected bit channels by these arbitrary-length techniques differs from that of the original bit channels, which can greatly affect the performance of the constructed polar codes. The proposed Non-Uniform Polarization based on Gaussian Approximation (NUPGA) is an efficient construction technique for rate-compatible arbitrary-length polar codes, which chooses the best channels (i.e., selects the positions of the information bits) by re-polarization of the codeword with desired length. A generalization of the Gaussian Approximation is devised for both polarization and re-polarization processes. We also present shortening and extension techniques for design polar codes. Simulations verify the effectiveness of the proposed NUPGA designs against existing rate-compatible techniques.

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Polar codes for non-identically distributed channels

Cited by 6 publications

References 12 publications

Successive cancellation decoding of polar codes using new hybrid processing element

Successive cancellation decoding of polar codes using new hybrid processing element

Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Study of Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

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