Progressive algebraic Chase decoding algorithms for Reed–Solomon codes

Zhao, Jiemin; Chen, Li; Ma, Xiao; Johnston, Martin

doi:10.1049/iet-com.2015.0873

Cited by 5 publications

(7 citation statements)

References 23 publications

(72 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following example shows how the APP matrix Π can be found by APP vector P . Consider a 3-bit symbols for RS (7,4) and assume that APP vector is calculated from (3) and so on. The element P i ∈ P stands for i th received symbol.…”

Section: Draft July 17 2017mentioning

confidence: 99%

“…These indices denote the two most probable symbols in the i th position and the value of these symbols are exactly j 1 i and j 2 i . Then the following parameter defines the reliability factor for symbol c i [4]…”

Section: Rayleigh Fading Channelmentioning

confidence: 99%

“…Recently, Chen et al, introduced progressive algebraic Chase decoding (PACD) algorithm that reduces complexity while maintaining the performance [4], [22]. In their proposed method, the test-vectors with higher reliability are decoded before the low reliability test-vectors.…”

Section: A Algebraic Soft Decision Decodingmentioning

confidence: 99%

“…They proved that list decoding problem for RS codes can be modeled by a curve-fitting problem over F n q . They presented decoding algorithm with polynomial-time complexity that corrects up to ⌊n − (n.k) − 1⌋ error which is better that n−k+1 2 for any value of k. The Guruswami-Sudan (GS) algorithm is a symbol level decoder that contains two major steps: interpolation and factorization [4]. Three years later, Koetter-Vardy (KV), proposed a softdecision list decoding algorithm, that inherited the algebraic decoding nature of GS algorithm while assigned weighted multiplicities to the symbols.…”

mentioning

confidence: 99%

“…, then there are several codewords within distance e of the received word and the decoding algorithm cannot find the correct answer [3], [4].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

Mani

Hemati

2019

IEEE Trans. Commun.

View full text Add to dashboard Cite

This paper proposes the Symbolic-Stochastic Chase Decoding Algorithm (S-SCA) for the Reed-Solomon (RS) and BCH codes. By efficient usage of void space between constellation points for q-ary modulations and using soft information at the input of the decoder, the S-SCA is capable of outperforming conventional Symbolic-Chase algorithm (S-CA) with less computational cost. Since the S-SCA starts with the randomized generation of likely test-vectors, it reduces the complexity to polynomial order and also it does not need to find the least reliable symbols to generate test-vectors. Our simulation results show that by increasing the number of test-vectors, the performance of the algorithm can approach the ML bound. The S-SCA(1K) provides near 2 dB gain in comparison with S-CA(1K) for (31, 25) RS code using 32-QAM. Furthermore, the algorithm provides near 3 dB further gain with 1K iteration compared with S-CA(65K) when (255, 239) RS code is used in an AWGN channel. For the Rayleigh fading channel and the same code, the algorithm provides more that 5 dB gain. Also for (63, 57) BCH codes and 8-PSK modulation the proposed algorithm provides 3dB gain with less complexity.This decoder is Soft-Input Soft-Output (SISO) decoder and is highly attractive in low power applications. Finally, the Symbolic-Search Bitwise-Transmission Stochastic Chase Algorithm (SSBT-SCA) was introduced for RS codes over BPSK transmission that is capable of generating symbolic test-vectors that reduce complexity and mitigate burst errors.The authors are with the DRAFT F n q (codeword space). The parameter d is the radius in which the codeword can be recovered [1].When a small fraction of the F n q space is used for codewords, a large d can be created. Specifically for Reed-Solomon (RS) codes, the code minimum distance is d = n − k + 1, which provides the largest possible code minimum distance for any linear code with the same input/output length.RS codes and Bose, Chaudhuri, and Hocquenghem (BCH) codes are linear codes suitable for high rate applications due to their large minimum distance. RS codes can be considered as a non-binary form of the BCH codes. In the same length n and approximately same rate, the BCH codes outperform RS codes, but the main reason that RS codes have frequent usage is that they can correct burst errors, which can occur in many applications like data storage devices.These codes are widely used in storage channels, satellite telecommunications (ETS 300 456), space telemetry systems (CCSDS and NTSS), digital video broadcasting (DVB-x) and wireless broadband systems (IEEE 802.x).The decoding problem is the problem of finding a codeword C ∈ F n q within a specific distance from a received code R ∈ R n q . The brute-force decoding method suffers from exponential complexity while the code length is increased linearly. The most common decoding algorithm for RS/BCH codes is hard decision decoding Berlekamp-Massey (HDD-BM) algorithm [2]. The HDD-BM algorithm has a running time complexity of O(n 2 ) and produces unique decoded message, w...

show abstract

Section: Draft July 17 2017mentioning

confidence: 99%

Section: Rayleigh Fading Channelmentioning

confidence: 99%

Section: A Algebraic Soft Decision Decodingmentioning

confidence: 99%

mentioning

confidence: 99%

“…, then there are several codewords within distance e of the received word and the decoding algorithm cannot find the correct answer [3], [4].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

Mani

Hemati

2019

IEEE Trans. Commun.

View full text Add to dashboard Cite

show abstract

Partially Parallel Low-Complexity Chase Decoding of Reed-Solomon Codes

Liang

Yang

Chen

2022

2022 IEEE Globecom Workshops (GC Wkshps)

View full text Add to dashboard Cite

Guessing random additive noise decoding with soft detection symbol reliability information - SGRAND

Duffy

Médard

2019

2019 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

In computer communications, discrete data are first channel coded and then modulated into continuous signals for transmission and reception. In a hard detection setting, only demodulated data are provided to the decoder. If soft information on received signal quality is provided, its use can improve decoding accuracy. Incorporating it, however, typically comes at the expense of increased algorithmic complexity. Here we introduce a mechanism to use binarized soft information in the Guessing Random Additive Noise Decoding framework such that decoding accuracy is increased, but computational complexity is decreased. The principle envisages a code-book-independent quantization of soft information where demodulated symbols are additionally indicated to be reliable or unreliable. We introduce two algorithms that incorporate this information, one of which identifies a Maximum Likelihood (ML) decoding and the other either reports an ML decoding or an error. Both are suitable for use with any block-code, and are capacityachieving. We determine error exponents and asymptotic complexity. They achieve higher rates with lower error probabilities and less algorithmic complexity than their hard detection counterparts. As practical illustrations, we compare performance with majority logic decoding of a Reed-Muller code, with Berlekamp-Massey decoding of a BCH code, and establish performance of Random Linear Codes.

show abstract

Progressive algebraic Chase decoding algorithms for Reed–Solomon codes

Cited by 5 publications

References 23 publications

Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

Symbol-Level Stochastic Chase Decoding of Reed-Solomon and BCH Codes

Partially Parallel Low-Complexity Chase Decoding of Reed-Solomon Codes

Guessing random additive noise decoding with soft detection symbol reliability information - SGRAND

Contact Info

Product

Resources

About