Hardware Design of Concatenated Zigzag Hadamard Encoder/Decoder System With High Throughput

Jiang, Sheng; Lau, Francis C. M.; Sham, Chiu-Wing

doi:10.1109/access.2020.3022537

Cited by 5 publications

(11 citation statements)

References 20 publications

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“…, d − 1). Compute the extrinsic MI of the information bit using (36), where p e (ξ|X = x) denotes the PDF of the LLR values given the bit x being "0" or "1". Form the extrinsic MI matrix {I eh (i, k)} of size m × d. (Details of the method is shown in Appendix B.)…”

Section: Code Design Optimizationmentioning

confidence: 99%

“…code-division multiple-access [29] and interleave-division multiple-access [30]) with severe inter-user interferences, or embedding low-rate information in a communication link. The most notable channel codes with performance close to this limit are turbo-Hadamard codes [31], [32], [33], [34], concatenated zigzag Hadamard codes [35], [36], and LDPC-Hadamard codes [27], [28]. Both turbo-Hadamard codes and concatenated zigzag Hadamard codes suffer from long decoding latency due to the forward/backward decoding algorithms [31], [35].…”

Section: Introductionmentioning

confidence: 99%

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Protograph-Based Low-Density Parity-Check Hadamard Codes

Zhang,

Lau,

Sham

2020

Preprint

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In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes -a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed protograph-based LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree-1 and/or punctured nodes. We find codes with decoding thresholds ranging from −1.53 dB to −1.42 dB. At a BER of 10 −5 , the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared.

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Section: Code Design Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Protograph-Based Low-Density Parity-Check Hadamard Codes

Zhang,

Lau,

Sham

2020

Preprint

Self Cite

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show abstract

“…In Fig. 5, the blue edges correspond to B 0 (12), the red ones correspond to B 1 (13), and the green ones correspond to B 2 (14). Note that the "connections" represented by the dashed (red and blue) lines do not exist.…”

Section: Spatially Coupled Ldpc Codesmentioning

confidence: 99%

“…In [9] and [10], very low-rate turbo Hadamard codes and zigzag Hadamard codes have been proposed. However, their decoders require the use of serial decoding [11], [12], [13] and cannot make use of parallel decoding as in LDPC decoders. The error performances of turbo Hadamard codes and zigzag Hadamard codes are also not as good as those of the LDPC-Hadamard codes that are subsequently proposed [14].…”

Section: Introductionmentioning

confidence: 99%

Spatially Coupled PLDPC-Hadamard Convolutional Codes

Zhang¹,

Lau²,

Sham³

2021

Preprint

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In this paper, we propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We also develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs. To estimate the decoding thresholds of SC-PLDPCH-CCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length.With the use of the proposed layered PEXIT method, we develop a genetic algorithm to look for good SC-PLDPCH-TDCs in a systematic way. Subsequently, we extend the coupling length of these SC-PLDPCH-TDCs with good thresholds to form good SC-PLDPCH-CCs. Based on the same set of split protomatrices, we regard the threshold of SC-PLDPCH-TDC as the proxy of SC-PLDPCH-CC when the SC-PLDPCH-TDC with long coupling length has almost the same code rate as the SC-PLDPCH-CC.Results show that our optimized SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations also illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts in terms of error performance. Moreover, for the rate-0.00295 SC-PLDPCH-CC, a BER of 10 −7 is achieved at E b /N 0 = −1.45 dB, which is only 0.14 dB from the ultimate Shannon limit.

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“…code-division multiple-access [37] and interleave-division multiple-access [38]) with severe interuser interferences, or embedding low-rate information in a communication link. The most notable channel codes with performance close to this limit are turbo-Hadamard codes [39], [40], [41], [42], concatenated zigzag Hadamard codes [43], [44], and LDPC-Hadamard codes [35], [36]. Both turbo-Hadamard codes and concatenated zigzag Hadamard codes suffer from long decoding latency due to the forward/backward decoding algorithms [39], [43].…”

Section: Introductionmentioning

confidence: 99%

Protograph-Based LDPC Hadamard Codes

Zhang

Lau

Sham

2021

IEEE Trans. Commun.

Self Cite

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In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codesa type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed protograph-based LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree-1 and/or punctured nodes. We find codes with decoding thresholds ranging from −1.53 dB to −1.42 dB. At a BER of 10 −5 , the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared.

show abstract

Hardware Design of Concatenated Zigzag Hadamard Encoder/Decoder System With High Throughput

Cited by 5 publications

References 20 publications

Protograph-Based Low-Density Parity-Check Hadamard Codes

Protograph-Based Low-Density Parity-Check Hadamard Codes

Spatially Coupled PLDPC-Hadamard Convolutional Codes

Protograph-Based LDPC Hadamard Codes

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