Upper bounds to error probabilities of coded systems beyond the cutoff rate

Divsalar, D.; Biglieri, E.

doi:10.1109/tcomm.2003.820746

Cited by 46 publications

(17 citation statements)

References 22 publications

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“…We attribute Algorithm 1 Search for suboptimum pairing of P Subopt 1: Inputs: m, n, N 0 ; 2: Initialization: 3) Extension to Rayleigh Fading Channels: The philosophies introduced in Section IV-B1 and Section IV-B2 may also be directly applied to Rayleigh fading scenarios. In contrast to the AWGN scenario, the only difference for the Rayleigh fading scenario is that a new square-shaped matrix, namely D Prod ∈ R M |u ×M |u is defined for replacing D Euc in (34), whose element at the i th row and j th column is given by…”

Section: ) a Particular Realization Of Pmentioning

confidence: 99%

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Cutoff Rate of Sparse Code Multiple Access in Downlink Broadcast Channels

Wang

et al. 2017

IEEE Trans. Commun.

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Abstract-For the sake of supporting massive connectivity in future 5G networks, non-orthogonal multiple access (NOMA) techniques are advocated. As a promising NOMA technique, in recent years sparse code multiple access (SCMA) has attracted substantial attention. However, there is a paucity of studies on the theoretical analysis of its error-freely achievable data rate, especially in the downlink context. Hence, we derive the cutoff rate of SCMA in downlink broadcast channels, which indicates the lower-bound of a system's errorfreely achievable rate. However, we will demonstrate that when considering the conventional categorization of pairwise error events, the accuracy of the cutoff rate rapidly degrades in the low-SNR region owing to the fact that multi-user SCMA systems typically encounter an extremely large constellation size. Alternatively, by invoking Bergmans' concept from 1973 in the categorization of pairwise error events, we obtain a more accurate cutoff rate both in the low-and the high-SNR regions. Moreover, we provide insights into the cutoff rate derivation process, which reveals some general guidelines for designing a beneficial codebook, capable of improving SCMA with respect to its original low-density signature (LDS) based counterpart.

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Section: ) a Particular Realization Of Pmentioning

confidence: 99%

“…Since we have R 0 ≤ C, the cutoff rate is also regarded as the lower-bound of a system's error-free data rate [33]. In contrast to capacity, the cutoff rate is typically formulated as a closed-form bound, but it becomes inaccurate at low SNRs owing to relying on the union bound approximation of [34].…”

Section: Introductionmentioning

confidence: 99%

Cutoff Rate of Sparse Code Multiple Access in Downlink Broadcast Channels

Wang

et al. 2017

IEEE Trans. Commun.

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“…The repetition decoder decodes by computing, for (22) where is the LLR value about the information bit from the channel. For AWGN channel with noise variance , we have where is the channel observation of the binary phase shift keying (BPSK) modulated information bit.…”

Section: B Decoding Of Rzh Codesmentioning

confidence: 99%

“…Assuming decoded by ML criterion over a binary input additive weight Gaussian noise (BIAWGN) channel, the simple ML bound [21], [22] is a tight upper bound on BER for an linear block code with code rate . Let being the number of codewords with input weight and output weight .…”

Section: Upper Bound Of Regular Rzh Under ML Decodingmentioning

confidence: 99%

Low-Rate Repeat-Zigzag-Hadamard Codes

Yue

Wang

et al. 2008

IEEE Trans. Inform. Theory

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Abstract-In this paper, we propose a new class of low-rate error correction codes called repeat-zigzag-Hadamard (RZH) codes featuring simple encoder and decoder structures, and flexible coding rate. RZH codes are serially concatenated turbo-like codes where the outer code is a repetition code and the inner code is a punctured zigzag-Hadamard (ZH) code. By analyzing the code structure of RZH codes, we prove that both systematic and nonsystematic RZH codes are good codes, in the sense that for an RZH code ensemble, there exists a positive number 0 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than 0, the average block error probability of maximum-likelihood (ML) decoding approaches zero. Two decoding algorithms-serial and parallel decoders for RZH codes-are proposed. We then employ the extrinsic information transfer (EXIT) chart technique to design irregular RZH codes. Results show that the optimized irregular RZH codes exhibit a performance that is very close to capacity in the low-rate regime.

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“…Spectral efficiency represents the ability of a system (e.g. modulation scheme [1][2]) to accommodate data within an allocated bandwidth. In addition to that, wireless systems suffer from fading due to the time-varying nature of the propagation channel [3].…”

Section: Introductionmentioning

confidence: 99%

Study on predistortion techniques and adaptive modulation used in fading channels

Liu¹,

Zhang²

2012

Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012)

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Abstract-Spectral efficiency is one of primary concern in the design of any wireless data communications systems, where fading is the main problem. An approach that can be taken to overcome the problem of fading is to adapt the modulation scheme according to the instantaneous propagation channel conditions. In this paper, we present a simplified mathematical model to calculate the probability of SER for any given constellation of M-QAM. This model plays an important role in designing spectrally efficient adaptive modulation over nonlinear mobile channels. Instantaneous spectral efficiency and its histogram distribution are found for linear and nonlinear channel cases. The achievable spectral efficiency is obtained for linear and nonlinear channel and compared with non-adaptive system and Shannon capacity.

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Upper bounds to error probabilities of coded systems beyond the cutoff rate

Cited by 46 publications

References 22 publications

Cutoff Rate of Sparse Code Multiple Access in Downlink Broadcast Channels

Cutoff Rate of Sparse Code Multiple Access in Downlink Broadcast Channels

Low-Rate Repeat-Zigzag-Hadamard Codes

Study on predistortion techniques and adaptive modulation used in fading channels

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