On Mutual Information-Maximizing Quantized Belief Propagation Decoding of LDPC Codes

He, Xuan; Cai, Kui; Mei, Zhen

doi:10.1109/globecom38437.2019.9013335

Cited by 26 publications

(60 citation statements)

References 28 publications

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“…. , δ N are sequentially located in a line segment, they are definitely located in the line segment and both (8) and (9) hold. We relabel the elements in X to satisfy…”

Section: Discussionmentioning

confidence: 99%

Dynamic Programming for Quantization of q-ary Input Discrete Memoryless Channels

Cai

Song

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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In this paper, under a general cost function, we present a dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for q-ary input discrete memoryless channel (DMC). The DP method has complexity O(q(N − M ) 2 M ), where N and M are the alphabet sizes of the DMC output and quantizer output, respectively. Then, starting from the quadrangle inequality (QI), two techniques are applied to reduce the DP method's complexity. One technique makes use of the SMAWK algorithm and achieves complexity O(q(N − M )M ). The other technique is much easier to be implemented and achieves complexity O(q(N 2 − M 2 )). We further derive a sufficient condition under which the optimal SDQ is optimal among all quantizers and the two techniques are also applicable. This generalizes the results in the literature for binary-input DMC. Next, we show that the cost function of α-mutual information (α-MI)-maximizing quantizer belongs to the general cost function we adopt earlier. We further prove that under a weaker condition than the sufficient condition we derived, the aforementioned two techniques are applicable to the design of α-MI-maximizing quantizer. Finally, we propose a new algorithm called iterative DP (IDP). Theoretical analysis and simulation results demonstrate that IDP can improve the quantizer design over the state-of-the-art methods in the literature.Index Terms-α-mutual information (α-MI), discrete memoryless channel (DMC), dynamic programming (DP), quadrangle inequality (QI), sequential deterministic quantizer (SDQ). P Z|Y (z|y) = 1 z = z , 0 z = z , or equivalently, we say y's quantization result Q(y) is a deterministic element in Z. In this paper, a general cost function given by (2) is considered, which is widely adopted in the literature [12]-[14]. Under such a condition, we show that there always exists at least one DQ that is optimal among all quantizers. Due to this reason as well as that DQ is more practical than non-deterministic quantizer, we focus only on DQs in this paper. For any DQ Q : Y → Z, denote Q −1 (z) ⊂ Y as the preimage of z ∈ Z.For binary-input DMC, dynamic programming (DP) [15, Section 15.3] was applied by Kurkoski and Yagi [16] to design quantizers that maximize the mutual information (MI) between X and Z, i.e., I(X; Z). The complexity (refer to the computational complexity throughout this paper unless the storage complexity is specified) of this DP method was reduced [17], [18] by applying the SMAWK algorithm [19]. However, for the general q-ary input DMC with q > 2, design of the optimal quantizers that maximize I(X; Z) is an NP-hard problem [14], [20]. Up till now, only the necessary condition [12], rather than the sufficient condition, has been established for the optimal quantizer; meanwhile, there only exist some suboptimal design methods in practice [5], [14], [21]-[23]. Moreover, to the best of our knowledge, so far no work has arXiv:1901.01659v3 [cs.IT] 28 Oct 2019

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“…. , δ N are sequentially located in a line segment, they are definitely located in the line segment and both (8) and (9) hold. We relabel the elements in X to satisfy…”

Section: Discussionmentioning

confidence: 99%

Dynamic Programming for Quantization of q-ary Input Discrete Memoryless Channels

Cai

Song

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

Self Cite

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“…However, the general design concepts proposed in this paper are crucial for any implementation of the learned function f (t in ). In literature, threshold-based implementations are proposed which require computations in a so-called computational domain at a higher internal resolution as compared to conventional information bottleneck decoder [29]. In contrast, at least for the check node, the min-sum operation can be performed using the integer-valued cluster indices as pointed out in Section II and proposed in [24].…”

Section: E Implementing the Lookup Tablesmentioning

confidence: 99%

Decoding Rate-Compatible 5G-LDPC Codes With Coarse Quantization Using the Information Bottleneck Method

Stark

Wang

Bauch

et al. 2020

IEEE Open J. Commun. Soc.

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Increased data rates and very low-latency requirements place strict constraints on the computational complexity of channel decoders in the new 5G communications standard. Practical low-density parity-check (LDPC) decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. In turn, performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing mappings that replace conventional finite-precision node computations. As a result, the exchanged messages in the IB approach can be represented with a very small number of bits. 5G LDPC codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include IB decoder design for puncturing and rate-compatibility. In contrast to existing IB decoder design techniques, the proposed decoder can be used for a large range of code rates with a static set of optimized mappings. The proposed construction approach is evaluated for a typical range of code rates and bit resolutions ranging from 3 bit to 5 bit. Frame error rate simulations show that the proposed scheme always outperforms min-sum decoding algorithms and operates close to double-precision sum-product belief propagation decoding. Furthermore, alternatives to the lookup table implementations of the mutual-information-maximizing mappings are investigated. INDEX TERMS LDPC codes, 5G, message-passing decoding, mutual-information based signal processing, information bottleneck method, machine learning.

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“…The HDQ approach designs a quantizer that maximizes mutual information in a greedy or progressive fashion. Quantizers aiming to maximize mutual information are widely used in nonuniform quantization design [1], [12]- [19], [26]- [29]. Due to the interest of this paper, the DRAFT cardinality of quantizer output is restricted to 2 to the power of b, i.e.…”

Section: A Motivationmentioning

confidence: 99%

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

Wang¹,

Wesel²,

Stark

et al. 2020

GLOBECOM 2020 - 2020 IEEE Global Communications Conference

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This paper uses the reconstruction-computation-quantization (RCQ) paradigm to decode low-density parity-check (LDPC) codes. RCQ facilitates dynamic non-uniform quantization to achieve good frame error rate (FER) performance with very low message precision. For message-passing according to a flooding schedule, the RCQ parameters are designed by discrete density evolution (DDE). Simulation results on an IEEE 802.11 LDPC code show that for 4-bit messages, a flooding MinSum RCQ decoder outperforms table-lookup approaches such as information bottleneck (IB) or Min-IB decoding, with significantly fewer parameters to be stored.

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On Mutual Information-Maximizing Quantized Belief Propagation Decoding of LDPC Codes

Cited by 26 publications

References 28 publications

Dynamic Programming for Quantization of q-ary Input Discrete Memoryless Channels

Dynamic Programming for Quantization of q-ary Input Discrete Memoryless Channels

Decoding Rate-Compatible 5G-LDPC Codes With Coarse Quantization Using the Information Bottleneck Method

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

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