Information-Optimum LDPC Decoders Based on the Information Bottleneck Method

Lewandowsky, Jan; Bauch, Gerhard

doi:10.1109/access.2018.2797694

Cited by 72 publications

(126 citation statements)

References 26 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…15, we observe that the 3-bit MIM-QBP decoder outperforms the 3-bit non-uniform QBP decoder [13]; meanwhile, the 4-bit MIM-QBP decoder performs comparably to the 4-bit non-uniform decoder, while it requires 2 bits less than the latter for the additions for CN update. Moreover, the 4-bit MIM-QBP decoder achieves better performance than the 4-bit discrete decoder [8], and it only lags behind the floating-point BP decoder by around 0.05 dB at the BER of 10 −6 .…”

Section: A Regular Codesmentioning

confidence: 99%

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

Cai

Mei

2019

2019 IEEE Global Communications Conference (GLOBECOM)

View full text Add to dashboard Cite

A severe problem for mutual informationmaximizing lookup table (MIM-LUT) decoding of low-density parity-check (LDPC) code is the high memory cost for using large tables, while decomposing large tables to small tables deteriorates decoding error performance. In this paper, we propose a method, called mutual information-maximizing quantized belief propagation (MIM-QBP) decoding, to remove the lookup tables used for MIM-LUT decoding. Our method leads to a very practical decoder, namely the MIM-QBP decoder, which can be implemented based only on simple mappings and fixed-point additions. We further present how to practically and systematically design the MIM-QBP decoder for both regular and irregular LDPC codes. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art MIM-LUT decoder. Furthermore, the MIM-QBP decoder with only 3 bits per message can outperform the floating-point belief propagation (BP) decoder at high signal-tonoise ratio (SNR) regions when testing on high-rate codes with a maximum of 10-30 iterations.Index Terms-Finite alphabet iterative decoding (FAID), lookup table (LUT), low-density parity-check (LDPC) code, mutual information (MI), quantized belief propagation (QBP).

show abstract

Section: A Regular Codesmentioning

confidence: 99%

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

Cai

Mei

2019

2019 IEEE Global Communications Conference (GLOBECOM)

View full text Add to dashboard Cite

show abstract

“…, δ N are located in a line segment. As a result, (8) holds. Further assume that the elements in X can be relabelled to make P Y |X satisfy (11), and we implement the relabelling in this way.…”

Section: Discussionmentioning

confidence: 96%

“…. , 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)

View full text Add to dashboard Cite

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

show abstract

“…Set the temperature parameter σ 2 = t η where η is a negative constant called a cooling factor. (5) Update trainable variables in Θ according to the update rule of a specified stochastic gradient descent algorithm. (6) If t < t max then increment t and return to Step (2).…”

Section: (4)mentioning

confidence: 99%

Quantizer Optimization Based on Neural Quantizerfor Sum-Product Decoder

Wadayama

Takabe

2018

2018 IEEE Global Communications Conference (GLOBECOM)

View full text Add to dashboard Cite

A low-precision analog-to-digital converter (ADC) is required to implement a frontend device of wideband digital communication systems in order to reduce its power consumption. The goal of this paper is to present a novel joint quantizer optimization method for minimizing lower-precision quantizers matched to the sum-product algorithms. The principal idea is to introduce a quantizer that includes a feed-forward neural network and the soft staircase function. Since the soft staircase function is differentiable and has non-zero gradient values everywhere, we can exploit backpropagation and a stochastic gradient descent method to train the feed-forward neural network in the quantizer. The expected loss regarding the channel input and the decoder output is minimized in a supervised training phase. The experimental results indicate that the joint quantizer optimization method successfully provides an 8-level quantizer for a low-density parity-check (LDPC) code that achieves only a 0.1-dB performance loss compared to the unquantized system.

show abstract

Information-Optimum LDPC Decoders Based on the Information Bottleneck Method

Cited by 72 publications

References 26 publications

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

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

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

Quantizer Optimization Based on Neural Quantizerfor Sum-Product Decoder

Contact Info

Product

Resources

About