Enhancing the Decoding of Short LDPC Codes with Stochastic Sequences

Abstract

Low-Density Parity-Check (LDPC) codes are one of the most popular codes used in nowadays’ communication due to their high coding efficiency at low decoding complexity. With these characteristics, LDPC codes are suitable for high-speed information transmission systems. The widely used decoding algorithm for LDPC codes is Belief Propagation (BP) decoding with which the performance of LDPC codes can approach the Shannon limit.
With the development of 5G, a lot of attention is given to the so-called ultra-reliable low latency communication scenario which needs the short code to transmit. However, short codes will not have a very good performance with BP decoding. To solve this problem, investigations have been done such as multiple-bases BP decoding. Although this decoding method has a better performance than BP decoding, it will cause a high complexity in the hardware implementation. Besides, an investigation on the stochastic decoding for shortcodes was proposed in 2003. This decoding method is hardware friendly, but its performance can only approach BP decoding.
Inspired by multiple-bases BP decoding and stochastic decoding, binary stochastic decoding with parallel decoders is proposed in this thesis firstly. It represents stochastic sequences with multiple parallel Tanner graphs and uses hard-decision decoding in the iterative part because of the binary input bits. However, this decoding method has a severe performance loss compared to BP decoding. To avoid this problem, the enhancement method is used to make the binary sequences be non-binary sequences that can form more powerful parallel decoders. Then the non-binary symbols of these new sequences are transformed to their corresponding log-likelihood ratio which enables the iterative part to use BP decoding. In addition, combining with the ML decision of list decoding, the decision part of our stochastic decoder can fully utilize the output to increase the efficiency of the decoding method.
After ensuring the performance of our non-binary stochastic decoding to be better than BP decoding, the complexity of the decoder is reduced to save the computational resources. Finally, with constant adjustments, the bit width of each non-binary symbol is determined to be 15, and the sequence length is reduced to 20 which can let the non-binary stochastic decoding has an acceptable complexity while keeping good performance.

Popular Abstract

In the process of transmitting digital signals, errors often occur in the transmitted data stream which will cause bad signals such as blurred images, discontinuous sound, and so on. Channel coding which can be divided into encoding and decoding is an important step in the whole communication system to protect the digital signals and correct the errors. In the encoding part, error correction codes (ECC) are used to encode digital signals. In the decoding part, the received signal can be corrected by corresponding decoding algorithms. There is an error correction code proposed by Gallager in 1962 called Low-Density Parity-Check (LDPC) code and it has gradually been widely used in the field of wireless communications in recent years. In the context of 5G and beyond, a lot of attention is given to the so-called ultra-reliable low latency communication (URLLC) scenario such as remote surgery and automation driving. To realize low latency in these scenarios, the transmitted code should be short. However, for the short code, the traditional decoding algorithm for LDPC, Belief Propagation (BP) decoding, is not the best option, because the probability that the receiver can decode a correct codeword will decrease as the code length gets shorter.
This thesis is to investigate stochastic decoding with non-binary quantized sequences to beat the performance of BP decoding for the short LDPC codes based on stochastic computation, multiple bases BP decoding, and list decoding. These three decoding methods as our inspiration were proposed to solve the bad performance of BP decoding on short block codes in the previous years. However, they have their corresponding disadvantages such as unfriendly implementation in hardware and unimpressive performance which can only approach BP decoding. To compensate for the drawbacks of these methods, our proposed stochastic decoder utilizes the stochastic computation to transform the received codewords from channel to the non-binary stochastic sequences as our initial input taken into the iterative part, takes BP decoding in the iterative part to decode these non-binary sequences, and uses the decision method taken from list decoding for the final output to make our stochastic decoder become more efficiency.
As a result, the performance of our non-binary stochastic decoder is proved to beat the performance of BP decoding with different kinds of LDPC codes. The decoding complexity of this decoder can be reduced to the acceptable level which is friendly to hardware implementation.

• author: Gu, Yuyuan and Li, Haien
• supervisor: Michael Lentmaier
• organization: Department of Electrical and Information Technology
• course: EITM02 20211
• year: 2021
• type: H2 - Master's Degree (Two Years)
• subject: Technology and Engineering
• keywords: 5G, channel coding, LDPC codes, stochastic decoding, stochastic computation
• report number: LU/LTH-EIT 2021-821
• language: English
• id: 9054862
• date added to LUP: 2021-06-16 14:05:08
• date last changed: 2021-06-16 14:05:08