Finite-Length Scaling Laws for Spatially-Coupled LDPC Codes
Doctoral thesis, 2022
This thesis concerns predicting the finite-length error-correcting performance of spatially-coupled low-density parity-check (SC-LDPC) code ensembles over the binary erasure channel. SC-LDPC codes are a very powerful class of codes; their use in practical communication systems, however, requires the system designer to specify a considerable number of code and decoder parameters, all of which affect both the code’s error-correcting capability and the system’s memory, energy, and latency requirements. Navigating the space of the associated trade-offs is challenging. The aim of the finite-length scaling laws proposed in this thesis is to facilitate code and decoder parameter optimization by providing a way to predict the code’s error-rate performance without resorting to Monte-Carlo simulations for each combination of code/decoder and channel parameters.
First, we tackle the problem of predicting the frame, bit, and block error rate of SC-LDPC code ensembles over the binary erasure channel under both belief propagation (BP) decoding and sliding window decoding when the maximum number of decoding iterations is unlimited. The scaling laws we develop provide very accurate predictions of the error rates.
Second, we derive a scaling law to accurately predict the bit and block error rate of SC-LDPC code ensembles with doping, a technique relevant for streaming applications for limiting the inherent rate loss of SC-LDPC codes. We then use the derived scaling law for code parameter optimization and show that doping can offer a way to achieve better transmission rates for the same target bit error rate than is possible without doping.
Last, we address the most challenging (and most practically relevant) case where the maximum number of decoding iterations is limited, both for BP and sliding window decoding. The resulting predictions are again very accurate.
Together, these contributions make finite-length SC-LDPC code and decoder parameter optimization via finite-length scaling laws feasible for the design of practical communication systems.
First, we tackle the problem of predicting the frame, bit, and block error rate of SC-LDPC code ensembles over the binary erasure channel under both belief propagation (BP) decoding and sliding window decoding when the maximum number of decoding iterations is unlimited. The scaling laws we develop provide very accurate predictions of the error rates.
Second, we derive a scaling law to accurately predict the bit and block error rate of SC-LDPC code ensembles with doping, a technique relevant for streaming applications for limiting the inherent rate loss of SC-LDPC codes. We then use the derived scaling law for code parameter optimization and show that doping can offer a way to achieve better transmission rates for the same target bit error rate than is possible without doping.
Last, we address the most challenging (and most practically relevant) case where the maximum number of decoding iterations is limited, both for BP and sliding window decoding. The resulting predictions are again very accurate.
Together, these contributions make finite-length SC-LDPC code and decoder parameter optimization via finite-length scaling laws feasible for the design of practical communication systems.
belief propagation decoding
spatially-coupled LDPC codes
window decoding
codes-on-graphs
finite-length code performance
Room EA, EDIT building, Hörsalsvägen 11
Opponent: Professor Olgica Milenkovic, University of Illinois, Urbana-Champaign, IL, USA
Author
Roman Sokolovskii
Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks
Finite-Length Scaling of Spatially Coupled LDPC Codes under Window Decoding over the BEC
IEEE Transactions on Communications,; Vol. 68(2020)p. 5988-5998
Journal article
On Doped SC-LDPC Codes for Streaming
IEEE Communications Letters,; Vol. 25(2021)p. 2123-2127
Journal article
Finite-Length Scaling of SC-LDPC Codes With a Limited Number of Decoding Iterations
IEEE Transactions on Information Theory,; Vol. 69(2023)p. 4869-4888
Journal article
Smartphones, laptops, and data centers exchange information by sending electromagnetic waves over a physical medium, mostly wirelessly or via fiber-optic cables. The electromagnetic signal is subject to interference from various sources, which can be viewed as a kind of noise. To be able to reconstruct the message in the presence of noise, some degree of redundancy is introduced to the transmitted data—in other words, the set of possible messages is restricted in a systematic way according to a set of rules.
The receiver then uses its knowledge of the rules to reconstruct the corrupted message. The same principle allows us to reconstruct the meaning of a phrase heard only partially in a crowded room or fill in the blank squares in a sudoku puzzle—we use our knowledge of the rules of language (and the rules of sudoku) to infer the missing or distorted bits. In digital communications, the good news is that we can choose the set of rules our messages must satisfy; modern coding theory has provided us with many good ways to construct the rulebook and to infer the transmitted message.
The problem with having a choice is having to make it. Communication system designers need to specify a wide range of parameters that affect both the system’s resilience to noise and its memory, latency, and energy requirements. To help navigate the space of the associated trade-offs, this thesis offers a way to predict a rulebook’s resilience to noise as a function of these parameters for progressively more practical setups. The class of rulebooks we consider is called spatially-coupled low-density parity-check (SC-LDPC) codes, and the theoretical tool we employ is known as finite-length scaling. The thesis deepens our understanding of the finite-length behavior of SC-LDPC codes and makes the life of communication system designers a little easier.
The receiver then uses its knowledge of the rules to reconstruct the corrupted message. The same principle allows us to reconstruct the meaning of a phrase heard only partially in a crowded room or fill in the blank squares in a sudoku puzzle—we use our knowledge of the rules of language (and the rules of sudoku) to infer the missing or distorted bits. In digital communications, the good news is that we can choose the set of rules our messages must satisfy; modern coding theory has provided us with many good ways to construct the rulebook and to infer the transmitted message.
The problem with having a choice is having to make it. Communication system designers need to specify a wide range of parameters that affect both the system’s resilience to noise and its memory, latency, and energy requirements. To help navigate the space of the associated trade-offs, this thesis offers a way to predict a rulebook’s resilience to noise as a function of these parameters for progressively more practical setups. The class of rulebooks we consider is called spatially-coupled low-density parity-check (SC-LDPC) codes, and the theoretical tool we employ is known as finite-length scaling. The thesis deepens our understanding of the finite-length behavior of SC-LDPC codes and makes the life of communication system designers a little easier.
Reliable Uncoordinated Medium Access for Critical Low-Latency Communication
Swedish Research Council (VR) (2016-04026), 2017-01-01 -- 2020-12-31.
Areas of Advance
Information and Communication Technology
Subject Categories
Telecommunications
Communication Systems
Infrastructure
C3SE (Chalmers Centre for Computational Science and Engineering)
ISBN
978-91-7905-660-5
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5126
Publisher
Chalmers
Room EA, EDIT building, Hörsalsvägen 11
Opponent: Professor Olgica Milenkovic, University of Illinois, Urbana-Champaign, IL, USA