Finite-Length Scaling Laws for Spatially-Coupled LDPC Codes
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
finite-length code performance
Chalmers, Elektroteknik, Kommunikation, Antenner och Optiska Nätverk, Kommunikationssystem
Finite-Length Scaling of Spatially Coupled LDPC Codes under Window Decoding over the BEC
IEEE Transactions on Communications,; Vol. 68(2020)p. 5988-5998
Artikel i vetenskaplig tidskrift
On Doped SC-LDPC Codes for Streaming
IEEE Communications Letters,; Vol. 25(2021)p. 2123-2127
Artikel i vetenskaplig tidskrift
Roman Sokolovskii, Alexandre Graell i Amat, and Fredrik Brännström, “Finite-Length Scaling of SC-LDPC Codes With a Limited Number of Decoding Iterations”
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.
Pålitliga accessmetoder för kritisk kommunikation med låga fördröjningar
Vetenskapsrådet (VR) (2016-04026), 2017-01-01 -- 2020-12-31.
Informations- och kommunikationsteknik
C3SE (Chalmers Centre for Computational Science and Engineering)
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5126
Room EA, EDIT building, Hörsalsvägen 11
Opponent: Professor Olgica Milenkovic, University of Illinois, Urbana-Champaign, IL, USA