Time-invariant spatially coupled low-density parity-check (TI-SC-LDPC) codes can be obtained by unwrapping quasi-cyclic (QC) LDPC codes. This results in a free distance that is lower bounded by the minimum distance of the underlying QC-LDPC codes. By introducing some variability in the syndrome former matrix, time-varying (TV) SC-LDPC codes are obtained, which trade an improved error correction performance for an increased decoding memory requirement and decoding complexity. A family of codes able to combine the advantages of TI-SC-LDPC codes with those of TV-SC-LDPC codes is that of periodically time-varying (PTV) SC-LDPC codes, based on a finite and periodic variation of the syndrome former matrix. In this paper we focus on such codes, and derive new upper bounds on the free distance of PTV-SC-LDPC code ensembles as well as on specific codes. By using these bounds, we show that PTV-SC-LDPC codes can achieve important improvements in the free distance over TI-SC-LDPC codes even using a very small period of variability, which corresponds to a minimal increase in memory and complexity. We also validate the new upper bounds through numerical experiments and assess the error correction performance of the corresponding codes through Monte Carlo simulations.

Bounds on the Free Distance of Periodically Time-Varying SC-LDPC Codes / Battaglioni, Massimo; Baldi, Marco; Chiaraluce, Franco. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - ELETTRONICO. - 70:4(2024), pp. 2419-2429. [10.1109/TIT.2024.3362387]

Bounds on the Free Distance of Periodically Time-Varying SC-LDPC Codes

Battaglioni, Massimo
Primo
;
Baldi, Marco;Chiaraluce, Franco
2024-01-01

Abstract

Time-invariant spatially coupled low-density parity-check (TI-SC-LDPC) codes can be obtained by unwrapping quasi-cyclic (QC) LDPC codes. This results in a free distance that is lower bounded by the minimum distance of the underlying QC-LDPC codes. By introducing some variability in the syndrome former matrix, time-varying (TV) SC-LDPC codes are obtained, which trade an improved error correction performance for an increased decoding memory requirement and decoding complexity. A family of codes able to combine the advantages of TI-SC-LDPC codes with those of TV-SC-LDPC codes is that of periodically time-varying (PTV) SC-LDPC codes, based on a finite and periodic variation of the syndrome former matrix. In this paper we focus on such codes, and derive new upper bounds on the free distance of PTV-SC-LDPC code ensembles as well as on specific codes. By using these bounds, we show that PTV-SC-LDPC codes can achieve important improvements in the free distance over TI-SC-LDPC codes even using a very small period of variability, which corresponds to a minimal increase in memory and complexity. We also validate the new upper bounds through numerical experiments and assess the error correction performance of the corresponding codes through Monte Carlo simulations.
2024
File in questo prodotto:
File Dimensione Formato  
DASITO_Bounds_on_the_Free_Distance_of_Periodically_Time-Varying_SC-LDPC_Codes.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza d'uso: Creative commons
Dimensione 3.27 MB
Formato Adobe PDF
3.27 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/326655
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact