TY - GEN
T1 - Computational complexity analysis of hamming codes polynomial co-decoding
AU - Ellero, F.
AU - Palese, G.
AU - Tomat, E.
AU - Vatta, F.
N1 - Funding Information:
This work is partly supported by the Italian Ministry of University and Research (MIUR) within the project FRA 2020 (University of Trieste, Italy), entitled “Integrazione tra sistemi nanosatellitari e 5G nel dominio delle onde millimetriche: un approccio multidisciplinare”.
Publisher Copyright:
© SoftCOM 2021. All rights reserved.
PY - 2021
Y1 - 2021
N2 - In mathematical terms, Hamming codes are a class of binary linear codes. Due to the limited redundancy that they add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory – usually random-access memory (RAM) – where bit errors are extremely rare and Hamming codes are widely used. A RAM with this correction system is a so-called error correction code (ECC) RAM (also known as ECC memory). ECC memory is used in most computers where data corruption cannot be tolerated under any circumstances, like industrial control applications, critical databases, and infrastructural memory caches. The parity-check matrix of a Hamming code contains all length k non-zero binary vectors. This paper is focused on their cyclic version, in order to exploit the mathematical advantages of cyclic codes. Since, as far as the Authors know, the computational complexity of Hamming codes polynomial decoding has not been addressed directly in the literature, in this paper the computational complexity of their co-decoding in polynomial form is analyzed in detail.
AB - In mathematical terms, Hamming codes are a class of binary linear codes. Due to the limited redundancy that they add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory – usually random-access memory (RAM) – where bit errors are extremely rare and Hamming codes are widely used. A RAM with this correction system is a so-called error correction code (ECC) RAM (also known as ECC memory). ECC memory is used in most computers where data corruption cannot be tolerated under any circumstances, like industrial control applications, critical databases, and infrastructural memory caches. The parity-check matrix of a Hamming code contains all length k non-zero binary vectors. This paper is focused on their cyclic version, in order to exploit the mathematical advantages of cyclic codes. Since, as far as the Authors know, the computational complexity of Hamming codes polynomial decoding has not been addressed directly in the literature, in this paper the computational complexity of their co-decoding in polynomial form is analyzed in detail.
KW - Error detection and correction (EDAC)
KW - Error-correcting codes (ECC)
KW - Hamming codes
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M3 - Conference contribution
AN - SCOPUS:85125966280
T3 - 2021 29th International Conference on Software, Telecommunications and Computer Networks, SoftCOM 2021
BT - 2021 29th International Conference on Software, Telecommunications and Computer Networks, SoftCOM 2021
A2 - Begusic, Dinko
A2 - Rozic, Nikola
A2 - Radic, Josko
A2 - Saric, Matko
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 29th International Conference on Software, Telecommunications and Computer Networks, SoftCOM 2021
Y2 - 23 September 2021 through 25 September 2021
ER -