scholarly journals On the decoding complexity of cyclic codes up to the BCH bound

2011 ◽  
Author(s):  
Davide Schipani ◽  
Michele Elia ◽  
Joachim Rosenthal
Keyword(s):  
Cyclic Codes ◽  
Decoding Complexity ◽  
Bch Bound

A Large Class of p-Ary Cyclic Codes and Sequence Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2272-2277
Author(s):  
Zhengchun ZHOU ◽  
Xiaohu TANG ◽  
Udaya PARAMPALLI
Keyword(s):  
Large Class ◽  
Cyclic Codes

A Family of q-Ary Cyclic Codes with Optimal Parameters

2020 ◽  
Vol E103.A (3) ◽  
pp. 631-633
Author(s):  
Wenhua ZHANG ◽  
Shidong ZHANG ◽  
Yong WANG ◽  
Jianpeng WANG
Keyword(s):  
Cyclic Codes ◽  
Optimal Parameters

A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

scholarly journals Monomial codes seen as invariant subspaces

2017 ◽  
Vol 15 (1) ◽  
pp. 1099-1107 ◽  
Author(s):  
María Isabel García-Planas ◽  
Maria Dolors Magret ◽  
Laurence Emilie Um
Keyword(s):  
Finite Field ◽  
Linear Algebra ◽  
Linear Transformation ◽  
Cyclic Codes ◽  
Invariant Subspaces ◽  
Hyperinvariant Subspaces ◽  
Computationally Expensive ◽  
The Relationship

Abstract It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field 𝔽 and hyperinvariant subspaces of 𝔽n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

scholarly journals Autonomous Power Decision for the Grant Free Access MUSA Scheme in the mMTC Scenario

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 116
Author(s):  
Wissal Ben Ameur ◽  
Philippe Mary ◽  
Jean-François Hélard ◽  
Marion Dumay ◽  
Jean Schwoerer
Keyword(s):  
Interference Cancellation ◽  
Error Propagation ◽  
Multiple Access ◽  
Transmission Rate ◽  
Free Access ◽  
Decoding Complexity ◽  
Machine Type ◽  
Machine Type Communications ◽  
Multiple Access Schemes ◽  
Lower Complexity

Non-orthogonal multiple access schemes with grant free access have been recently highlighted as a prominent solution to meet the stringent requirements of massive machine-type communications (mMTCs). In particular, the multi-user shared access (MUSA) scheme has shown great potential to grant free access to the available resources. For the sake of simplicity, MUSA is generally conducted with the successive interference cancellation (SIC) receiver, which offers a low decoding complexity. However, this family of receivers requires sufficiently diversified received user powers in order to ensure the best performance and avoid the error propagation phenomenon. The power allocation has been considered as a complicated issue especially for a decentralized decision with a minimum signaling overhead. In this paper, we propose a novel algorithm for an autonomous power decision with a minimal overhead based on a tight approximation of the bit error probability (BEP) while considering the error propagation phenomenon. We investigate the efficiency of multi-armed bandit (MAB) approaches for this problem in two different reward scenarios: (i) in Scenario 1, each user reward only informs about whether its own packet was successfully transmitted or not; (ii) in Scenario 2, each user reward may carry information about the other interfering user packets. The performances of the proposed algorithm and the MAB techniques are compared in terms of the successful transmission rate. The simulation results prove that the MAB algorithms show a better performance in the second scenario compared to the first one. However, in both scenarios, the proposed algorithm outperforms the MAB techniques with a lower complexity at user equipment.

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