How to Generate Cyclically Permutable Codes From Cyclic Codes

Kuribayashi, Minoru; Tanaka, Hatsukazu

doi:10.1109/tit.2006.881834

Cited by 17 publications

(18 citation statements)

References 8 publications

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“…However, the construction from F n 2 , even for n prime, is a combinatorial problem, especially the decoding. Hence, to reduce the combinatorial complexity, many approaches starting from cyclic codes and extract all codewords with maximal cyclic order [28]- [30]. Since a cyclic (n, k, d min ) code corrects up to (d min − 1)/2 bit errors, any CPC code extraction will inherit the error correction capability.…”

Section: Using Cyclically Permutable Codesmentioning

confidence: 99%

“…To exploit the cardinality most efficiently, the goal is to find cyclic codes such that each non-zero codeword has maximal cyclic order. We will follow a construction of Kuribayashi and Tanaka in [28] for prime code lengths of the form n = 2 m − 1, also known as Mersenne primes. For m = 2, 3, 5, 7 this applies to K = n = 3, 7, 31, 127, which are relevant signal lengths for binary short-messages.…”

Section: Using Cyclically Permutable Codesmentioning

confidence: 99%

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MOCZ for Blind Short-Packet Communication: Basic Principles

Walk

Jung

Hassibi

2019

IEEE Trans. Wireless Commun.

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We will investigate practical aspects for a recently introduced blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), which enables reliable transmission of sporadic and short-packets at ultra-low latency in unknown wireless multipath channels, which are static over the receive duration of one packet. Here the information is modulated on the zeros of the transmitted discrete-time baseband signal's z−transform. Due to ubiquitous impairments between transmitter and receiver clocks a carrier frequency offset (CFO) will occur after a down-conversion to the baseband, which results in a common rotation of the zeros. To identify fractional rotations of the base angle in the zero-pattern, we propose an oversampled direct zero testing decoder to identify the most likely one. Integer rotations correspond to cyclic shifts of the binary message, which we compensate by a cyclically permutable code (CPC). Additionally, the embedding of CPCs into cyclic codes, allows to exploit additive error correction which reduces the bit-error-rate tremendously. Furthermore, we use the trident structure in the signals autocorrelation to estimate timing offsets and the channels effective delay spread. We finally demonstrate how these impairment estimations can be largely improved by receive antenna diversity, which enables extreme bursty reliable communication at low latency and SNR.

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Section: Using Cyclically Permutable Codesmentioning

confidence: 99%

Section: Using Cyclically Permutable Codesmentioning

confidence: 99%

MOCZ for Blind Short-Packet Communication: Basic Principles

Walk

Jung

Hassibi

2019

IEEE Trans. Wireless Commun.

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“…The construction proposed here is more efficient than the RS-based construction proposed in [3], especially for large p. The binary codes resulting from our Construction can be either constant-weight or not. Finally, the nonlinear binary code construction presented in this paper contributes to widen the range of available choices [16], [17] of protocol sequences for the CCWFB.…”

Section: Commentsmentioning

confidence: 99%

New cyclically permutable codes

Rocha

Lemos-Neto

2011

2011 IEEE Information Theory Workshop

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A cyclically permutable code is a binary code the codewords of which are cyclically distinct and have full cyclic order. The purpose of this paper is to construct cyclically permutable codes by means of linear p-ary constacyclic codes, where p denotes a prime number. An efficient method is used to select codewords from a constacyclic code which are constacyclically distinct and have full constacyclic order. Through a cyclic representation for the elements of GF(p) and by a correspondence of two-dimensional arrays and N-tuples, the codewords selected produce the codebook of a cyclically permutable code. The cyclically permutable codes constructed are used in the construction of protocol sequences for the Mactive-out-of-T users collision channel without feedback.

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“…Gilbert [2] defined a cyclic-permutable code as a binary block code of block length n such that each codeword has a cyclic order n and the codewords are cyclically distinct. Later Maracle and Wolverton [3] proposed an efficient algorithm for generating these codes [4], where all these codes are generated from binary block codes.…”

Section: Introductionmentioning

confidence: 99%

Distance-optimality study for permutation codes using cyclic-shift prefix/suffix technique

2009

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Distance-preserving mappings is a technique that maps binary sequences to permutation sequences. Many mapping algorithms, which are called constructions have been introduced. Few constructions have been considered to be optimum on the sum of distances since they reached the upper bound on the sum of the Hamming distances for certain lengths of the permutation sequence. We introduce a technique based on the cyclic shift of a permutation symbol to understand the conditions that make any construction optimum.

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How to Generate Cyclically Permutable Codes From Cyclic Codes

Cited by 17 publications

References 8 publications

MOCZ for Blind Short-Packet Communication: Basic Principles

MOCZ for Blind Short-Packet Communication: Basic Principles

New cyclically permutable codes

Distance-optimality study for permutation codes using cyclic-shift prefix/suffix technique

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