Physical Sciences and Mathematics Commons^™

On Binary Reflected Gray Codes And Functions, Martin W. Bunder, Keith P. Tognetti, Glen Wheeler

Dr Keith Tognetti

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of length m. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder’s result that the jth letter of the kth word of the binary reflected Gray code of length n, is (2n − 2n−j − 1 [2n − 2n−j−1 − k/2]) mod 2, by replacing the binomial coefficient by [(k-1)/(2n-j+1)+1/2].

Application Of Quasi-Orthogonal Space-Time-Frequency Codes In Mb-Ofdm Uwb, Alfred Mertins, Le Chung Tran

Dr Le Chung Tran

This paper examines the application of Quasi-Orthogonal Space-Time-Frequency Codes (QOSTFCs) to advance either data rate or error performance in recently proposed Space-Time-Frequency Coded Multiband OFDM Ultra-Wideband (STFC MB-OFDM UWB) communications systems. It is shown that QOSTFCs can provide significantly better error performance, compared to the conventional MB-OFDM UWB (without STFCs) and to the Orthogonal STFCs (OSTFCs) of the same order, at the same data rate, without increasing the total transmission power. In other words, QOSTFCs can provide higher data rates with the same error performance, compared to OSTFCs.

Unitary Differential Space-Time-Frequency Codes For Mb-Ofdm Uwb, Le Chung Tran, Alfred Mertins, E. Dutkiewicz, Xiaojing Huang

Dr Le Chung Tran

In a multiple-input multiple-output (MIMO) multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) system, coherent detection where the channel state information (CSI) is assumed to be exactly known at the receiver requires the transmission of a large number of symbols for channel estimation, thus reducing the bandwidth efficiency. This paper examines the use of unitary differential space-time frequency codes (DSTFCs) in MB-OFDM UWB, which increases the system bandwidth efficiency due to the fact that no CSI is required for differential detection. The proposed DSTFC MB-OFDM system would be useful when the transmission of multiple channel estimation symbols is impractical or …

On The Use Of Quasi-Orthogonal Space-Time-Frequency Codes In Mb-Ofdm Uwb, Le Chung Tran, Alfred Mertins

Dr Le Chung Tran

Space-Time-Frequency Codes (STFCs), which haverecently been proposed in the literature for Multiband OFDMUltra-Wideband (MB-OFDM UWB) systems to improve thesystem capacity, error performance and wireless communicationrange, are all constructed based on orthogonal structures. Thispaper examines the application of Quasi-Orthogonal STFCs(QOSTFCs) to enhance further either data rate or error performancein the recently proposed STFC MB-OFDM UWB systems.It will be shown that QOSTFCs can provide significantly bettererror performance, compared to the conventional MB-OFDMUWB (without STFCs) as well as to the Orthogonal STFCs(OSTFCs) of the same order, at the same data rate, withoutincreasing the total transmission power. Equivalently, QOSTFCscan provide higher data rates with …

On Binary Reflected Gray Codes And Functions, Martin W. Bunder, Keith P. Tognetti, Glen Wheeler

Dr Martin Bunder

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of length m. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder’s result that the jth letter of the kth word of the binary reflected Gray code of length n, is (2n − 2n−j − 1 [2n − 2n−j−1 − k/2]) mod 2, by replacing the binomial coefficient by [(k-1)/(2n-j+1)+1/2].

On Binary Reflected Gray Codes And Functions, Martin W. Bunder, Keith P. Tognetti, Glen Wheeler

Dr Glen Wheeler

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of length m. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder’s result that the jth letter of the kth word of the binary reflected Gray code of length n, is (2n − 2n−j − 1 [2n − 2n−j−1 − k/2]) mod 2, by replacing the binomial coefficient by [(k-1)/(2n-j+1)+1/2].

Classification Of The Deletion Correcting Capabilities Of Reed–Solomon Codes Of Dimension Over Prime Fields, L. Mcaven, R. Safavi-Naini

Reihaneh Safavi-Naini

Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRSk(l,q,alpha,v), is a code of length l over GF(q) with qk codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are also capable of correcting deletions. We consider a subclass of GRS codes with dimension k=2 and q prime, and study them with respect to deletion correcting capability. We give transformations that either preserve the code or maintain its deletion correction capability. …

Some Results On Self-Orthogonal And Self-Dual Codes, S. Georgiou, C. Koukouvinos, Jennifer Seberry

Professor Jennifer Seberry

We use generator matrices G satisfying GGT = aI+bJ over Zk to obtain linear self-orthogonal and self-dual codes. We give a new family of linear self-orthogonal codes over GF(3) and Z4 and a new family of linear self-dual codes over GF(3).

Encryption/Decryption Dickwads Of Cipherspace, Raleigh Muns

Raleigh Muns