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Error-correcting coding is introduced in associative memories based on Hopfield networks in order to increase the learning diversity as well as the recall robustness in presence of erasures and errors. To achieve this, the graph associated with the classical Hopfield network is transformed into a bipartite graph in which incoming information is linked to orthogonal or quasi-orthogonal codes. Whereas...
We propose a windowed decoding scheme for protograph-based LDPC convolutional codes (LDPC-CC) that allows us to efficiently trade-off decoding performance for gains in latency. We study the performance of regular LDPC-CC with the windowed decoding scheme. In particular, we show that the class of LDPC-CC proposed in the literature with good belief propagation performance is ill-suited for windowed...
It is now well established that iterative decoding approaches the performance of Maximum Likelihood Decoding of sparse graph codes, asymptotically in the block length. For a finite length sparse code, iterative decoding fails on specific subgraphs generically termed as trapping sets. Trapping sets give rise to error floor, an abrupt degradation of the code error performance in the high signal to noise...
The large system analysis of randomly spread direct-sequence code-division multiple-access systems operating over frequency-selective fading channels is considered. Iterative multiuser detection and decoding (MUDD) based on generalized posterior mean estimation and single-user sum-product decoding is assumed to be used at the receiver. The channel state information (CSI) at the MUDD is mismatched...
In this paper, we study the transmission problem in multiple-input multiple-output (MIMO) systems with imperfect channel state information at the transmitter (CSIT). A scheme based on joint FEC coding and linear precoding at the transmitter and iterative linear minimum mean squared error (LMMSE) detection at the receiver is considered. The new scheme combines the advantages of beamforming, water-filling,...
In the wiretap channel model, symbols transmitted through a main channel to a legitimate receiver are observed by an eavesdropper across a wiretapper's channel. The goal of coding for wiretap channels is to facilitate error-free decoding across the main channel, while ensuring zero information transfer across the wiretapper's channel. Strong secrecy requires the total information transfer to the eavesdropper...
This paper presents a turbo trellis coded modulation (TTCM) scheme for which the encoding is implemented by serially concatenating a demultiplexer, a multilevel delay processor, and a signal mapper to the encoder of a binary turbo code. Through the delay processor and the signal mapper, interblock memory is introduced between consecutive binary turbo codewords. The proposed TTCM can be decoded based...
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a linear-programming based decoder which is an inverse polynomial in the block length. Our bound is valid for any memoryless, binary-input, output-symmetric (MBIOS) channel...
Time-variant Low-Density Parity-Check convolutional codes (LDPCccs) can be derived from unwrapping Quasi-Cyclic (QC) LDPC block codes. Rather than analyzing cycles in a large-scale time-domain parity check matrix, we propose a new way to describe cycle properties in compact form by a “polynomial syndrome former”, i.e., a syndrome former in an equivalent polynomial representation. According to the...
Forward error correction is an essential part of digital communication systems. Non-binary low-density parity-check (NB-LDPC) codes have an excellent communications performance for short block lengths. The higher the field size is, the better the communications performance is. Non-binary LDPC codes can outperform all other state-of-the-art code classes. However, the algorithmic decoding complexity...
A new memory mapping technique using a VLSI circuit based on recursive quadratic polynomial equations is described. The proposed methodology allows parallel processing elements, such as used in Turbo and Low Density Parity Check (LDPC) decoders, to work independently across memory segments, thus enabling parallel, high throughput, and power efficient LSI circuits.
Turbo equalization is a powerful method to iteratively detect and decode convolutionally encoded data that is corrupted by inter symbol interference (ISI) and Gaussian noise. It is based on the exchange of reliability information between the equalizer and the decoder, which is typically some sort of maximum a posteriori (MAP) decoder. While the number of remaining errors in the received sequence decreases...
This paper introduces a protograph-based method for designing q-ary LDPC codes for use with modulations larger than QPSK. Simulations focus on a GF(16), 16-QAM example. The proposed construction method achieves the maximum gain when the average column weight is chosen so that the linear minimum distance growth property is satisfied. In this region, the benefit of a protograph-based design over a standard...
Cooperative communication is a well known technique to yield transmit diversity in the case of fading channels and to increase the spectral efficiency in the case of Gaussian channels. Error-correcting codes have to be carefully designed to achieve the promised gains. Good LDPC codes are known for fading channels and for Gaussian channels, but an LDPC code ensemble that performs well on both channels...
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