Farnaz Shayegh

Rateless codes for cognitive radio in a virtual unlicensed spectrum

In this paper we investigate the use of rateless codes by secondary users equipped with cognitive radio in a virtual unlicensed spectrum. Assuming a Poisson model for the arrival of primary users, we analyze the goodput and the throughput of secondary users. Rateless codes are used for transmitting the secondary data through parallel subchannels available in a spectrum. They can compensate for the packet loss in secondary transmission due to appearance of primary users. We calculate the overall frame error probability at the secondary receiver and use it for calculating the throughput and goodput. Numerical results indicate that LT codes as a class of rateless codes provide reliable transmissions with high throughput and small redundancy. Except for very small Poisson arrival rates, the throughput is much higher than the case without erasure coding. Therefore, in real-time multimedia transmission that retransmitting lost information packets is not possible, the use of rateless codes is very beneficial.

A Low Complexity Iterative Technique for Soft Decision Decoding of Reed-Solomon Codes

A new iterative soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method is based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In our proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the geometry of the factor graph will change and deterministic errors can be avoided. Our method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods.

Direct conversion EHM transceivers design for millimeter-wave wireless applications

A direct conversion modulator-demodulator with even harmonic mixers for fixed wireless applications is presented. The circuits consist of even harmonic mixers (EHMs) realized with antiparallel diode pairs (APDPs). A communication link is set up to examine the overall performance of proposed modulator-demodulator. The transmission of 16-QAM signal with 110Mbps data rate over fixed wireless link has been examined. We also evaluate the different levels of I/Q imbalances and DC offsets and use signal space concepts to analyze the bit error rate (BER) of the proposed transceiver using-ary QAM schemes. The results show that this structure can be efficiently used for fixed wireless applications in Ka band.

Efficient soft decoding of reed-solomon codes based on sphere decoding

A novel soft-decision decoding method motivated by the idea of sphere decoding is proposed for Reed–Solomon (RS) codes. Sphere decoding reduces the complexity of finding the closest lattice point to a given point by confining the search to points that fall inside a sphere around the given point. In the authors’ proposed scheme, in order to reduce the search even further, the search effort is concentrated on the most probable lattice points. To do so, they first find the most reliable positions of the codeword. Then a sphere decoder is used to select symbol values for these positions. The proposed sphere decoder chooses the acceptable symbol values for each position from a pre-determined ordered set of most probable transmitted symbols. Each time the most reliable code symbols are selected, they are used to find the rest of RS symbols. If the resulting codeword is within the search radius, it is saved as a candidate transmitted codeword. The ordering used in the algorithm helps finding the candidate codewords quickly resulting in an efficient decoding method. Simulation results indicate considerable coding gains over hard decision decoding with a feasible complexity. The performance is also superior to the soft decision Koetter–Vardy method.

Low complexity implementations of sphere decoding for MIMO detection

A new low complexity sphere decoding method for multiple-input multiple-output (MIMO) maximum-likelihood (ML) detection is proposed. One method that reduces the complexity of sphere decoding is the decoding order of MIMO sphere decoder using the soft-output signal of a suboptimum receiver as a reference. We refer to this method as ordered sphere decoder and we try to reduce its complexity. In order to do this, we use the reliability information of the transmitted vector to do channel ordering. This means that we make decisions on the elements of the transmitted vector starting from its most reliable element. To this end, we arrange the reliabilities in an increasing order. This ordering will define a permutation. The elements of the reference signal and also the columns of the channel matrix will be arranged according to this permutation. Then, we detect the permuted transmitted vector using ordered sphere decoder with the new permuted channel matrix and reference signal. In our proposed method, we start detecting the transmitted vector from its most reliable element and for each element, we start from the most probable transmitted symbol based on the information from the reference signal. This kind of ordering will help finding the candidate transmitted vectors quickly. Our method results in reducing the complexity of sphere decoder specially in low signal to noise ratios without compromising the performance of ML detection.

Soft Decision Decoding of Reed-Solomon Codes Using Sphere Decoding

A new soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method uses sphere decoding in an effort to reduce the decoding complexity. With sphere decoding, instead of considering all of the possible transmitted codewords to determine the most probable one, we only consider the codewords whose distances from the received signal are smaller than a specific search radius. This results in a considerable reduction in the complexity. For an (N,K) RS code, we consider a set of K most reliable and independent positions of a codeword and for each of these positions, an ordered list of most probable transmitted symbols in decreasing order of probability is determined. We start from the hard-decision decoded codeword and we try to find more probable codewords. The search is started by selecting a tentative solution consisting of the K most reliable code symbols whose distance from the corresponding symbols in the received vector is less than the search radius. The acceptable values for each of these K code symbols are determined based of the ordered set of most probable transmitted symbols which means that for each code symbol, we start from the most probable one. We re-encode these K code symbols. If the resulting codeword is within the search radius, we add it to the list of the candidate transmitted codewords. The ordering that was discussed earlier will help finding the candidate codewords quickly. Our method results in considerable improvement of the performance of RS codes compared to hard decision decoding with a moderate increase in complexity.

Collaborative algebraic decoding of interleaved Reed–Solomon codes

We derive and analyse an algorithm for collaborative decoding of heterogeneous interleaved Reed–Solomon (IRS) codes. They are generated by interleaving several codewords from different Reed–Solomon codes with the same length over the same Galois field. The basis of the decoding algorithm is similar to the Guruswami–Sudan (GS) decoding method. However, here multivariate interpolation is used to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, we show that the error-correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error-correction capability is equal to the decoding radius of the GS algorithm for the Reed–Solomon code with the largest dimension. Also, concatenated codes using IRS codes as their outer codes and binary linear block codes as their inner codes are considered. Assuming maximum likelihood decoding of the inner code, we derive upper and lower bounds for the word error probability of concatenated codes over additive white Gaussian noise channel with binary phase-shift keying modulation for both cases of independent and collaborative decoding of the outer IRS codes. We show that collaborative decoding provides considerable coding gain compared with independent decoding. Copyright

Multivariate interpolation decoding of heterogeneous Interleaved Reed-Solomon codes

We derive and analyze an algorithm for collaborative decoding of heterogeneous Interleaved Reed-Solomon (IRS) codes. In order to generate IRS codes, several codewords from different RS codes with the same length over the same Galois field are interleaved. The basis of the decoding algorithm is similar to the Guruswami-Sudan (GS) decoding method. However, here multivariate interpolation is used in order to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, it is shown that the error correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error correction capability is equal to the decoding radius of the GS algorithm for the RS code with the largest dimension.

Efficient Iterative Techniques for Soft Decision Decoding of Reed-Solomon Codes

Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the distribution of reliability values will change and deterministic errors can be avoided. This method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods. The second method is based on information correction in BP decoding. It means that we determine least reliable bits and by changing their channel information, the convergence of the decoder is improved. Compared to the first method, this method needs less BP iterations (less complexity) but its performance is not as good.

Iterative soft decoding of Reed-Solomon codes using information correction

A new iterative soft decision decoding method with very low complexity for Reed-Solomon (RS) codes is proposed. This method is based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. Our proposed method is based on information correction in BP decoding. It means that we determine least reliable bits and by changing their channel information, the convergence of the decoder is improved. Our method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior or comparable to some popular soft decision decoding methods.