In this paper, the statistical characteristic of the Error Detection Delay (EDD) of Finite Precision Binary Arithmetic Codes (FPBAC) is discussed. It is observed that, apart from the probability of the Forbidden Symbol (FS) inserted into the list of the source symbols, the probability of the source sequence and the operation precision as well as the position of the FS in the coding interval can affect the statistical characteristic of the EDD. Experiments demonstrate that the actual distribution of the EDD of FPBAC is quite different from the geometric distribution of infinite precision arithmetic codes. This phenomenon is researched deeply, and a new statistical model (gamma distribution) of the actual distribution of the EDD is proposed, which can make a more precise prediction of the EDD. Finally, the relation expressions between the parameters of gamma distribution and the related factors affecting the distribution are given.

An optical CDMA (OCDMA) system is a flexible technology for future broadband multiple access networks. A secure OCDMA network in broadband optical access technologies is also becoming an issue of great importance. In this paper, we propose novel reconfigurable wavelength-time (W-T) optical codes that lead to secure transmission in OCDMA networks. The proposed W-T optical codes are constructed by using quasigroups (QGs) for wavelength hopping and one-dimensional optical orthogonal codes (OOCs) for time spreading; we call them QGs/OOCs. Both QGs and OOCs are randomly generated by a computer search to ensure that an eavesdropper could not improve its interception performance by making use of the coding structure. Then, the proposed reconfigurable QGs/OOCs can provide more codewords, and many different code set patterns, which differ in both wavelength and time positions for given code parameters. Moreover, the bit error probability of the proposed codes is analyzed numerically. To realize the proposed codes, a secure system is proposed by employing reconfigurable encoders/decoders based on array waveguide gratings (AWGs), which allow the users to change their codeword patterns to protect against eavesdropping. Finally, the probability of breaking a certain codeword in the proposed system is evaluated analytically. The results show that the proposed codes and system can provide a large codeword pattern, and decrease the probability of breaking a certain codeword, to enhance OCDMA network security.

This paper clarifies the adequacy of the linear channel coding approach for the source coding with partial side information at the decoder. A sufficient condition for an ensemble of linear codes which achieves the Wyner's bound is given. Our result reveals that, by combining a good lossy code, an LDPC code ensemble gives a good code for source coding with partial side information at the decoder.

The stopping distance and stopping redundancy of a linear code are important concepts in the analysis of the performance and complexity of the code under iterative decoding on a binary erasure channel. In this paper, we studied the stopping distance and stopping redundancy of Finite Geometry LDPC (FG-LDPC) codes, and derived an upper bound of the stopping redundancy of FG-LDPC codes. It is shown from the bound that the stopping redundancy of the codes is less than the code length. Therefore, FG-LDPC codes give a good trade-off between the performance and complexity and hence are a very good choice for practical applications.

In this letter, a simple but effective antenna selection algorithm for orthogonal space-time block codes with a linear complex precoder (OSTBC-LCP) is proposed and compared with two conventional algorithms in temporally and spatially correlated fading channels. The proposed algorithm, which minimizes pairwise error probability (MinPEP) with an error codebook (EC) constructed from the error vector quantization, is shown to provide nearly the same performance of MinPEP based on all possible error vectors, while keeping the complexity close to that of antenna selection algorithm based on maximum power criterion (Maxpower).

Wireless communication systems usually employ a concatenated error control coding scheme consisting of an outer error detection code and an inner error correction code. Traditionally, these two codes are decoded separately. When the sub-block structure is used, each data block (input sequence) at the inner encoder consists of several sub-blocks and each of these sub-blocks is protected with the error detection code. The sub-block structure is used in the Wideband CDMA (WCDMA) system specified by the 3rd Generation Partnership Project (3GPP). In this paper, a sub-block recovery scheme is proposed for this concatenated error control coding scheme to utilize the error detection capability introduced by the outer code in the decoding of the inner code. We demonstrate that, if the inner code is a turbo code with a highly structured interleaver and iterative sub-optimal decoding is used, the sub-block recovery scheme is helpful in correcting a typical error pattern, which helps to improve the block error rate performance. We analyze the decoding performance when sub-block recovery is used together with the maximum likelihood (ML) algorithm as well as the log maximum-a-posteriori probability (Log-MAP) and the soft output Viterbi algorithm (SOVA) and demonstrate gains introduced by the sub-block recovery in the latter two cases using computer simulations.

We propose a new stopping criterion for decoding LDPC codes which consists of a measure of decoder behaviors and a decision rule to predict decoding failure. We will show that the proposed measure, the number of satisfied check nodes, does not need (or minimizes) additional complexity, and the decision rule is efficient and more importantly channel independent, which was not possible in the previous work.

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) have attracted a great deal of attention due to their full-diversity and linear maximum likelihood (ML) decodability. In this letter, we propose a simple detection technique, particularly for full-rate STBCs from CIODs to overcome the performance degradation caused by time-selective fading channels. Furthermore, we evaluate the effects of time-selective fading channels and imperfect channel estimation on STBCs from CIODs by using a newly-introduced index, the results of which demonstrate that full-rate STBCs from CIODs are more robust against time-selective fading channels than conventional full-rate STBCs.

We propose a fast decoding algorithm for the p-ary first-order Reed-Muller code guaranteeing correction of up to errors and having complexity proportional to nlog n, where n = pm is the code length and p is an odd prime. This algorithm is an extension in the complex domain of the fast Hadamard transform decoding algorithm applicable to the binary case.

This paper presents a novel high-speed low-complexity pipelined degree-computationless modified Euclidean (pDCME) algorithm architecture for high-speed RS decoders. The pDCME algorithm allows elimination of the degree-computation so as to reduce hardware complexity and obtain high-speed processing. A high-speed RS decoder based on the pDCME algorithm has been designed and implemented with 0.13-µm CMOS standard cell technology in a supply voltage of 1.1 V. The proposed RS decoder operates at a clock frequency of 660 MHz and has a throughput of 5.3 Gb/s. The proposed architecture requires approximately 15% fewer gate counts and a simpler control logic than architectures based on the popular modified Euclidean algorithm.

In this letter, we analyze symbol error probability (SEP) and diversity gain of orthogonal space-time block codes (OSTBCs) in spatially correlated Rician fading channel. We derive the moment generating function (MGF) of an effective signal-to-noise ratio (SNR) at the receiver and use it to derive the SEP for M-PSK modulation. We use this result to show that the diversity gain is achieved by the product of the rank of the transmit and receive correlation matrix, and the loss in array gain is quantified as a function of the spatial correlation and the line of sight (LOS) component.

For coherent detection, decoding Orthogonal Space-Time Block Codes (OSTBC) requires full channel state information at the receiver, which basically is obtained by channel estimation. However, in practical systems, channel estimation errors are inevitable and may degrade the system performance more as the number of antennas increases. This letter shows that, using fewer receive antennas can enhance the performance of OSTBC systems in presence of channel estimation errors. Furthermore, a novel adaptive receive antenna selection scheme, which adaptively adjusts the number of receive antennas, is proposed. Performance evaluation and numerical examples show that the proposed scheme improves the performance obviously.

In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the ε-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.

Coded modulation systems based on low density parity check (LDPC) codes of finite lengths are considered. The union bounds on the bit error probabilities of the maximum likelihood (ML) decoding are presented for both additive white Gaussian noise (AWGN) and flat Rayleigh fading channels. The tightness of the derived bound is verified by simulating the ML decoding of a very short LDPC code. For medium-length codes, performance of the sum-product decoding can asymptotically approach the bounds.

A method is presented that can substantially reduce the memory requirements of non-binary turbo decoders by efficient representation of the extrinsic information. In the case of the duo-binary turbo decoder employed by the IEEE 802.16e standard, the extrinsic information memory can be reduced by about 43%, which decreases the total decoder complexity by 18%. We also show that the proposed algorithm can be implemented by simple hardware architecture.

Yamada, Harashima, and Miyakawa proposed to use a trellis constructed based on a syndrome former for the purpose of Viterbi decoding of rate-(n-1)/n convolutional codes. In this paper, we extend their code-trellis construction to general rate-k/n convolutional codes. We show that the extended construction is equivalent to the one proposed by Sidorenko and Zyablov. Moreover, we show that the proposed method can also be applied to an error-trellis construction with minor modification.

Full-diversity transmission for space-time block codes (STBCs) with multiple transmit antennas can be achieved by using coordinate interleaved orthogonal designs (CIODs). To effectively evaluate the performance of CIODs, we derive union upper and lower bounds on the symbol-error rate (SER) and a corresponding asymptotic diversity order of symmetric structured CIOD, in particular, with two transmit antennas over quasi-static spatially uncorrelated/correlated frequency-nonselective Rayleigh fading channels. Some numerical results are provided to verify our analysis.

This study presents a partition decoding algorithm for an (mN, mK) binary image of an (N, K) Reed Solomon code over GF(2m). A proposed partition decoding algorithm includes several steps. Firstly we compute m's segmental reliability values of a received subvector of length N and determine which one with the least segmental reliability value. A permutation is performed on a binary generator matrix of an RS code and a received vector, which are then partitioned into two submatrices and two subvectors. The first subvector of length N(m-1) associate with the first submatrix and the second subvector with the least segmental reliability value relates to the second submatrix. Secondly, an MLD algorithm based on the first submatrix is employed to decode the first subvector. Thirdly, an MLD algorithm based on a BCH generator matrix is employed to decode the second subvector. A codeword is finally outputted after performing the inverse permutation on a concatenation of code vectors decoded from these two decoding. The error coefficient and minimum Hamming distance of the code sequences generated in the first submatrix are fewer than those of a corresponding binary image. Simulation results show that at low and medium SNRs, the effect of error coefficient becomes more significant than that of minimum Hamming distance. Minimum Hamming distances and error coefficients of code sequences generated in the first submatrices and their corresponding binary images have been explored in this work. For (60,36,7)RS(b), (155,125,7)RS(b), (155,105,11)RS(b) and (889, 847,7))RS(b) being binary images of (15,9,7)RS, (31,25,7)RS, (31,21,11)RS and (127,121,7)RS codes respectively, with BPSK signaling over AWGN channels, the decoding performances of proposed partition decoding algorithm are a little poorer than those of MLD [10] by 1.0 to 1.4 dB at BER 10-5, but better than those of GMD decoding by [1] 0.8 to 1.1 dB. For SNR of 5 dB, proposed partition decoding algorithm only takes 50% to 60% amount of bit operations of an MLD [10]. Under a constraint of decoding complexity, proposed partition decoding algorithm may be a solution to decode binary images of long RS codes, which provides superior performance to GMD decoding with much lower complexity than an MLD.

A high-speed physical-layer architecture for next-generation higher-speed Ethernet for VSR and backplane applications was developed. VSR and backplane networks provide 100-Gb/s data transmission in "mega data centers" and blade servers, which have new and broad potential markets of LAN technologies. It supports 100-Gb/s-throughput, high-reliability, and low-latency data transmission, making it well suited to VSR and backplane applications for intra-building and intra-cabinet networks. Its links comprise ten 10-Gb/s high-speed serial lanes. Payload data are transmitted by ribbon fiber cables for very short reach and by copper channels for the backplane board. Ten lanes convey 320-bit data synchronously (32 bits10 lanes) and parity data of forward-error correction code (newly developed (544, 512) code FEC), providing highly reliable (BER<1E-22) data transmission with a burst-error correction with low latency (31.0 ns on the transmitter (Tx) side and 111.6 ns on the receiver (Rx) side). A 64B/66B code-sequence-based skew compensation mechanism, which provides low-latency compensation for the lane-to-lane skew (less than 51 ns), is used for parallel transmission. Testing this physical-layer architecture in an ASIC showed that it can provide 100-Gb/s data transmission with a 772-kgate circuit, which is small enough for implementation in a single LSI.

In this paper we look at the serial concatenation of short linear block codes with a rate-1 recursive convolutional encoder, with a goal of designing high-rate codes with low error floor. We observe that under turbo-style decoding the error floor of the concatenated codes with extended Hamming codes is due to detectable errors in many cases. An interleaver design addressing this is proposed in this paper and its effectiveness is verified numerically. We next examine the use of extended BCH codes of larger minimum distance, resulting in an improved weight spectrum of the overall code. Reduced complexity list decoding is used to decode the BCH codes in order to obtain low decoding complexity for a negligible loss in performance.