In this paper, we consider fast decoding of soft-decision (SD) Hamming codes as inner codes in concatenated forward error-correction (FEC) schemes for high-speed optical communication. The goal is single FPGA implementations at speeds of 400 Gb/s and beyond. A low complexity maximum a posteriori (MAP) probability decoding is applied to a (128,120) Hamming code. Chase decoding of a (128,119) Hamming code is also implemented. The VHDL designs for both decoding schemes are presented. The FEC performance and FPGA resource utilization are investigated and compared. Synthesis results indicate that, both the Chase and the MAP decoder leave sufficient resources available to also accommodate a powerful outer hard decision code, on a single FPGA. Furthermore, MAP decoding of (128,120) Hamming code features lower hardware complexity and provides a higher data throughput.

Decoding of FEC (forward error correction) for optical communication beyond 1 Tb/s is investigated. A configurable single FPGA solution is presented having configurations supporting bit-rates in the range from 40 Gb/s to 1.6 Tb/s. The design allows for trade-offs of bit-rate, footprint, and latency within the resources of the FPGA. A proof-of-concept lab experiment at 40 Gb/s was conducted and pre-FEC — post-FEC performance validated with simulated results.

In this paper the capacity of a Multiple Input Multiple Output (MIMO) channel is considered, subject to average power constraint, for multi-dimensional discrete input, in the case when no channel state information is available at the transmitter. We prove that when the constellation size grows, the QAM constrained capacity converges to Gaussian capacity, directly extending the AWGN result from [1]. Simulations show that for a given constellation size, a rate close to the Gaussian capacity can be achieved up to a certain SNR point, which can be found efficiently by optimizing the constellation for the equivalent orthogonal channel, obtained by the singular value decomposition. Furthermore, lower bounds on the constrained capacity are derived for the cases of square and tall MIMO matrix, by optimizing the constellation for the equivalent channel, obtained by QR decomposition.

In this paper the problem of constellation shaping is considered. Mapping functions are designed for a many-to-one signal shaping strategy, combined with a turbo coded Bit-interleaved Coded Modulation (BICM), based on symmetric Huffman codes with binary reflected Gray-like properties. An algorithm is derived for finding the Huffman code with such properties for a variety of alphabet sizes, and near-capacity performance is achieved for a wide SNR region by dynamically choosing the optimal code rate, constellation size and mapping function based on the operating SNR point and assuming perfect channel quality estimation. Gains of more than 1dB are observed for high SNR compared to conventional turbo coded BICM, and it is shown that the mapping functions designed here significantly outperform current state of the art Turbo-Trellis Coded Modulation and other existing constellation shaping methods.

In this paper we propose a novel scheme for on the fly code rate adjustment for forward error correcting (FEC) codes on optical links. The proposed scheme makes it possible to adjust the code rate independently for each optical frame. This allows for seamless rate adaption based on the link state of the optical light path and the required amount of throughput going towards the destination node. The result is a dynamic FEC, which can be used to optimize the connections for throughput and/or energy efficiency, depending on the current demand.

This paper considers using BCH codes for distributed source coding using feedback. The focus is on coding using short block lengths for a binary source, X, having a high correlation between each symbol to be coded and a side information, Y, such that the marginal probability of each symbol, Xi in X, given Y is highly skewed. In the analysis, noiseless feedback and noiseless communication are assumed. A rate-adaptive BCH code is presented and applied to distributed source coding. Simulation results for a fixed error probability show that rate-adaptive BCH achieves better performance than LDPCA (Low-Density Parity-Check Accumulate) codes for high correlation between source symbols and the side information.

The problem of achieving robust speech transmission on a digital mobile radio channel subjected to severe fading is addressed. The study includes a performance comparison between the Reed-Solomon and the punctured convolutional types of channel coders, which were used in conjunction with speech coders with bit rates ranging from 6.6 kb/s down to 5.4 kb/s. Speech coding within this range is of particular interest for the standardization of the GSM half-rate system, where the gross bit rate is limited to 11.4 kb/s. The properties of the speech coders and the channel coders are described, as well as results of a series of experiments comparing speech quality and robustness against the transmission errors of a typical GSM half-rate channel.>

Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m/sup 2//8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding the error locator is O(n/sup 7/3/), where n is the length of the code. For codes from Hermitian curves the complexity of finding the error values, given the error locator, is O(n/sup 2/), and the same complexity can be obtained in the general case if only d*/2-m/sup 2//2 errors are corrected.>

The authors describe their contribution to the ETSI (European Telecommunications Standards Institute) effort for a definition of a GSM (Group Special Mobile) standard half-rate coding system for the pan-European digital mobile cellular radio system. The system consists of a speech coder and a channel coder. An overview of the speech coding algorithm is given. The results from a study of the different versions of the speech coder are described. A two-stage channel coding scheme is presented, and the performance test results are shown. An overview of the DSP implementation, computational requirements, and memory usage is also presented.>

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes.>

This paper gives a tabulation of binary convolutional codes with maximum free distance for rates\frac{1}{2}, \frac{1}{3}, and\frac{1}{4}for all constraint lengths (measured in information digits)\nuup to and includingnu = 14. These codes should be of practical interest in connection with Viterbi decoders.

In the above paper,^1Bahl et aL described a bidirectional search algorithm for computing the free distance of convolutional codes. There are some flaws in that algorithm. This correspondence contains a corrected version of the algorithm together with a proof that the corrected version always computes the free distance for noncatastrophic codes.