DVB-S2 LDPC Decoding Using Robust Check Node Update Approximations

Broadband satellite services to fixed terminals are currently offered in the forward link by the 2nd generation (2G) digital video broadcasting satellite (DVB-S2) standard. For this standard the use of powerful low-density parity-check (LDPC) error correcting codes has been adopted performing within approximately 1 dB from the Shannon capacity limit. This paper studies and compares for the first time in a systematic manner different approximation methods used in check node update computation of DVB-S2 LDPC decoding with the aim of reducing computational complexity. Various performance evaluation results are presented for a wide range of DVB-S2 parameters, such as LDPC codeword size, coding rate, modulation format and including several decoding algorithms. It is shown that the proposed check node update approximations have a robust behavior, i.e. the resulting performance is quite independent of the DVB-S2 modulation and coding parameters. It is further shown that these approximations perform very close to the optimal sum-product algorithm (SPA) in degradation, which is less than 0.2 dB. Despite this small degradation, the reduction in computational complexity compared to the optimal SPA is significant and can be as high as 40% in computational time savings.     

SISO algorithms based on combined max/max* operations for turbo decoding

New soft-input soft-output (SISO) decoding algorithms are proposed that combine both the max operation of the max-log-MAP algorithm and the max* operation (Jacobian logarithm) of the log-MAP algorithm. This combination is restricted not only to the reliability estimation, as in one previous publication, but is also expanded to include the case of the forward and backward metrics computation in the turbo decoding process     

Modification of branch metric calculation to improve iterative SOVA decoding of turbo codes

It is known that the performance of a SOVA (soft output Viterbi algorithm) turbo decoder can be improved, as the extrinsic information that is produced at its output is over-optimistic. A new parameter associated with the branch metrics calculation in the standard Viterbi algorithm is introduced that affects the turbo code performance. Different parameter values show a simulation improvement in the AWGN channel as well as in an uncorrelated Rayleigh fading channel. By choosing the best value of this parameter, a coding gain improvement of 0.25 dB at BER of 10/sup -5/ is achieved compared to existing schemes.     

Simplified sum-product algorithm for decoding LDPC codes with optimal performance

A simple, yet effective decoding algorithm is proposed for low-density parity-check (LDPC) codes, which significantly simplifies the check node update computation of the optimal sum-product algorithm. It achieves essentially optimal performance by applying scaling in the decoder?s extrinsic information. If no such scaling is applied, then the proposed algorithm has small performance degradation, e.g. in the order of 0.1 to 0.2 dB, depending on the coded block size.     

Novel Generalized max* Approximation Method for Simplified Decoding of Turbo and TTCM Codes

A novel method for approximating the optimal max* operator used in Log- MAP decoding of turbo and turbo trellis-coded modulation (TTCM) codes is proposed being derived from a well-known inequality, which has not been published before. The max* operation is generalized, for the first time, and performed on n > 2 rather than n = 2 arguments, as it is the conventional approach. Complexity comparisons reveal a significant reduction in the number of operations required per decoding step for the proposed approximation, as compared with the optimal Log-MAP algorithm. Performance evaluation results are presented for both turbo and TTCM codes, showing the near optimal performance of the novel approximation method in both the additive white Gaussian noise (AWGN) and uncorrelated, i.e. fully interleaved, Rayleigh fading channels.     

Increased power output from micro porous layer (MPL) cathode microbial fuel cells (MFC)

Microbial fuel cells are bio-electrochemical transducers that utilise microorganisms to generate electricity, through the oxidation of organic matter. They consist of a negative anode and a positive cathode, separated by an ion selective membrane. The key to improve power, in open-to-air cathode MFCs, is the efficient utilisation of oxygen, by using high surface area materials and effective gas diffusion. This study investigated the effect of single micro porous layers, used as the coating on various electrode substrata, on the performance of small-scale MFCs. Furthermore, 2 of the modified small-scale (6.25 mL) MFCs were implemented as the power source for the TI Chronos digital wristwatch, thus successfully substituting the 3 V button cell, at least for the duration of the experiment.     

SISO algorithms based on Max-Log-MAP and Log-MAP turbo decoding

Novel soft-input soft-output (SISO) decoding algorithms suitable for turbo codes are proposed with good compromise between complexity and bit error rate (BER) performance. The algorithms are based on the application of the max/max* (i.e. Jacobian logarithm) operations at different levels when computing the decoder soft-output value. It is observed that some decoding schemes from the authors' previously published work fall into the family of methods described here. The effect is to provide a range of possibilities allowing system designers to make their own choices for turbo code BER performance against complexity     

Modified sum-product algorithms for decoding low-density parity-check codes

The authors deal with the sum-product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10^-6. Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly     

Design of Efficiently Encodable Rate-Compatible LDPC Codes Using Vandermonde Extension Matrices

A low-complexity algorithm for the design of efficiently-encodable rate-compatible (RC) low-density parity-check (LDPC) codes by deterministically extending an irregular repeat-accumulate (IRA) is introduced. The extending structure is based on circulants shifted according a truncated Vandermonde matrix (VM) and therefore termed as “extended VM” (eVM). The novel extending algorithm is significantly less computationally complex than other known similar methods since it does not require any optimization of the extending profile or any post-construction girth conditioning. To improve the codes’ properties and correcting capabilities in low code rate applications, the optimal proportions of degree-1 and degree-2 parity bits for the extended nodes are investigated and, in contrast to existing deterministic extending approaches for RC-IRA codes, an extending increment step equal to half the information block length is chosen. Various bit error rate (BER) and frame error rate (FER) have been obtained for different code rates, R, and information block length k ₀ = 512 and 1024 bits considering an additive white Gaussian noise (AWGN) channel. The results have demonstrated that the proposed eVM RC-LDPC codes, despite their very simple structure and very low computational complexity, exhibit excellent performance only slightly inferior to both dedicated IRA and previously known RC-IRA codes for different data block sizes.