Serial concatenation of interleaved convolutional codes andM-ary continuous phase modulations

We consider the serial concatenation of a convolutional code and a continuous phase modulation separated by a random interleaver. It is shown that the continuous phase modulator has the same behavior as a recursive systematic convolutional code in serial turbo codes. The interleaver gain produced by the modulator and the random interleaving depends only on the minimum Hamming distance of the outer code. A soft-input soft-output detection algorithm is described and applied in an iterative joint detection-decoding scheme. Simulated performance over Gaussian and Rayleigh channels shows a dramatic gain over both uncoded modulation and classic detection cases.     

Irregular LDPC codes as concatenation regular LDPC codes

In this letter, the construction of irregular LDPC codes obtained by concatenating regular ones is considered. These codes are analyzed for the binary symmetric channel (BSC). It is shown via proper distribution evolution that such concatenated codes have in general a threshold value weaker (but not necessarily much different) than their unconstrained counterparts for the BSC. On the other hand, they can offer advantages in term of convergence and error performance for lengths of practical interest and long enough to validate the degree distribution selection.     

Serial concatenation of block and convolutional codes

Parallel concatenated coding schemes employing convolutional codes as constituent codes linked by an interleaver have been proposed in the literature as `turbo codes'. They yield very good performance in connection with simple suboptimum decoding algorithms. The authors propose an alternative scheme consisting in the serial concatenation of block or convolutional codes and evaluate its average performance in terms of bit error probability     

Serial concatenation of Hermitian codes with ring‐TCM codes

Hermitian codes are a class of very long algebraic‐geometric (AG) codes constructed from Hermitian curves, which outperform Reed–Solomon codes defined over the same finite fields and with the same code rates, as recently demonstrated by the authors. However, since there are no soft‐decision decoding algorithms for AG codes in the literature, the performance of Hermitian codes is limited and their potential is yet to be realized. An alternative method for achieving more significant coding gains is presented in this paper by serially concatenating long Hermitian codes with ring‐trellis‐coded modulation codes over the ring of integers ?₄ and evaluating their performance through simulation results on the AWGN and Rayleigh fading channels. The scheme achieves large coding gains over single Hermitian and Reed–Solomon codes with no increase in bandwidth use and a performance comparable with the well‐known capacity‐approaching codes. Copyright © 2007 John Wiley & Sons, Ltd.     

Serial concatenation of interleaved codes: performance analysis,design, and iterative decoding

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as “turbo codes” are performed, showing that the new scheme can offer superior performance     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

Selective serial concatenation of turbo codes

A serial concatenation scheme consisting of a Bose-Chaudhuri-Hocquenghem (BCH) outer code and a turbo inner code is proposed. We first establish that only a small number of bit positions at the turbo decoder output are likely to be in error at high signal-to-noise ratios. A double-error correcting BCH outer code is used to protect these particular error prone bits. Simulation results for an additive white Gaussian noise (AWGN) channel show that the bit-error rate (BER) floor of the turbo code can be lowered by using this serial concatenation scheme. The proposed technique offers higher throughput efficiency and lower complexity than other serial concatenation schemes     

Improved decoding of LDPC coded modulations

A coded modulation belief propagation (CMBP) decoder is proposed for decoding LDPC codes with multilevel modulations. The decoder takes into account statistical dependencies among bits originating in the same symbol, providing better performance than the marginal BP (MBP) decoder. Asymptotically it converges to MAP decoding. The CMBP decoder is based on a single-level coding (SLC) scheme and does not suffer from practical disadvantages of multi-level coding (MLC) schemes. Furthermore, the CMBP decoder can close the capacity gap of the bit interleaved coded modulation (BICM) SLC scheme. The BICM capacity gap increases when the modulation size increases and in scenarios where gray mapping is not possible.     

Improved space-time codes using serial concatenation

In this letter, a new family of space-time codes is proposed. These codes employ a serially concatenated coding scheme with a standard space-time code as the outer code and a very simple rate-1 recursive code as the inner code. Adding this simple rate-1 recursive inner code does not decrease the bit rate and introduces only negligible complexity increase to the transmitter when compared to cases with standard space-time codes. An interleaver is embedded between the inner coder and the outer coder and the size of this interleaver determines the performance gain. We also provide a relatively low complexity iterative decoding procedure. For applications which can tolerate delay, significant gain can be achieved with the proposed approach     

Low-complexity LDPC coded BICM-ID with orthogonal modulations

A low-complexity low density parity check (LDPC) coded bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme with orthogonal modulations is proposed. With a novel mapping strategy of coded bits to symbols, the proposed scheme is equivalent to a generalised LDPC code with Hadamard constraints and thus orthogonal demodulation can be merged into the iterative LDPC decoding process, resulting in a simpler implementation and a lower computational complexity.     

QuaSi-Systematic Block-Circulant LDPC codes

A class of Quasi-Systematic Block-Circulant Low-Density Parity-Check （QSBC-LDPC） codes is proposed. Block-circulant LDPC codes have been studied a lot recently, because the simple structures of their parity-check matrices are very helpful to reduce the implementation complexities. QSBC-LDPC codes are special block-circulant LDPC codes with quasi-systematic parity-check matrices. The memories for encoders of QSBC-LDPC codes are limited, and the encoding process can be carried out in a simple recursive way with low complexities. Researches show that the QSBC-LDPC codes can provide remarkable performances with low encoding complexities.     

Low-complexity decoding of LDPC codes

The offset BP-based algorithm is a reduced-complexity derivative of the belief-propagation algorithm for decoding of low-density parity- check codes. It uses a constant offset term to simplify decoding, but at the cost of performance. A method to obtain a 'variable' offset parameter is presented here, to improve the performance of the algorithm.     

LDPC codes over mixed alphabets

The notion of low-density parity-check (LDPC) codes over mixed alphabets is introduced. It is shown that these codes can provide good performance/complexity trade-offs compared to their single-alphabet counterparts     

Low-floor decoders for LDPC codes

One of the most significant impediments to the use of LDPC codes in many communication and storage systems is the error-rate floor phenomenon associated with their iterative decoders. The error floor has been attributed to certain subgraphs of an LDPC code?s Tanner graph induced by so-called trapping sets. We show in this paper that once we identify the trapping sets of an LDPC code of interest, a sum-product algorithm (SPA) decoder can be custom-designed to yield floors that are orders of magnitude lower than floors of the the conventional SPA decoder. We present three classes of such decoders: (1) a bi-mode decoder, (2) a bit-pinning decoder which utilizes one or more outer algebraic codes, and (3) three generalized-LDPC decoders. We demonstrate the effectiveness of these decoders for two codes, the rate-1/2 (2640,1320) Margulis code which is notorious for its floors and a rate-0.3 (640,192) quasi-cyclic code which has been devised for this study. Although the paper focuses on these two codes, the decoder design techniques presented are fully generalizable to any LDPC code.     

LDPC codes from generalized polygons

We use the theory of finite classical generalized polygons to derive and study low-density parity-check (LDPC) codes. The Tanner graph of a generalized polygon LDPC code is highly symmetric, inherits the diameter size of the parent generalized polygon, and has minimum (one half) diameter-to-girth ratio. We show formally that when the diameter is four or six or eight, all codewords have even Hamming weight. When the generalized polygon has in addition an equal number of points and lines, we see that the nonregular polygon based code construction has minimum distance that is higher at least by two in comparison with the dual regular polygon code of the same rate and length. A new minimum-distance bound is presented for codes from nonregular polygons of even diameter and equal number of points and lines. Finally, we prove that all codes derived from finite classical generalized quadrangles are quasi-cyclic and we give the explicit size of the circulant blocks in the parity-check matrix. Our simulation studies of several generalized polygon LDPC codes demonstrate powerful bit-error-rate (BER) performance when decoding is carried out via low-complexity variants of belief propagation.     

Joint Source-Channel Decoding of Huffman codes with LDPC codes

In this paper, we present a Joint Source-Channel Decoding algorithm （JSCD） for Low-Density Parity Check （LDPC） codes by modifying the Sum-Product Algorithm （SPA） to account for the source redundancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm （SSCD）.     

Systematic recursive construction of LDPC codes

This letter presents a systematic and recursive method to construct good low-density parity-check (LDPC) codes, especially those with high rate. The proposed method uses a parity check matrix of a quasi-cyclic LDPC code with given row and column weights as a core upon which the larger code is recursively constructed with extensive use of pseudorandom permutation matrices. This construction preserves the minimum distance and girth properties of the core matrix and can generate either regular, or irregular LDPC codes. The method provides a unique representation of the code in compact notation.     

Memory-efficient sum-product decoding of LDPC codes

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.     

Several properties of short LDPC codes

In this paper, we present several properties on minimum distance(d/sub min/) and girth(G/sub min/) in Tanner graphs for low-density parity-check (LDPC) codes with small left degrees. We show that the distance growth of (2, 4) LDPC codes is too slow to achieve the desired performance. We further give a tight upper bound on the maximum possible girth. The numerical results show that codes with large G/sub min/ could outperform the average performance of regular ensembles of the LDPC codes over binary symmetric channels. The same codes perform about 1.5 dB away from the sphere-packing bound on additive white Gaussian noise channels.