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Background With the inherent high density and durable preservation, DNA has been recently recognized as a distinguished medium to store enormous data over millennia. To overcome the limitations existing in a recently reported high-capacity DNA data storage while achieving a competitive information capacity, we are inspired to explore a new coding system that facilitates the practical implementation of DNA data storage with high capacity. Result In this work, we devised and implemented a DNA data storage scheme with variable-length oligonucleotides (oligos), where a hybrid DNA mapping scheme that converts digital data to DNA records is introduced. The encoded DNA oligos stores 1.98 bits per nucleotide (bits/nt) on average (approaching the upper bound of 2 bits/nt), while conforming to the biochemical constraints. Beyond that, an oligo-level repeat-accumulate coding scheme is employed for addressing data loss and corruption in the biochemical processes. With a wet-lab experiment, an error-free retrieval of 379.1 KB data with a minimum coverage of 10x is achieved, validating the error resilience of the proposed coding scheme. Along with that, the theoretical analysis shows that the proposed scheme exhibits a net information density (user bits per nucleotide) of 1.67 bits/nt while achieving 91% of the information capacity. Conclusion To advance towards practical implementations of DNA storage, we proposed and tested a DNA data storage system enabling high potential mapping (bits to nucleotide conversion) scheme and low redundancy but highly efficient error correction code design. The advancement reported would move us closer to achieving a practical high-capacity DNA data storage system.

This paper provides a performance analysis of channel coding in multiple antenna TWRC with physical layer network coding. Data is transmitted from two source nodes S1 and S2 to a relay node with multiple antennas. The best antenna for transmission is selected and the data is transmitted through a Rayleigh fading channel with AWGN Noise after channel coding and BPSK modulation. Then this relay performs channel decoding and network coding operations and retransmits the coded sequence to their respective destinations. The channel coding employed here is repeat accumulate code. The BER analysis at the relay with and without channel coding is done using Monte Carlo simulations. The results show that the BER of a Bidirectional relay with channel coding is less than that without channel coding for multiple antennas. Also the analysis of SIMO, MISO and MIMO has been made for TWRC with channel coding. The results show that the performance of TWRC with channel coding has increased with increase in the number of antennas.

We investigate the information rate of channels affected by phase noise, aiming at predicting the ultimate performance limits in this scenario. Moreover, a closed-form upper bound is also derived for phase shift keying (PSK) modulations. Finally, we consider the design of nonsystematic irregular repeat-accumulate (RA) codes for this channel trying to give new insights on the codes to be employed for such an application.

An approximate upper bound is derived to the maximum likelihood decoding threshold of weighted nonbinary repeat-accumulate (WNRA) codes over GF(q) with q-ary orthogonal modulation and coherent detection over the additive white Gaussian noise channel. As with binary RA codes, WNRA codes show the potential for achieving the channel capacity with decreasing code rate for large enough q.

In this paper, the existence of capacity-achieving codes for memoryless binary-input output-symmetric (MBIOS) channels under maximum-likelihood (ML) decoding with bounded graphical complexity is investigated. Graphical complexity of a code is defined as the number of edges in the graphical representation of the code per information bit and is proportional to the decoding complexity per information bit per iteration under iterative decoding. Irregular repeat-accumulate (IRA) codes are studied first. Utilizing the asymptotic average weight distribution (AAWD) of these codes and invoking Divsalar's bound on the binary-input additive white Gaussian noise (BIAWGN) channel, it is shown that simple nonsystematic IRA ensembles outperform systematic IRA and regular low-density parity-check (LDPC) ensembles with the same graphical complexity, and are at most 0.124 dB away from the Shannon limit. However, a conclusive result as to whether these nonsystematic IRA codes can really achieve capacity cannot be reached. Motivated by this inconclusive result, a new family of codes is proposed, called low-density parity-check and generator matrix (LDPC-GM) codes, which are serially concatenated codes with an outer LDPC code and an inner low-density generator matrix (LDGM) code. It is shown that these codes can achieve capacity on any MBIOS channel using ML decoding and also achieve capacity on any BEC using belief propagation (BP) decoding, both with bounded graphical complexity. Moreover, it is shown that, under certain conditions, these capacity-achieving codes have linearly increasing minimum distances and achieve the asymptotic Gilbert-Varshamov bound for all rates.

Using nonbinary low-density parity-check (LDPC) codes with random-coset mapping, Bennatan and Burshtein constructed bandwidth-efficient modulation codes with remarkable performance under belief propagation (BP) decoding. However, due to the random nature of LDPC codes, most of the good LDPC codes found in the literature do not have a simple encoding structure. Thus, the encoding complexity of those LDPC codes can be as high as O(N 2), where N is the codeword length. To reduce the encoding complexity, in this paper, nonbinary irregular repeat-accumulate (IRA) codes with time-varying characteristic and random-coset mapping are proposed for bandwidth-efficient modulation schemes. The time-varying characteristic and random-coset mapping result in both permutation-invariance and symmetry properties, respectively, in the densities of decoder messages. The permutation-invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using Gaussian distributions. Under the Gaussian approximation, extrinsic information transfer (EXIT) charts for nonbinary IRA codes are developed and several codes of different spectral efficiencies are designed based on EXIT charts. In addition, by proper selection of nonuniform signal constellations, the constructed codes are inherently capable of obtaining shaping gains, even without separate shaping codes. Simulation results indicate that the proposed codes not only have simple encoding schemes, but also have remarkable performance that is even better than that constructed using nonbinary LDPC codes.

In this letter, a new rate-control scheme, called splitting, is proposed to construct low-rate codes from high-rate codes, which splits rows of parity-check matrices of repeat accumulate-type (RA-Type) LDPC codes by adding new parity bits. When a high-degree check node is split into two low-degree check nodes, by making the check node degree distribution in a concentrated form, the performance of low-rate codes can be improved. We also explicitly construct rate-compatible repeat RA-Type LDPC (RC RA-type LDPC) codes using splitting for code rates from 1/3 to 4/5 and compare this with other RC RA-type LDPC codes.

This paper provides simple lower bounds on the number of iterations which is required for successful message-passing decoding of some important families of graph-based code ensembles (including low-density parity-check (LDPC) codes and variations of repeat-accumulate codes). The transmission of the code ensembles is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. The simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree-2 variable nodes, the target bit erasure probability, and the gap between the channel capacity and the design rate of the ensemble. This paper demonstrates that the number of iterations which is required for successful message-passing decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish (hence, the number of iterations becomes unbounded as the gap to capacity vanishes).

In this paper we design practical interleavers for regular, systematic repeat-accumulate (RA) codes. The new interleavers, which we call L-type and modified L-type interleavers, are deterministic, described by a single parameter, and straightforward to implement. Despite their simple description, the new interleavers are shown to perform equally as well as, or better than, traditional interleavers over a wide range of code lengths and rates.

In digital communication systems employing binary phase-shift keying and non-data-aided carrier phase recovery, a 180°carrier phase ambiguity is inevitable. Here, we propose a simple modification to the standard regular repeat-accumulate (RA) code structure by exploiting the differential encoding inherent to the inner encoder of RA codes resulting in codes that are 180°rotationally invariant. The proposed code structure exhibit performance virtually identical to that of standard regular RA codes with zero carrier phase offset under both zero and 180°carrier phase offsets with negligible additional hardware complexity.

This paper presents some decoding methods based on Tanner graph for the analysis of the repeat accumulate code which has been proved to be linear time encoding and linear time decoding. We study the structure of the repeat accumulate code and make a detail derivation of the procedure of these iterative algorithms. The extensive simulation results show that these efficient decoding methods based on the message passing algorithm are suitable for the repeat accumulate code both in performance and complexity.

As powerful error correcting codes, Low-Density Parity-Check (LDPC) codes have been adopted as a fundamental building block by dirty paper coding (DPC), which indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and is a promising strategy in future communication systems. However, to achieve this performance gain demands huge computation complexity. For its lower cost and better flexibility, the GPU-based LDPC decoder is an emerging research subject. Based on the perspective of GPU hardware architecture, a multi-stage optimizing mapping strategy (MSOMS) is proposed and implemented to accelerate LDPC decoding. The performance is boosted significantly by balancing the memory access and computation load, optimizing execution configuration and the memory access pattern, and fully utilizing the on-chip high speed resources. Proposed decoders can achieve 383-and 442-speedup compared to CPU-based decoder for LDPC and RA code (another ensemble of LDCP code), and the achieved throughput is comparable to existed GPU-based decoders, which confirm the efficiency of the MSOMS strategy.

A technique for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency-division multiplexing symbols is considered. By extending the method of selected mapping, we achieve PAPR reduction and significant bit error rate improvement. A set of distinct sequences are generated from the data using a modified repeat accumulate code. The sequence with the lowest PAPR is selected for transmission. Using iterative decoding at the receiver, the original data is recovered without prior knowledge of which sequence was selected.

In this paper, we propose a joint design of MIMO-PNC (multiple-input multiple-output physical layer network coding) and channel decoding in two way relay channels. The paper shows that if we adopt the same Repeat Accumulate (RA) channel code at the two end nodes, there would be a compatible decoder at the relay which can transform the received superimposed packet to the network coding form of the two packets efficiently. Specifically, we redesign the belief propagation decoding algorithm of the RA code for traditional point-to-point channel to suit the need of the MIMO PNC channel. The simulation results show that our new scheme outperforms the previously proposed schemes which combined MIMO NC with channel coding/decoding significantly in terms of BER with little added complexity.

In this letter the impact of tail-biting (TB) on the distance spectrum of repeat accumulate (RA) codes is analyzed. The average weight enumerator (WE) functions for RA ensembles with and without TB are derived, showing that in the short and moderate block length regimes TB is effective in reducing the multiplicities of low weight codewords. Finally, the asymptotic case is discussed.

Based on the good degree distribution of a kind of irregular repeat accumulate (IRA) code, the base check matrix is designed according to quasi-cyclic method, and the length-4 short circles are eliminated. The obtained IRA code has flexible code length from 150 to 6000, with link-level performance close to the LDPC code specified by IEEE802.16e standard. The proposed IRA code family is suitable for multimedia communication system.

The systematic repeat-accumulate (RA) code is constituted by a repeater, an interleaver, a combiner and an accumulator. Under the sum-product decoding on the Tanner graph of the code, the performance of RA codes with random interleaver is affected by short cycles of parity-check matrix. In this paper, we present combinatorial design of interleaver. The RA code with new interleaver can produce very high code rate and its parity-check matrix is free of 4-cycles. Thus the codes are likely to be used in long haul optical fiber communication system. We analyze the performance of the systematic RA code in three optical fiber transmission models. Simulation results show that RA codes with combinatorial interleaver have better performance than that of the code with random interleaver in fiber communication system. The decoder based on Chi-square also has better performance than of the decoder based on Gaussian models

In this paper, we propose an additional data transmission scheme for the ATSC (Advanced Television Systems Committee) terrestrial DTV (digital television) systems based on a low rate systematic irregular repeat-accumulate (SIRA) code. Unlike the previously proposed additional data transmission scheme using TxID (transmitter identification) signals, the proposed scheme conjuncted with a DTV VSB signal cancellation technique is suitable for high data transmission. Compared to the previous additional data transmission scheme based on a low rate systematic repeat-accumulate code, the BER performance of the proposed scheme is significantly improved. The additional data is encoded with a simplified IRA channel coding scheme and injected to the conventional VSB signals with the bury ratio (BR) of −27 dB. With the proposed scheme, an additional data of rate up to 1 Mbps can be transmitted along with the ATSC terrestrial DTV signals by minimizing the detrimental effects on the ATSC terrestrial DTV systems.

Network intruders try to hide their identity by relaying their traffic through a number of intermediate hosts, called stepping stones. Network flow watermarks have been used to detect such attacks by inserting a special timing pattern into one flow by means of artificial delays and detecting relayed flows by searching for the same pattern. We study the application of coding schemes to improve the efficiency of network flow watermarks. In particular, we use the Repeat-Accumulate codes, a class of low complexity, high performance error-correcting codes, to improve the detection performance of a recent flow watermark, the RAINBOW. We show the effectiveness of the improved scheme, C-RAINBOW, through simulation and discuss design tradeoffs.

In this study, the authors discuss the implementation of a low latency decoding algorithm for turbo codes and repeat accumulate codes and compare the implementation results in terms of maximum available clock speed, resource consumption, error correction performance and the data (information bit) rate. In order to decrease the latency a parallellised decoder structure is introduced for these mentioned codes and the results are obtained by implementing the decoders on a field programmable gate array. The memory collision problem is avoided by using collision-free interleavers. Through a proposed quantisation scheme and normalisation in forward/backward recursions, computational issues are handled for overcoming the overflow and underflow issues in a fixed point arithmetic. Also, the effect of different implementation styles are observed.

In multiple-input multiple-output(MIMO) wireless systems, combining good channel codes(e.g., Non-binary Repeat Accumulate codes) with adaptive turbo equalization is a good option to get better performance and lower complexity under Spatial Correlated Frequency Selective(SCFS) Channel. The key of this method is after joint antennas MMSE detection (JAD/MMSE) based on interruption cancelling using soft information, considering the detection result as an output of a Gaussian equivalent flat fading channel, and performing maximum likelihood detection(ML) to get more correct estimated result. But the using of ML brings great complexity increase, which is not allowed. In this paper, a low complexity method called list sphere decoding is introduced and applied to replace the ML in order to simplify the adaptive iterative turbo equalization system.

RA (Repeat Accumulate) code has been widely used in wireless communication systems. But the BP (Belief Propagation) decoding algorithm which is commonly used in RA Code has high complexity. In order to reduce the complexity of BP algorithm while maintaining coding performance, we proposed Chebyshev-Polynomial-Fitting based BP (CPF-BP) decoding algorithm. In CPF-BP decoding algorithm, we used polynomial which is generated by chebyshev fitting algorithm instead of hyperbolic tangent operation in BP decoding algorithm to reduce the implementation complexity. Experiment and simulation results show that this low-complexity algorithm removes hyperbolic tangent operation in conventional BP algorithm with same amount of multiplier under the parameters setting in the paper. The performance degradation of CPF-BP algorithm is negligible which is less than 0.6dB at BER of 10−4 compared with conventional BP algorithm.

Error correction codes of suitable redundancy are used for ensuring perfect data recovery in noisy channels. For iterative decoding based methods, the decoder needs to be initialized with proper confidence values, called the log likelihood ratios (LLRs), for all the embedding locations. If these confidence values or LLRs are accurately initialized, the decoder converges at a lower redundancy factor, thus leading to a higher effective hiding rate. Here, we present an LLR allocation method based on the image statistics, the hiding parameters and the noisy channel characteristics. It is seen that this image-dependent LLR allocation scheme results in a higher data-rate, than using a constant LLR across all images. The data-hiding channel parameters are learned from the image histogram in the discrete cosine transform (DCT) domain using a linear regression framework. We also show how the effective data-rate can be increased by suitably increasing the erasure rate at the decoder.

Analyzing the capacity of relay networks is often based on the max-flow min-cut theorem providing an upper bound on the true capacity which is generally still unknown. This paper analyzes the achievable rates of a simple relay network by a semi-analytical approach considering ideal capacity achieving codes of appropriate rates and optimum symbol-by-symbol soft-output decoding at the relay. Applying the information combining technique, regions are illustrated where the upper bound provided by the max-flow min-cut theorem can be reached. Moreover, the results show that the lower bound obtained by the constraint of error-free decoding at the relay can be exceeded in many scenarios. Simulations with a nearly capacity achieving half-rate repeat accumulate code confirm the semi-analytic results.

Relay networks have attracted great attention in recent years due to their ability to extend the coverage of cellular systems. Their capacity is often analyzed by the max-flow min- cut theorem which provides an upper bound on the true capacity. However, the exact capacity is generally still unknown. This paper applies information combining to determine the achievable rate of a simple relay network. Presupposing an ideal code of appropriate rate and optimum symbol-by-symbol soft-output decoding at the relay, this semi-analytical approach delivers upper and lower bounds on the achievable mutual information of the network. The obtained results identify three different regions concerning the optimum rate of the code. Simulations of a nearly capacity achieving half-rate repeat accumulate code confirm the semi-analytic results.

This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q≫2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and Turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.

In previous works, density evolution schemes have been used to design an irregular low-density parity-check (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.

In this paper, we propose the novel concept of Repeat Accumulate Code Division Multiple Access (RA-CDMA), which employs unique, user-specific channel code generator matrices (interleavers) for differentiating the users. We also suggest a Multilevel Structured (MLS) interleaver generation technique for the sake of reducing the memory storage requirements of our system and compare its correlation properties to those of the conventional random interleaver. A novel hybrid detector is designed for our system with the aid of EXtrinsic Information Transfer (EXIT) charts. Furthermore, we also design a low-complexity unequal power allocation scheme, assigning a different power to each user of this near-capacity transmission scheme. It is shown that when a sufficiently high interleaver length is employed, the RA-CDMA system is capable of approaching the Gaussian channel’s capacity.

This paper presents the uncoded and coded multiuser error performance results of a novel super-orthogonal (SO) 4D CDMA communication platform under AWGN and multi- path fading channel conditions. The communication platform employs a special class of root-of-unity filtered (RUF) constant- envelope (CE) complex spreading sequences (CSS) with zero cross-correlation (ZCC) properties. The uncoded communication platform employs multi-layered-modulation (MLM) to improve spectral efficiency compared with existing multi-level modulation techniques, and the coded system uses the multiple dimensions to transmit redundancy to improve error performance. Three classes of sparse graph coding schemes are evaluated and compared on the multi-dimensional (MD) communication platform. The channel codes include a 3D block-turbo-code (BTC) with extended Reed-Muller (RM) constituent codes, low- density parity-check (LDPC) codes and repeat-accumulate (RA) codes. It is shown that the three channel codes have comparable error performance results and approximately 6 dB performance improvement over BPSK is achieved at Pc(bit) = 1 x 10 -5.

This work is concerned with codes, graphs and their links. Graph based codes have recently become very prominent in both information theory literature and practical applications. While most research has centered around their performance under iterative decoding, another line of study has focused on more combinatorial aspects such as their weight distribution. This is the angle we explore in the first part of this thesis, investigating the trade-off between rate and relative distance. More precisely, we show, using a probabilistic argument, that there exist graph-based codes approaching the asymptotic Gilbert-Varshamov bound, and that are encodable in time O(n1+ε) for any ε > 0, where n is the block length. The second part is concerned with more practical issues, more specifically the erasure channel. Although the codes mentioned above have been shown to perform very well in this setting, this nonetheless requires their lengths to be quite large. When short blocks are required, certain algebraic constructions become viable solutions. In particular Reed-Solomon (RS-) codes are used in a wide range of applications. However, there do not appear to be any practical uses of the more general Algebraic-Geometric (AG-) codes, despite numerous advantages. We explore in this work the use of very short AG-codes for transmissions over the erasure channel. We present their advantages over RS-codes in terms of the encoder/decoder running times, and evaluate the drawbacks by designing an efficient algorithm for computing the error probabilities of AG-codes. The work was done as part of an industrial collaboration with specific transmission problems in mind, and we include some practical data to illustrate the theoretical improvements. Graphs and codes can be related in different ways, and a graph being a good expander often yields a code with certain desirable properties. In the third part we deal with graph products and their expansion properties. Just as the derandomized squaring operation essentially takes the square of a graph and removes some edges according to a second graph, we introduce the derandomized tensoring operation which removes edges from the tensor product of two graphs according to a third graph. We obtain a bound on the expansion of the product in terms of the expansions of the constituent graphs. We also apply the same ideas to a code product, leading to the derandomized code concatenation operation and its analysis.

This work adopts an information theoretic framework for the design of collusion-resistant coding/decoding schemes for digital fingerprinting. More specifically, the minimum distance decision rule is used to identify 1 out of t pirates. Achievable rates, under this detection rule, are characterized in two distinct scenarios. First, we consider the averaging attack where a random coding argument is used to show that the rate 1/2 is achievable with t=2 pirates. Our study is then extended to the general case of arbitrary $t$ highlighting the underlying complexity-performance tradeoff. Overall, these results establish the significant performance gains offered by minimum distance decoding as compared to other approaches based on orthogonal codes and correlation detectors. In the second scenario, we characterize the achievable rates, with minimum distance decoding, under any collusion attack that satisfies the marking assumption. For t=2 pirates, we show that the rate $1-H(0.25)\approx 0.188$ is achievable using an ensemble of random linear codes. For $t\geq 3$, the existence of a non-resolvable collusion attack, with minimum distance decoding, for any non-zero rate is established. Inspired by our theoretical analysis, we then construct coding/decoding schemes for fingerprinting based on the celebrated Belief-Propagation framework. Using an explicit repeat-accumulate code, we obtain a vanishingly small probability of misidentification at rate 1/3 under averaging attack with t=2. For collusion attacks which satisfy the marking assumption, we use a more sophisticated accumulate repeat accumulate code to obtain a vanishingly small misidentification probability at rate 1/9 with t=2. These results represent a marked improvement over the best available designs in the literature., Comment: 26 pages, 6 figures, submitted to IEEE Transactions on Information Forensics and Security

We study an incremental redundancy (IR) cooperative coding scheme for wireless networks. To exploit the spatial diversity benefit we propose a cluster-based collaborating strategy for a quasi-static Rayleigh fading channel model and based on a network geometric distance profile. Our scheme enhances the network performance by embedding an IR cooperative coding scheme into an existing noncooperative route. More precisely, for each hop, we form a collaborating cluster of M-1 nodes between the (hop) sender and the (hop) destination. The transmitted message is encoded using a mother code and partitioned into M blocks corresponding to the each of M slots. In the first slot, the (hop) sender broadcasts its information by transmitting the first block, and its helpers attempt to relay this message. In the remaining slots, the each of left-over M-1 blocks is sent either through a helper which has successfully decoded the message or directly by the (hop) sender where a dynamic schedule is based on the ACK-based feedback from the cluster. By employing powerful good codes (e.g., turbo codes, LDPC codes, and raptor codes) whose performance is characterized by a threshold behavior, our approach improves the reliability of a multi-hop routing through not only cooperation diversity benefit but also a coding advantage. The study of the diversity and the coding gain of the proposed scheme is based on a new simple threshold bound on the frame-error rate (FER) of maximum likelihood decoding. A average FER upper bound and its asymptotic (in large SNR) version are derived as a function of the average fading channel SNRs and the code threshold., Comment: revised version

Modern turbo-like codes (TLCs), including concatenated convolutional codes and low density parity check (LDPC) codes, have been shown to approach the Shannon limit on the additive white Gaussian noise (AWGN) channel Many design aspects remain relatively unexplored, however, including TLC design for maximum flexibility, very low error rate performance, and amenability to simple or very high-speed hardware codecs. In this paper we address these design issues by suggesting a new class of TLCs that we call systematic with serially concatenated parity (S-SCP) codes. One example member of this family is the Generalized (or Systematic) repeat accumulate code. We describe two other members of this family that both exhibit good performance over a wide range of block sizes, code rates, modulation, and target error probability. One of these provides error floor performance not previously demonstrated with any other TLC construction and the other is shown to offer very low complexity decoding with good performance. These two codes have been implemented in high-speed hardware codecs and performance curves based on these down to bit error rates below 10-10 are provided.

A fast irregular repeat accumulator (IRA) encoder that reduces the encoder latency for generating parity bits is proposed. The transformation of the parity check matrix into the blockwise form and the usage of the partial parallel process bring a reduction of the number of system clocks for the IRA codes encoding.