Repeat-accumulate code

Abstract: We study an incremental redundancy (IR) cooperative coding scheme for wireless networks. To exploit the distributed spatial diversity we propose a cluster-based collaborating strategy for a quasi-static Rayleigh-fading channel model. Our scheme allows for enhancing the reliability performance of a direct communication over a single hop. The collaborative cluster consists of M - 1 nodes between the sender and the destination. The transmitted message is encoded using a mother code which is partitioned into M blocks each assigned to one of M transmission slots. In the first slot, the sender broadcasts its information by transmitting the first block, and its helpers attempt to decode this message. In the remaining slots, each of the next M - 1 blocks is sent either through a helper which has successfully decoded the message or directly by the sender where a dynamic schedule is based on the ACK-based feedback from the cluster. By employing powerful good codes including turbo, low-density parity-check (LDPC), and repeat-accumulate (RA) codes, our approach illustrates the benefit of collaboration through not only a cooperation diversity gain but also a coding advantage. The basis of our error rate performance analysis is based on a derived code threshold for the Bhattacharyya distance which describes the behavior of good codes. The new simple code threshold is based on the modified Shulman-Feder bound and the relationship between the Bhattacharyya parameter and the channel capacity for an arbitrary binary-input symmetric-output memoryless channel. An average frame-error rate (FER) upper bound and its asymptotic (in signal-to-noise ratio (SNR)) version are derived as a function of the average fading channel SNRs and the code threshold. Based on the asymptotic bound, we investigate both the diversity, the coding, and the transmission energy gain in the high and moderate SNR regimes for three different scenarios: transmitter clustering, receiver clustering, and cluster hopping. We observe that the energy saving of the IR cooperative coding scheme is universal for all good code families in the sense that the gain does not depend on the sender-to-destination distance and the code threshold.

Abstract: 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.

Abstract: 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.

Abstract: 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.