Degree Distribution Design Research Articles

Design of Degree Distribution with Maximum Distance Separable Codes for User Priority

Design of Degree Distribution with Maximum Distance Separable Codes for User Priority

Statistical Degree Distribution Design for Using Fountain Codes to Control the Peak-To-Average Power Ratio in an OFDM System.

Utilizing fountain codes to control the peak-to-average power ratio (PAPR) is a classic scheme in Orthogonal Frequency Division Multiplexing (OFDM) wireless communication systems. However, because the robust soliton distribution (RSD) produces large-degree values, the decoding performance is severely reduced. In this paper, we design statistical degree distribution (SD) under a scenario that utilizes fountain codes to control the PAPR. The probability of the PAPR produced is combined with RSD to design PRSD, which enhances the smaller degree value produced. Subsequently, a particle swarm optimization (PSO) algorithm is used to search the optimal degree value between the binary exponential distribution (BED) and PRSD distribution according to the minimum average degree principle. Simulation results demonstrate that the proposed method outperforms other relevant degree distributions in the same controlled PAPR threshold, and the average degree value and decoding efficiency are remarkably improved.

Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions by Linear Programming

In this paper, we propose new design algorithms of irregular spatially-coupled low-density parity-check (SC-LDPC) codes with non-uniform degree distributions using linear programming (LP). In general, irregular SC-LDPC codes with non-uniform degree distributions are difficult to design with low complexity because their density evolution equations are multi-dimensional. To overcome this problem, proposed design algorithms are based on three main ideas: a local design of degree distributions, pre-computation of the input/output message relationship, and selection of a proper objective function. These ideas make it possible to design degree distributions of irregular SC-LDPC codes by solving low-complexity LP problems over the binary erasure channel (BEC). It is shown that the proposed irregular SC-LDPC codes designed by the proposed algorithms are superior to regular SC-LDPC codes in terms of both asymptotic and finite-length performances over the BEC. We also confirm that the proposed irregular SC-LDPC code achieves better performance compared with an optimized irregular block LDPC code in the same blocklength, which implies that the proposed design algorithms also provide a new way to construct capacity-approaching block LDPC codes.

Design of Degree Distributions for Finite Length LT Codes

In this paper we investigate the design of degree distributions for finite length LT codes over the binary erasure channel. A decreasing ripple size in literature provides the state of the art degree distributions for finite length LT codes. However, study on releasing multiple encoding symbols in each decoding step shows that the ripple size increases first and then decreases during the decoding process. Therefore, we propose the corresponding ripple size evolution model considering multiple releases. In the design procedure with any ripple size evolution models, the computational cost increases greatly as the length of source symbols increases. Thus, we design a suboptimal degree distribution of low computational complexity. The proposed degree distributions are compared to others through simulations and a increase in performance with respect to block error rate is provided.

New degree distribution design scheme for LT codes

The decoding efficiency deteriorates badly when the existing degree distributions are used to encode the source packets with small size. In this paper, we present a new way to design a degree distribution for LT codes. First, we combine two degree distributions with certain proportion and further adjust the degree by optimising the ripple size, so as to get a new degree distribution which can perform well when the message size is small. Through Monte-Carlo simulation experiments, we have verified that the degree distribution generated by our scheme can highly improve the performances of encoding and decoding, which remain fair even when the source data size gets small.

New degree distribution design scheme for LT codes

New degree distribution design scheme for LT codes

Optimization Design and Asymptotic Analysis of Systematic Luby Transform Codes Over BIAWGN Channels

In this paper, we study systematic Luby transform (SLT) codes over binary input additive white Gaussian noise (BIAWGN) channels. To improve the bit-error-rate (BER) performance of SLT codes on the BIAWGN channel, this paper presents a novel optimization design of degree distributions. First, we apply the Gaussian approximation (GA) to analyze the asymptotic BER performance of SLT codes and calculate overhead thresholds for successful decoding. Second, we derive an approximate closed-form expression for lower bound on BER by applying the GA and further simplify the expression in low and high signal-to-noise ratio regimes, respectively. Third, we adopt the conventional linear programming (CLP) constrained by the GA to optimize the degree distribution of SLT codes. The objective of CLP is to minimize the average degree of the degree distribution that may result in bad error floor. To improve the error floor caused by CLP, we put forth a novel optimization model constrained by the lower bound on BER, and using the model we can design the degree distribution more flexibly with any desired BER. Simulation results show that the proposed degree distribution can provide better BER performance of SLT codes over the BIAWGN channel.

Raptor Codes in the Low SNR Regime

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise (BIAWGN) channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.

Fountain Code Design for Broadcasting Systems With Intermediate-State Users

Several studies on fountain codes have proposed degree distribution optimization schemes to maximize symbol recovery rate. However, if the number of transmitted coded symbols is limited or the channel erasure probability is high, it may be impossible that a user recovers all of the data symbols regardless of degree distribution employed by the source. In this study, we focus on a new system model where one source transmits fountain-coded symbols to multiple users who already possess some data symbols and coded symbols. Assuming that each user can transmit a feedback packet containing its own state information before the source transmits coded symbols, we propose two types of degree distribution design schemes that are suitable for the system model. Simulation results demonstrate the efficiency of our proposed schemes by comparing with conventional methods in terms of symbol recovery rate and full recovery rate.

Joint network and fountain codes design for relay-assisted multi-user system

In relay-assisted multi-user system, relay coding is important to enhance the robustness and reliability of cooperative transmission. For better adaptability and efficiency, two joint network and fountain coding (JNFC) schemes are proposed. When the condition of all direct channels is worse, JNFC scheme based on distributed LT(DLT) codes is used. Otherwise, JNFC scheme based on multi-dimensional LT(MD-LT) codes is suited. For both two above-mentioned schemes, the united degree distribution design method for short-length fountain codes is proposed. For the latter scheme, MD-LT codes are proposed for equal error protection (EEP) of each user. Simulation results and analysis show that the united degree distribution need less decoding overhead compared with other degree distribution for short-length fountain codes. And then, all users are protected equally in despite of asymmetric uplinks.

Performance Analysis of Joint Degree Distribution (JDD) in Luby Transform Codes

Luby Transform (LT) codes, the first realization of rateless codes are widely used in wireless communication mainly for its adaptability to varying channel conditions and its capacity approaching performance. In spite of the above advantages and its simplicity in implementation, LT codes suffer from a bottle neck of premature termination due to the poor design of degree distribution. In this study, a novel degree distribution called Joint Degree Distribution (JDD) is proposed for the successful completion of LT encoder/decoder processes. The efficient utilization of the bandwidth is tried to be achieved by using only 'k' encoded symbols for 'k' source symbols, unlike in traditional systems. JDD is carefully designed to ensure that the encoding/decoding delay does not exceed that which is existent in the traditional systems. The performance of JDD for throughput and bit error rate, experimented over Additive White Gaussian Noise (AWGN) channel compared to conventional degree distribution was observed to be much better.

On Raptor Code Design for Inactivation Decoding

Based on a new vision of the inactivation decoding process, we set a new degree distribution design criterion for the LT part of Raptor codes. Under an infinite block length assumption, a family of degree distributions that satisfy the new design criterion is analytically derived. The finite length performance of this family is investigated by using computer simulations and is shown to outperform the conventional design.

Degree Distribution Design for LDPC Codes: A Derivative Matching Approach

A deterministic method to design degree distributions for low-density parity-check codes over the binary erasure channel is proposed. This method consists of matching the first and high-order derivatives of the extrinsic information transfer (EXIT) function of the variable node set to the corresponding derivatives of the inverse EXIT function of the check node set, in order to reduce the gap between the two curves in the EXIT chart. A sufficient condition for a check-concentrated distribution to achieve derivative matching up to some order is first obtained, and then a deterministic design algorithm, enabled by the Fourier-Budan theorem, is developed exploiting this sufficient condition. A comparison with other deterministic design techniques is also provided, revealing the potential of the proposed algorithm.

Design of degree distributions for LDPCA codes

A degree distribution design method of low-density parity-check accumulate (LDPCA) codes is proposed for rate-compatible asymmetric Slepian-Wolf coding (SWC) of correlated binary memoryless sources. The degree distribution is designed by seeking the simultaneous optimum at the lowest and the highest compression rates of the specified range with density evolution algorithm. The experimental results show that the coding efficiency of codes constructed with the designed degree distribution is close to the Slepian-Wolf limit over the entire target range and better than all other reported results of the rate-compatible asymmetric SWC.