A Better Understanding of the Performance of Rate-1/2 Binary Turbo Codes that Use Odd-Even Interleavers

The effects of the odd-even constraint - as an interleaver design criterion - on the performance of rate-1/2 binary turbo codes are revisited. According to the current understanding, its adoption is favored because it makes the information bits be uniformly protected, each one by its own parity bit. In this paper, we provide instances that contradict this point of view suggesting for a different explanation of the constraint's behavior, in terms of distance spectrum

Turbo Codes Construction for Robust Hybrid Multitransmission Schemes

In certain applications the user has to cope with some random packet erasures due, e.g., to deep fading conditions on wireless links, or to congestion on wired networks. In other applications, the user has to cope with a pure wireless link, in which all packets are available to him, even if seriously corrupted. The ARQ/FEC schemes already studied and presented in the literature are well optimized only for one of these two applications. In a previous work, the authors aimed at bridging this gap, giving a design method for obtaining hybrid ARQ schemes that perform well in both conditions, i.e., at the presence of packet erasures and packet fading. This scheme uses a channel coding system based on partially-systematic periodically punctured turbo codes. Since the computation of the transfer function and, consequently, the union bound on the Bit or Frame Error Rate of a partiallysystematic punctured turbo code becomes highly intensive as the interleaver size and the puncturing period increase, in this work a simplified and more efficient method to calculate the most significant terms of the average distance spectrum of the turbo encoder is proposed and validated

On the error statistics of turbo decoding for hybrid concatenated codes design

In this paper we propose a model for the generation of error patterns at the output of a turbo decoder using a Context Tree based modelling technique. This model can be used not only to generate the decoder error pattern behaviour with little effort, avoiding simulations, but also to investigate \u2013 with no need of performing neither a turbo code distance spectrum analysis, nor the probabilistic characterization of log-likelihood ratios or of the extrinsic information at a turbo decoder output \u2013 the performance of hybrid concatenated coding (HCC) schemes having a turbo code as component code. These coding schemes combine the features of parallel and serially concatenated codes and thus offer more freedom in code design. It has been demonstrated, in fact, that HCCs can perform closer to capacity than serially concatenated codes while still maintaining a minimum distance that grows linearly with block length

Network flow algorithms for wireless networks and design and analysis of rate compatible LDPC codes

While Shannon already characterized the capacity of point-to-point channels back in 1948, characterizing the capacity of wireless networks has been a challenging problem. The deterministic channel model proposed by Avestimehr, etc. (2007 - 1) has been a promising approach for approximating the Gaussian channel capacity and has been widely studied recently. Motivated by this model, an improved combinatorial algorithm is considered for finding the unicast capacity for wireless information flow on such deterministic networks in the first part of this thesis. Our algorithm fully explores the useful combinatorial features intrinsic in the problem. Our improvement applies generally with any size of finite fields associated with the channel model. Comparing with other related algorithms, our improved algorithm has very competitive performance in complexity. In the second part of our work, we consider the design and analysis of rate-compatible LDPC codes. Rate-compatible LDPC codes are basically a family of nested codes, operating at different code rates and all of them can be encoded and decoded using a single encoder and decoder pair. Those properties make rate-compatible LDPC codes a good choice for changing channel conditions, like in wireless communications. The previous work on the design and analysis of LDPC codes are all targeting at a specific code rate and no work is known on the design and analysis of rate-compatible LDPC codes so that the code performance at all code rates in the family is manageable and predictable. In our work, we proposed algorithms for the design and analysis of rate-compatible LDPC codes with good performance and make the code performance at all code rates manageable and predictable. Our work is based on E2RC codes, while our approaches in the design and analysis can be applied more generally not only to E2RC codes, but to other suitable scenarios, like the design of IRA codes. Most encouragingly, we obtain families of rate-compatible codes whose gaps to capacity are at most 0.3 dB across the range of rates when the maximum variable node degree is twenty, which is very promising compared with other existing results

Staircase Codes: FEC for 100 Gb/s OTN

Staircase codes, a new class of forward-error-correction (FEC) codes suitable for high-speed optical communications, are introduced. An ITU-T G.709-compatible staircase code with rate R=239/255 is proposed, and FPGA-based simulation results are presented, exhibiting a net coding gain (NCG) of 9.41 dB at an output error rate of 1E-15, an improvement of 0.42 dB relative to the best code from the ITU-T G.975.1 recommendation. An error floor analysis technique is presented, and the proposed code is shown to have an error floor at 4.0E-21.Comment: To appear in IEEE/OSA J. of Lightwave Technolog

On the Error Statistics of Turbo Decoding for Hybrid Concatenated Codes Design

In this paper we propose a model for the generation of error patterns at the output of a turbo decoder. One of the advantages of this model is that it can be used to generate the error sequence with little effort. Thus, it provides a basis for designing hybrid concatenated codes (HCCs) employing the turbo code as inner code. These coding schemes combine the features of parallel and serially concatenated codes and thus offer more freedom in code design. It has been demonstrated, in fact, that HCCs can perform closer to capacity than serially concatenated codes while still maintaining a minimum distance that grows linearly with block length. In particular, small memory-one component encoders are sufficient to yield asymptotically good code ensembles for such schemes. The resulting codes provide low complexity encoding and decoding and, in many cases, can be decoded using relatively few iterations

Spatially coupled generalized LDPC codes: asymptotic analysis and finite length scaling

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.This work was supported in part by the National Science Foundation under Grant ECCS-1710920, Grant OIA-1757207, and Grant HRD-1914635; in part by the European Research Council (ERC) through the European Union's Horizon 2020 research and innovation program under Grant 714161; and in part by the Spanish Ministry of Science, Innovation and University under Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU)