Improved Performance Upper Bounds for Terminated Convolutional Codes

In this letter, we propose tight performance upper bounds for convolutional codes terminated with an input sequence of finite length. To obtain the upper bounds, a weight enumerator is defined to represent the relation between the Hamming distance of the coded output and the Hamming distance of the input bits of the code. The upper bounds on frame error rate (FER) and average bit error rate (BER) are obtained from the weight enumerator. A simple method is presented to compute the weight enumerator of a terminated convolutional code based on a modified trellis diagram.     

卷积码Viterbi译码算法的FPGA实现

探讨了卷积码Viterbi译码的FPGA实现问题。在Viterbi译码算法中，提出了减少路径量度的位数和流水线回索法的幸存路径等方法，能有效地减少存储量、降低功耗、提高速度，使得K=7的Viterbi译码算法可在以单片FPGA为主的器件上实现。     

High-Rate Punctured Convolutional Codes for Soft Decision Viterbi Decoding

The high-rate punctured codes of rates 2/3 through 13/14 are derived from rate 1/2 specific convolutional codes with maximal free distance. Coding gains of derived codes are compared based on their bit error rate performances under soft decision Viterbi decoding.     

卷积码Viterbi译码的优化与实现

给出了一种(2,1,6)卷积码Viterbi译码器的FPGA设计方案,重点对加比选单元进行了优化,采用预计算和查表技术来实现加比选单元,以替代传统的加比选结构,具有节省资源,速度快,性能稳定等特点。     

高编码率维特比译码器的设计

本文提出了一种高编码维特比译码器设计方案，并采用单片机加以实现。因此方案具有一定的实用性。     

Error Probabilities for Spread-Spectrum Packet Radio with Convolutional Codes and Viterbi Decoding

The use of convolutional coding in packet radio systems introduces problems in evaluating performance, since the errors out of the decoder are not independent. A new bound on the packet error probability out of a Viterbi decoder may be used to evaluate these systems. We present results on the packet error probability for frequencyhop and direct-sequence spread-spectrum systems. In addition, we show that the assumption of independent errors out of the decoder gives an upper bound that is not as tight as our new bound. Comparisons are made with frequency-hop systems using Reed-Solomon codes.     

Distance Bounds for an Ensemble of LDPC Convolutional Codes

An ensemble of $(J,K)$ -regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance $d _ {rm L}$ of code segments of finite length $L$ and on the free distance $d _{rm free}$ are derived. For sufficiently large constraint lengths $nu$ , the distances are shown to grow linearly with $nu$ and the ratio $d_ {rm L}/nu$ approaches the ratio $d _{ {rm free}}/nu$ for large $L$ . Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of $(J,K)$-regular LDPC block codes.      

卷积码Viterbi译码器的硬件实现

第三代移动通信系统标准中普遍采用卷积码和Turbo码作为信道编码方案.本文首先阐述了维特比译码算法,然后论述了(2,1,3)卷积码编码电路和维特比译码的单片机实现方案.最后把维特比算法与交织方案相结合,统计结果表明纠错性能有较大改善.     

Low-Latency Low-Complexity Architectures for Viterbi Decoders

Look-ahead techniques are applied in the nonlinear add-compare-select unit for achieving high throughput in Viterbi decoders. Multiple steps of the binary trellis are combined into an equivalent one-step complex trellis in time sequence, which is referred to as the branch metric precomputation (BMP). As the look-ahead level increases, the BMP dominates the complexity and delay of the overall system architecture. This paper systematically proposes an optimal branch metric computation scheme with the minimal complexity and latency. The proof of its optimality is also given. This highly efficient scheme leads to a novel overall optimal BMP architecture for any look-ahead level. Furthermore, an alternative technique other than the look-ahead is proposed for reducing the latency at very low complexity cost. This alternative technique can be either applied in combination with the proposed architecture to achieve the lowest latency at a slight increase in complexity or used on its own for low complexity compared with other look-ahead-based architectures. Results show that the three proposed architectures can either reduce complexity by up to 84% or reduce the latency by up to 72.50%.     

卷积码Viterbi译码器的FPGA的设计与实现

给出了一种基于FPGA的切实可行的卷积码Viterbi译码器的实现方案。该方案只需要很少的硬件资源,速度较快。可以很方便地和Turbo译码器结合在单片的FPGA上,并应用于3GPPWCDMA移动通信系统中。     

卷积码及维特比译码在卫星通信中的应用

在功率受限的卫星信道中,卷积码与BPSK(或QPSK)结合在一起被看作是可靠通信的一种有效的系统。该文讨论了卫星通信信道特性,介绍了卷积编码、BPSK信号和软判决,给出了卷积码最大似然译码——维特比译码算法。     

An SEU-Tolerant Approach for Space-Borne Viterbi Decoders

In the space environment, Viterbi decoder implemented on SRAM-based FPGA is sensitive to Single event upsets （SEUs）, which may lead to functional failure of the decoder. Conventional SEU mitigation techniques like modular redundancy could not exploit the characters of Viterbi decoders, therefore could not provide optimized SEU tolerance when the device resource utilization cost is a constraint. Leveraging the properties of the decoding algorithm, three effective mitigation techniques are adopted, including structure optimization, Error detection and correction （EDAC） for Block RAM （BRAM） protection, and Partial triple-modular redundancy （PTMR）, which are applied to the modules of the decoder in accordance with their characteristics. Analysis of effectiveness shows that compared with unmitigated design, the SEU induced failure rate in the proposed SEU tolerant decoder can be reduced to 1/4 at the cost of 61.1% extra resource utilization. Error detec- tion and correction （EDAC）.     

Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudocodewords. These failures can cause the large signal-to-noise ratio (SNR) performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood (ML) decoding union bound.      

基于FPGA的卷积码Viterbi译码器性能研究

基于FPGA的卷积码Viterbi译码器,其性能与译码算法参数设置密切相关。在采用VHDL语言设计实现译码器的基础上,通过仿真,分析了Viterbi译码器参数的设置情况,就幸存路径长度、编码存储度等参数对FPGA译码器性能的影响进行了讨论,并给出了这些参数的最佳取值。对卷积码编译码参数设计具有较好的指导性和实用性。     

Performance of Unequally Punctured Convolutional Codes

In practical applications, some coded symbols are unequally punctured for rate matching of terminated convolutional codes. In this letter, performance upper bounds are proposed for a terminated convolutional code punctured with an arbitrary pattern. To obtain the upper bounds, a weight enumerator is defined to represent the relation between the Hamming weight of the coded outputs and that of the selected input information bits. A method is presented to compute the weight enumerator based on a modified trellis diagram. Simulation and numerical analysis show that the proposed bounds are tight to the performance of terminated convolutional codes.     

Performance Bounds for Unequal Error Protecting Turbo Codes

In many communications systems, data can be divided into different importance levels. For these systems, unequal error protection (UEP) techniques are used to guarantee lower BER for the more important classes. In particular, if the precise characteristics of the channel are not known, UEP can be used to recover the more important classes even in poor receiving conditions. In this paper, we derive bounds on the performance of unequal error protecting turbo codes. These bounds serve as an important tool in predicting the performance of these codes. In order to derive the bounds, we introduce the notion of UEPuniform interleaver which is a random interleaver that does not change the order of classes in the turbo code frame. We also present a method to derive the weight enumerating function for UEP turbo codes.     

Gallager Bounds for Noncoherent Decoders in Fading Channels

Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound.      

Finite-Dimensional Bounds on Zm and Binary LDPC Codes With Belief Propagation Decoders

This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of Zopf_m and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented, admitting systematic searches for new bounds. Two noise measures are considered: the Bhattacharyya noise parameter and the soft bit value for a maximum a posteriori probability (MAP) decoder on the uncoded channel. For Zopf _m LDPC codes, an iterative m-dimensional bound is derived for m-ary-input/symmetric-output channels, which gives a sufficient stability condition for Zopf_m LDPC codes and is complemented by a matched necessary stability condition introduced herein. Applications to coded modulation and to codes with nonequiprobably distributed codewords are also discussed. For binary codes, two new lower bounds are provided for symmetric channels, including a two-dimensional iterative bound and a one-dimensional noniterative bound, the latter of which is the best known bound that is tight for binary-symmetric channels (BSCs), and is a strict improvement over the existing bound derived by the channel degradation argument. By adopting the reverse channel perspective, upper and lower bounds on the decodable Bhattacharyya noise parameter are derived for nonsymmetric channels, which coincides with the existing bound for symmetric channels     

A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding

Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rateP_bfor a constraint length 3 decoder has been plotted versus the channel transition probabilitypand shows close agreement with the improved bound on the bit error probability.     

数字通信中的卷积编码及Viterbi译码器设计

讨论了基于DSP技术的信道编、译码的问题。