Reliability-based incremental redundancy with convolutional codes

Incremental redundancy, or Hybrid type-II ARQ (HARQ), algorithms use a combination of forward error correction and retransmissions to guarantee reliable packet data communications. In this work, we propose a HARQ algorithm that exploits received packet reliability to improve system performance. Specifically, the receiver uses the average magnitude of the log-likelihood ratios of the information bits as the packet reliability metric, which is then used to determine the sizes of subsequent retransmissions. The proposed retransmission strategy attempts to maximize user throughput while satisfying a maximum packet delay constraint. The performance of our reliability-based HARQ algorithm is evaluated in static and time-varying channels through simulations. Furthermore, analytical results on the relationship between the reliability metric, the code rate and the block error rate are presented.     

Analysis of memory and incremental redundancy ARQ schemes over anonstationary channel

A generalized type II automatic-repeat-request (ARQ) scheme using punctured convolutional coding on a two-state Markov model of a nonstationary channel is analyzed. A simple ARQ scheme with memory is also analyzed. It is shown that the simple memory ARQ scheme offers a substantial throughput improvement over a conventional ARQ scheme at severe channel conditions. Furthermore, the generalized type II ARQ scheme yields a better performance than the conventional type II ARQ scheme under all channel conditions, thus making it attractive for use over time-varying channels     

Incremental redundancy hybrid ARQ schemes based on low-density parity-check codes

We study the throughput of hybrid automatic retransmission request (H-ARQ) schemes based on incremental redundancy (IR) over a block-fading channel. We provide an information-theoretic analysis assuming binary random coding and typical-set decoding. Then, we study the performance of low-density parity-check (LDPC) code ensembles with iterative belief-propagation decoding, and show that, under the hypothesis of infinite-length codes, LDPCs yield almost optimal performance. Unfortunately, standard finite-length LDPC ensembles incur a considerable performance loss with respect to their infinite-length counterpart, because of their poor frame-error rate (FER) performance. In order to recover part of this loss, we propose two simple yet effective methods: using a modified LDPC ensemble designed to improve the FER; and using an outer selective-repeat protocol acting on smaller packets of information bits. Surprisingly, these apparently very different methods yield almost the same performance gain and recover a considerable fraction of the optimal throughput, thus making practical finite-length LDPC codes very attractive for data wireless communications based on IR H-ARQ schemes.     

基于并行级联LDPC码的递增冗余HARQ方案及性能分析

并行级联LDPC码是由多个码率不同的子码,经并行级联后得到的码率可变的LDPC码.本文提出了基于并行级联:LDPC码的递增冗余HARQ方案,给出了这种方案的吞吐量性能封闭解.在AWGN信道和Rayleigh衰落信道下,通过仿真将新方案的性能和随机LDPC码的性能进行了比较.结果显示,并行级联LDPC码的递增冗余HARQ方案性能接近随机LDPC码,但编、译码更简单,参数选择范围更广.     

Superimposed codes based on punctured convolutional codes

Punctured convolutional codes of rates k₁/n and k₂ /n are applied to |u|u+v construction, and then a superimposed code of rate (k₁+k₂)/(2n) is constructed. A suboptimal decoding procedure is presented for the superimposed codes, and it reduces the decoding complexity as compared with maximum likelihood decoding for the known convolutional codes     

DC-free error-correcting codes based on convolutional codes

A new construction of direct current (DC)-free error-correcting codes based on convolutional codes is proposed. The new code is constructed by selecting a proper subcode from a convolutional code composed of two different component codes. The encoder employs a Viterbi algorithm as the codeword selector so that the selected code sequences satisfy the DC constraint. A lower bound on the free distance of such codes is proposed, and a procedure for obtaining this bound is presented. A sufficient condition for these codes to have a bounded running digital sum (RDS) is proposed. Under the assumption of a simplified codeword selection algorithm, we present an upper bound on the maximum absolute value of the RDS and derive the sum variance for a given code. A new construction of standard DC-free codes, i.e., DC-free codes without error-correcting capability, is also proposed. These codes have the property that the decoder can be implemented by simple symbol-by-symbol hard decisions. Finally, under the new construction, we propose several codes that are suitable for the systems that require small sum variance and good error-correction capability     

Permutation codes for the Gaussian channel

The initial vector problem is considered for group codes for the Gaussian channel and, in particular, for codes generated by permutation groups. Variant I and variant II permutation codes are defined, and optimal initial vectors for these codes are constructed. A numerical algorithm for constructing optimal group codes is presented together with examples of this algorithm applied to several permutation groups     

On the decoding of convolutional codes on an unknown channel

An algorithm is proposed for universal decoding of convolutional/trellis codes employed over unknown channels. On discrete memoryless channels and at rates below the channel's computational cutoff rate (for a uniform input distribution), the algorithm achieves an asymptotic complexity-performance tradeoff similar to the tradeoff achieved by the Viterbi (1979) algorithm, but with the benefit that the algorithm's implementation does not require knowledge of the channel law. The algorithm is also applicable to channels with memory, and in particular to intersymbol interference (ISI) channels, to channels with nonlinear ISI, and even to general finite-state channels     

Commutative group codes for the Gaussian channel

A class of codes for the Gaussian channel is analyzed. The code class is a subclass of the group codes for the Gaussian channel described by Slepian. Using the vector model for the Gaussian channel, the code vectors are obtained by transformations of an initial vector. The class of codes in which the transformations form a commutative group is called the class of commutative group codes. The performance of the codes is evaluated using the union bound on the error probability as a performance measure. The union bound is shown to be closely related to the moments of the scalar product between the code vectors. Commutative group codes are described. It is shown that linear algebraic codes may be represented as commutative group codes. The code class is also shown to include simplex and biorthogonal codes in all dimensions.     

Decoding spherical codes for the Gaussian channel

A decoding algorithm for permutation codes that is equivalent to maximum-likelihood decoding, but less complex than the correlation decoder, is presented. A general construction for iteratively maximum-likelihood decodable (IMLD) codes is proved and used to construct IMLD codes for every dimension n. D. Slepian (1965) defined permutation modulation codes and presented an efficient algorithm for their decoding. Slepian's decoding scheme is one of the principal components of the permutation code decoding algorithm presented     

Modulation and coding for the Gaussian collision channel

We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed. More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. The outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided     

Symbol-by-symbol reception of signals corresponding to high-rate convolutional codes and turbo codes based on these convolutional codes

Computational procedures for symbol-by-symbol reception of signal ensembles corresponding to binary high-rate convolutional codes and to turbo codes formed by these convolutional codes are described. It is shown that the developed procedures are based on an optimum symbol-by-symbol reception algorithm that uses the fast Walsh-Hadamard transform algorithm.     

Performance of convolutional codes in a direct-detection opticalPPM channel

Several strategies for combining convolutional codes (CCs) and pulse position modulation (PPM) in a direct-detection optical channel are considered, including binary and 2ⁿ-ary PPM with rate-1/ n CCs, 2^m-ary PPM with a dual-m CC, and interleaved 2^L-ary PPM with a rate-1/n CC. In the latter case, J.L. Massey's (1981) concept of coding of L separate component channels constituting a 2^L-ary PPM erasure channel is carried out for both the ideal photon counting and the avalanche photodetection (APD) cases, providing a comparative evaluation of the various strategies in terms of bit error probability and achievable coding gain for different code structures and decoding schemes     

Performance of lattice codes over the Gaussian channel

We derive an upper bound on the error probability of lattice codes combined with Quadrature Amplitude Modulation (qam) over the additive white Gaussian noise channel. This bound depends on a lattice figure of merit and is readily put in exponential form by using Chernoff bound. An interesting lower bound is derived by a similar reasoning. We also examine the estimation of the average information rate based upon the continuous approximation of the average power normalized to two dimensions, and suggest to improve it by using the sphere packing idea. Examples of performance evaluation are given for a few lattices. Finally, we present upper and lower bounds on the best fundamental coding gains per dimension (due to both density and thickness) for an arbitrarily large number of dimensions. It is shown in the Appendix that, as the Ungerboeck codes, the lattice codes do not shape the signal power spectrum.     

Class of block codes for the Gaussian channel

A method is developed for computing elements of a new class of quantised equal-energy block codes {(N, M, L)} for any number of code words M with arbitrary length N. These codes are asymptotically optimal for the Gaussian channel whenever the total number of possible amplitude levels L tends to infinity.     

Accumulate codes based on 1+D convolutional outer codes

A new construction of good, easily encodable, and soft-decodable codes is proposed in this paper. The construction is based on serially concatenating several simple 1+D convolutional codes as the outer code, and a rate-1 1/(1+D) accumulate code as the inner code. These codes have very low encoding complexity and require only one shift-forward register for each encoding branch. The input-output weight enumerators of these codes are also derived. Divsalar?s simple bound technique is applied to analyze the bit error rate performance, and to assess the minimal required signal-to-noise ratio (SNR) for these codes to achieve reliable communication under AWGN channel. Simulation results show that the proposed codes can provide good performance under iterative decoding.     

Evaluating the performance of convolutional codes over block fadingchannels

This correspondence considers union upper bound techniques for error control codes with limited interleaving over block fading Rician channels. A modified bounding technique is presented that relies on limiting the conditional union bound before averaging over the fading process. This technique, although analytically not very attractive, provides tight and hence useful numerical results     

Serially concatenated space-time codes with iterative decoding and performance limits of block-fading channels

This work considers space-time channel coding for systems with multiple-transmit and a single-receive antenna, over space uncorrelated block-fading (quasi-static) channels. Analysis of the outage probability over such channels reveals the existence of a threshold phenomenon. The outage probability can be made arbitrary small by increasing the number of transmit antennas, only if the E/sub b//N/sub 0/ is above a threshold which depends on the coding rate. Furthermore, it is shown that when the number of transmit antennas is increased, the /spl epsi/-capacity of a block-fading Rayleigh channel tends to the Shannon capacity of an additive white Gaussian noise channel. This paper also presents space-time codes constructed as a serial concatenation of component convolutional codes separated by an interleaver. These schemes provide full transmit diversity and are suitable for iterative decoding. The rate of these schemes is less than 1 bit/s/Hz, but can be made arbitrary close to 1 bit/s/Hz by the use of Wyner-Ash codes as outer components. Comparison of these schemes with structures from literature shows that performance gains can be obtained at the expense of a small decrease in rate. Computer simulation results over block-fading Rayleigh channels show that the frame-error rate of several of these schemes is within 2-3 dB from the theoretical outage probability.     

The performance of convolutional codes on the block erasure channelusing various finite interleaving techniques

Consider the transmission of a finitely interleaved rate 1/n convolutionally encoded message over a channel with memory having two internal states Ξ₀ and Ξ₁ where when in state Ξ₀, the channel resembles a noiseless binary symmetric channel (BSC), whereas when in state Ξ₁, the channel is totally blocked and is well approximated by a binary-input single-output channel. Assume that the channel's internal state is drawn at random once every h channel uses, and then remains constant for the following h channel uses. Further assume that the message is short in comparison to h, and that due to delay constraints, the message must be decoded within Nh channel uses, where N need not be large in comparison to the code's constraint length. Such a model is appropriate for describing a convolutionally coded slow frequency hopping system with non-ideal interleaving, in which every frequency is either totally erased or else noiseless. The probability of a message error, the normalized expected number of bits in error, and the bit error rate (BER) are analytically computed for the periodic N×h bit and word interleavers, where a bit refers to a binary code symbol, and a word refers to a n-tuple of consecutive bits. An analytic expression for the BER is also given for pseudo-random word and bit interleavers and for the corresponding limiting cases of infinite interleaving, i.e., N→∞. As an example for the use of our methods, we analyze the performance of the GSM system with various interleaving depths and methods. We introduce the notion of “matched” code and interleaver pairs, and argue that this is a desirable property. Several exhaustive searches are carried out for matched codes and interleavers     

Adaptive interleaver based on rate-compatible punctured convolutional codes

This letter focuses on the design of an adaptive Bit- Interleaved Coded Modulation (BICM) scheme for frequency selective slow fading channels where the transmitter has certain knowledge of the channel response. In particular, we consider the design of the interleaver stage for a specific convolutional code operating with OFDM modulation. The adaptive interleaver uses the puncturing tables of the Rate-Compatible Punctured Convolutional Codes (RCPC codes) to rearrange the bits as a function of the fading values and the specific constellation. The performance of different interleavers are compared, revealing that the adaptive RCPC-based interleaver produces larger Euclidean distances between the received codewords and reduces the packet error rate (PER), specially when the number of deep-faded subcarriers increases. Numerical results also evidence the importance of the interleaver choice when comparing the performance of different power allocation strategies.