Bootstrap sequential decoding at high spectral efficiencies

An erasure-free sequential decoding algorithm for trellis codes, called the buffer looking algorithm (BLA), is introduced. Several versions of the algorithm can be obtained by choosing certain parameters and selecting a resynchronization scheme. These can be categorized as block decoding or continuous decoding, depending on the resynchronization scheme. Block decoding is guaranteed to resynchronize at the beginning of each block, but suffers some rate loss when the block length is relatively short. The performance of a typical block decoding scheme is analyzed, and we show that significant coding gains over Viterbi decoding can be achieved with much less computational effort. A resynchronization scheme is proposed for continuous sequential decoding. It is shown by analysis and simulation that continuous sequential decoding using this scheme has a high probability of resynchronizing successfully. This new resynchronization scheme solves the rate loss problem resulting from block decoding. The channel cutoff rate, demodulator quantization, and the tail's influence on performance are also discussed. Although this paper considers only the decoding of trellis codes, the algorithm can also be applied to the decoding of convolutional codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Convolutional coding and Viterbi decoding, along with binary phase-shift keyed modulation, is presented as an efficient system for reliable communication on power limited satellite and space channels. Performance results, obtained theoretically and through computer simulation, are given for optimum short constraint length codes for a range of code constraint lengths and code rates. System efficiency is compared for hard receiver quantization and 4 and 8 level soft quantization. The effects on performance of varying of certain parameters relevant to decoder complexity and cost is examined. Quantitative performance degradation due to imperfect carrier phase coherence is evaluated and compared to that of an uncoded system. As an example of decoder performance versus complexity, a recently implemented 2-Mbit/s constraint length 7 Viterbi decoder is discussed. Finally a comparison is made between Viterbi and sequential decoding in terms of suitability to various system requirements.

Different attempts have been made to compare the performance of coded orthogonal frequency division multiplexing (COFDM) and a corresponding single carrier system employing a linear equalizer often by comparing the average bit error rates. The random coding technique is used to analyze the performance of these systems for signaling over piecewise constant channels. The probabilities that the cutoff rates are less than a desired rate are calculated and compared. It is shown that for low SNRs and low code rates, the cutoff rates of both systems are approximately the same. With an increasing SNR the cutoff rate for the linearly equalized system, however, converges faster to its maximum value than the cutoff rate for the COFDM system. Simulation results for the outage probability are presented for the two-ray Rayleigh fading channel with QPSK as the fundamental modulation technique. For code rates close to one or for uncoded transmission, the linearly equalized single carrier system substantially outperforms the COFDM system. For low to medium code rates COFDM and a linearly equalized single carrier system perform approximately identically.

Suboptimal decoding of convolutional codes, motivated by the need to deal with large constraint length codes, has in the past been achieved by stack algorithms or sequential decoding, which typically do not produce soft outputs, which may be desirable in some modern iterative decoding frame-works. Motivated by an approximate posterior equalizer, we present a suboptimal decoder which employs a similar decomposition for binary convolutional codes observed in additive white Gaussian noise. This results in mixed-field arithmetic (GF(2) and R). The GF(2) (convolutional code) arithmetic means that the central limit theorem does not apply. Instead, we invoke Gallager's lemma to compute the distribution of the interfering terms. Under various assumptions of independence (resulting in different complexities) the channel posterior probability can be approximated, resulting in a soft-output decoder. Initial results indicate effective performance when dependencies among rows are incorporated. The method may also extend to arbitrary binary linear codes.

Fast Maximum Likelihood Decodable Space-Time Block Codes (STBCs) have recently gained a lot of interest for use in wireless communication systems. Several strategies have been introduced in the literature to build such codes, among them we mention the conditional detection strategy, where the code matrix can be expressed as the sum of two Orthogonal STBCs by means of a unitary matrix. Thus, the decoder benefits from the orthogonality by estimating an orthogonal set of symbols assuming knowledge of the other set of symbols. Even if this strategy permits high rates, numerical optimization of the coding gain becomes unrealizable for high-order constellations. Another strategy has been proposed in the literature, the g-group decodable codes, where the minimization of the Maximum Likelihood (ML) metric can be made over several independent subsets of symbols. Moreover, the g-group decodability strategy enables us to optimize the coding gain for each subset of symbols separately which permits the optimization of the coding gain for high-order constellations. On the other hand, the rate of g-group decodable codes is limited. In this paper, we reformulate the problem of finding Unitary Weight (UW)-2-group decodable codes in a simpler way based on necessary and sufficient conditions. Then, a simple routine is used to search for the desired code. We determine the maximum achievable rate for a specified type of weight matrices.

The stop-and-wait ARQ protocol with convolutional code and sequential decoding is considered. The channel throughput and optimum time-out before retransmission are obtained and the effects of the link parameters discussed. The results are extended to a twohop radio link, where a repeater receives the source's data and forwards them on the same radio channel to the destination. The ARQ protocols for the source and the repeater are discussed and a method presented for choosing the optimum time-out intervals for both.

Recently, Arikan has proposed a new scheme to transfer the error correction part to external codes for encoding, namely polarization-adjusted convolutional (PAC) coding. However, all existing decoding methods of current research for PAC codes focused on the classic sequential decoding-Fano decoding. The stack decoding which is another well-known sequential decoding, has not been reported. In this paper, we try to do a thorough study of the stack decoding for PAC codes. First, we find that the traditional stack decoding (SD) is not very effective for the PAC codes, especially in terms of complexity. Therefore, we propose a soft output stack decoding (SOSD) for PAC codes, which can reduce the computation very much. In the SOSD algorithm, the discarded paths are recorded and used in the final decision of decoding codeword. The SOSD algorithm can reduce the stack size (amount of computation) very much with almost no decoding performance loss. By carefully choosing the stack size and soft output threshold, in the case of a PAC code with code length 128 and rate 1/2, the SOSD algorithm can reduce 82% of the computation by comparing the conventional SD algorithm.

Sequential decoding of the channel code in a trellis-coded modulation system with trellis shaping can be used to reduce the system complexity and to achieve high coding gain with large constraint-length codes. It is shown that almost all the shaping gain that can be achieved when Viterbi decoding is used for the channel code can also be achieved when sequential decoding is used for the channel code. It is also shown that the real shaping gain is a function of both the SNR and the spectral efficiency.

The principle of coding in the signal space follows directly from Shannon’s analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signal-space coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imai’s and Ungerböck’s pioneering works on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re-)discovered. Bit-Interleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signal-space coding perspective, whilst allowing for the use of powerful families of binary codes with virtually any modulation format. BICM avoids the need for the complicated and somewhat less flexible design typical of coded modulation. As a matter of fact, most of today’s systems that achieve high spectral efficiency such as DSL, Wireless LANs, WiMax and evolutions thereof, as well as systems based on low spectral efficiency orthogonal modulation, feature BICM, making BICM the de-facto general coding technique for waveform channels. The theoretical characterization of BICM is at the basis of efficient coding design techniques and also of improved BICM decoders, e.g., those based on the belief propagation iterative algorithm and approximations thereof. In this text, we review the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. This framework allows an accurate analysis without any particular assumptions on the length of the interleaver or independence between the multiple bits in a symbol. We further consider the sensitivity of the BICM capacity with respect to the signal-to-noise ratio (SNR), and obtain a wideband regime (or low-SNR regime) characterization. We review efficient tools for the error probability analysis of BICM that go beyond the standard approach of considering infinite interleaving and take into consideration the dependency of the coded bit observations introduced by the modulation. We also present bounds that improve upon the union bound in the region beyond the cutoff rate, and are essential to characterize the performance of modern randomlike codes used in concatenation with BICM. Finally, we turn our attention to BICM with iterative decoding, we review extrinsic information transfer charts, the area theorem and code design via curve fitting. We conclude with an overview of some applications of BICM beyond the classical coherent Gaussian channel.

Maximum likelihood decoding of convolutional codes by Viterbi decoding method is an effective error correcting technique. However, little study on Viterbi decoding of high rate codes has been done since the number of paths entering each trellis state increases as the code rate increases. This paper presents a new maximum likelihood decoding of convolutional codes of rate (n ‐ 1)/n using a trellis. the trellis is drawn according to the state transitions of the syndrome former of the code, and has only one or two paths entering each state rather than 2n‐1 paths as in the case of conventional trellises. Thus, we can replace the 2n‐1‐ary comparisons at each state needed in the conventional Viterbi decoding for the code of rate (n ‐ 1)/n by binary comparisons. the implementation of maximum likelihood decoders for high rate convolutional codes is simplified greatly by this approach. Moreover, this decoding method shows the same performance as that of conventional Viterbi decoding method from the viewpoint of selecting the maximum likelihood code sequence.

Two importance sampling techniques are presented for estimating the distribution of computation of sequential decoding for specific convolutional codes (not ensemble averages). Only stack algorithm decoders are considered. Numerical examples are presented for both the BSC and the AWGN channel. >

Error control (detection and correction) of data plays a pivotal role in networking to facilitate the reliable transmission of messages from source to destination. Convolution code is one of the popularly known error control mechanism which is considered superior to several legacy error control algorithms like the Hamming code. The Fano algorithm is a sequential decoding algorithm used to decode long constraint length convolution codes. However, this algorithm has failed to offer 100% error detection and correction capabilities. These lead to the inferior performance of this algorithm to correct errors at the destination. This paper proposes an enhanced Fano (e-Fano) algorithm that offers 100% error detection and correction up to finite bits of error. Through the MATLAB simulations, e-Fano and the conventional Fano algorithm are compared for the % of error detection and correction in the received data.

Majority-logic decoding of convolutional codes, proposed by Massey [308], is a sub-optimum but simple decoding scheme that allows a high-speed implementation. Its performance is sub-optimum since each of its decoding decision is based only on one output constraint length of received bits. This “limited vision” is not there in Viterbi or sequential decoding which, in principle, consider the entire received sequence before making decoding decisions.

The following paper adapts the classical Zigangirov-Jelinek algorithm to the decoding of nonbinary block codes under severe mixed jamming. To ensure reliable communications in this scenario we combine reception techniques based on distribution free statistical tests with sequential decoding on syndrome trellises. It will be shown that the proposed approach can ensure relatively high transmission rate with reasonable complexity.

In this paper, we analyze the sequential message- passing decoding algorithm of low-density parity-check (LDPC) codes by partitioning check nodes. This decoding algorithm shows better bit error rate (BER) performance than the conventional message-passing decoding algorithm, especially for the small number of iterations. Analytical results indicate that as the number of partitioned subsets of check nodes increases, the BER performance is improved. We also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a Gaussian approximation. From these equations, the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding BER values are calculated. They show that the sequential decoding algorithm converges faster than the conventional one. Finally, the analytical results are confirmed by the simulation results.