894 research outputs found
On Low Complexity Maximum Likelihood Decoding of Convolutional Codes
This paper considers the average complexity of maximum likelihood (ML)
decoding of convolutional codes. ML decoding can be modeled as finding the most
probable path taken through a Markov graph. Integrated with the Viterbi
algorithm (VA), complexity reduction methods such as the sphere decoder often
use the sum log likelihood (SLL) of a Markov path as a bound to disprove the
optimality of other Markov path sets and to consequently avoid exhaustive path
search. In this paper, it is shown that SLL-based optimality tests are
inefficient if one fixes the coding memory and takes the codeword length to
infinity. Alternatively, optimality of a source symbol at a given time index
can be testified using bounds derived from log likelihoods of the neighboring
symbols. It is demonstrated that such neighboring log likelihood (NLL)-based
optimality tests, whose efficiency does not depend on the codeword length, can
bring significant complexity reduction to ML decoding of convolutional codes.
The results are generalized to ML sequence detection in a class of
discrete-time hidden Markov systems.Comment: Submitted to IEEE Transactions on Information Theor
Coordinated design of coding and modulation systems
The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems
Constructions of Generalized Concatenated Codes and Their Trellis-Based Decoding Complexity
In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis omplexity than Euclidean geometry (EG), Reed–Muller (RM), or Bose–Chaudhuri–Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes
Tail-biting convolutional codes extend the classical zero-termination
convolutional codes: Both encoding schemes force the equality of start and end
states, but under the tail-biting each state is a valid termination. This paper
proposes a machine-learning approach to improve the state-of-the-art decoding
of tail-biting codes, focusing on the widely employed short length regime as in
the LTE standard. This standard also includes a CRC code.
First, we parameterize the circular Viterbi algorithm, a baseline decoder
that exploits the circular nature of the underlying trellis. An ensemble
combines multiple such weighted decoders, each decoder specializes in decoding
words from a specific region of the channel words' distribution. A region
corresponds to a subset of termination states; the ensemble covers the entire
states space. A non-learnable gating satisfies two goals: it filters easily
decoded words and mitigates the overhead of executing multiple weighted
decoders. The CRC criterion is employed to choose only a subset of experts for
decoding purpose. Our method achieves FER improvement of up to 0.75dB over the
CVA in the waterfall region for multiple code lengths, adding negligible
computational complexity compared to the circular Viterbi algorithm in high
SNRs
Efficient Transmission Techniques in Cooperative Networks: Forwarding Strategies and Distributed Coding Schemes
This dissertation focuses on transmission and estimation schemes in wireless relay network, which involves a set of source nodes, a set of destination nodes, and a set of nodes helps communication between source nodes and destination nodes, called relay nodes. It is noted that the overall performance of the wireless relay systems would be impacted by the relay methods adopted by relay nodes. In this dissertation, efficient forwarding strategies and channel coding involved relaying schemes in various relay network topology are studied.First we study a simple structure of relay systems, with one source, one destination and one relay node. By exploiting “analog codes” -- a special class of error correction codes that can directly encode and protect real-valued data, a soft forwarding strategy –“analog-encode-forward (AEF)”scheme is proposed. The relay node first soft-decodes the packet from the source, then re-encodes this soft decoder output (Log Likelihood Ratio) using an appropriate analog code, and forwards it to the destination. At the receiver, both a maximum-likelihood (ML) decoder and a maximum a posterior (MAP) decoder are specially designed for the AEF scheme.The work is then extended to parallel relay networks, which is consisted of one source, one destination and multiple relay nodes. The first question confronted with us is which kind of soft information to be relayed at the relay nodes. We analyze a set of prevailing soft information for relaying considered by researchers in this field. A truncated LLR is proved to be the best choice, we thus derive another soft forwarding strategy – “Z” forwarding strategy. The main parameter effecting the overall performance in this scheme is the threshold selected to cut the LLR information. We analyze the threshold selection at the relay nodes, and derive the exact ML estimation at the destination node. To circumvent the catastrophic error propagation in digital distributed coding scheme, a distributed soft coding scheme is proposed for the parallel relay networks. The key idea is the exploitation of a rate-1 soft convolutional encoder at each of the parallel relays, to collaboratively form a simple but powerful distributed analog coding scheme. Because of the linearity of the truncated LLR information, a nearly optimal ML decoder is derived for the distributed coding scheme. In the last part, a cooperative transmission scheme for a multi-source single-destination system through superposition modulation is investigated. The source nodes take turns to transmit, and each time, a source “overlays” its new data together with (some or all of) what it overhears from its partner(s), in a way similar to French-braiding the hair. We introduce two subclasses of braid coding, the nonregenerative and the regenerative cases, and, using the pairwise error probability (PEP) as a figure of merit, derive the optimal weight parameters for each one. By exploiting the structure relevance of braid codes with trellis codes, we propose a Viterbi maximum-likelihood (ML) decoding method of linear-complexity for the regenerative case. We also present a soft-iterative joint channel-network decoding. The overall decoding process is divided into the forward message passing and the backward message passing, which makes effective use of the available reliability information from all the received signals. We show that the proposed “braid coding” cooperative scheme benefits not only from the cooperative diversity but also from the bit error rate (BER) performance gain
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