4,114 research outputs found

    A new description of combined trellis coding with asymmetric modulation

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    The combination of rate k/(k+t) trellis codes with digital modulations described by an asymmetric 2 sup k+1-point signal constellation has been recently shown to yield performance improvement over the traditional symmetric constellation combined with the same trellis code. The approach taken is to specify an underlying trellis code and then map the output code symbols into the fixed signal constellation based on a rule called mapping by set partitioning. The latter process is tantamount to assigning signals from the constellation to the trellis code transitions so as to maximize the free Euclidean distance of the code. Recently, a new description of trellis codes has been given that combines the above two steps into one. The ideas introduced are further explored, placing particular emphasis on the optimization of the signal constellation asymmetry. It can be concluded that the trellis-coded amplitude modulation (AM) designs given are very close to being optimum

    Synchronization recovery and state model reduction for soft decoding of variable length codes

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    Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence. If the number of symbols and/or bits transmitted are known by the decoder, termination constraints can be incorporated in the decoding process. All the paths in the trellis which do not lead to a valid sequence length are suppressed. This paper presents an analytic method to assess the expected error resilience of a VLC when trellis decoding with a sequence length constraint is used. The approach is based on the computation, for a given code, of the amount of information brought by the constraint. It is then shown that this quantity as well as the probability that the VLC decoder does not re-synchronize in a strict sense, are not significantly altered by appropriate trellis states aggregation. This proves that the performance obtained by running a length-constrained Viterbi decoder on aggregated state models approaches the one obtained with the bit/symbol trellis, with a significantly reduced complexity. It is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size

    Discriminated Belief Propagation

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    Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a combination of constituent codes with low complexity trellis representations. Their decoding algorithm is an instance of (loopy) belief propagation and is based on an iterative transfer of constituent beliefs. The beliefs are thereby given by the symbol probabilities computed in the constituent trellises. Even though weak constituent codes are employed close to optimal performance is obtained, i.e., the encoder/decoder pair (almost) achieves the information theoretic capacity. However, (loopy) belief propagation only performs well for a rather specific set of codes, which limits its applicability. In this paper a generalisation of iterative decoding is presented. It is proposed to transfer more values than just the constituent beliefs. This is achieved by the transfer of beliefs obtained by independently investigating parts of the code space. This leads to the concept of discriminators, which are used to improve the decoder resolution within certain areas and defines discriminated symbol beliefs. It is shown that these beliefs approximate the overall symbol probabilities. This leads to an iteration rule that (below channel capacity) typically only admits the solution of the overall decoding problem. Via a Gauss approximation a low complexity version of this algorithm is derived. Moreover, the approach may then be applied to a wide range of channel maps without significant complexity increase

    Turbo codes for deep-space communications

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    Turbo codes were recently proposed by Berrou, Glavieux, and Thitimajshima, and it has been claimed these codes achieve near-Shannon-limit error correction performance with relatively simple component codes and large interleavers. A required E(b)/N(o) of 0.7 dB was reported for a bit error rate of 10(exp -5), using a rate 1/2 turbo code. However, some important details that are necessary to reproduce these results were omitted. This article confirms the accuracy of these claims, and presents a complete description of an encoder/decoder pair that could be suitable for deep-space applications, where lower rate codes can be used. We describe a new simple method for trellis termination, analyze the effect of interleaver choice on the weight distribution of the code, and introduce the use of unequal rate component codes, which yield better performance
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