| 1. |
- Agrell, Erik, 1965, et al.
(författare)
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On the symbol error probability of regular polytopes
- 2011
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 57:6, s. 3411-3415
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Tidskriftsartikel (refereegranskat)abstract
- An exact expression is derived for the symbol error probability when the vertices of the four-dimensional 24-cell are used for digital transmission in Gaussian noise. Corresponding expressions for other regular convex polytopes are summarized. Numerically stable versions of these error probabilities are also obtained. © 2011 IEEE.
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| 2. |
- Agrell, Erik, 1965, et al.
(författare)
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Optimal Alphabets and Binary Labelings for BICM at Low SNR
- 2011
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 57:10, s. 6650-6672
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Tidskriftsartikel (refereegranskat)abstract
- Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.
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| 3. |
- Agrell, Erik, 1965, et al.
(författare)
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Signal Shaping for BICM at Low SNR
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:4, s. 2396-2410
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Tidskriftsartikel (refereegranskat)abstract
- The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.
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| 4. |
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| 5. |
- Bocharova, Irina, et al.
(författare)
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A Closed Form Expression for the Exact Bit Error Probability for Viterbi Decoding of Convolutional Codes
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:7, s. 4635-4644
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Tidskriftsartikel (refereegranskat)abstract
- In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decoding of the rate R=1/2, memory m=1 (2-state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their formula was later extended to the rate R=1/2, memory m=2 (4-state) convolutional encoder with generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al. In this paper, a different approach to derive the exact bit error probability is described. A general recurrent matrix equation, connecting the average information weight at the current and previous states of a trellis section of the Viterbi decoder, is derived and solved. The general solution of this matrix equation yields a closed form expression for the exact bit error probability. As special cases, the expressions obtained by Best et al. for the 2-state encoder and by Lentmaier et al. for a 4-state encoder are obtained. The closed form expression derived in this paper is evaluated for various realizations of encoders, including rate R=1/2 and R=2/3 encoders, of as many as 16 states. Moreover, it is shown that it is straightforward to extend the approach to communication over the quantized additive white Gaussian noise channel.
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| 6. |
- Bocharova, Irina, et al.
(författare)
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Searching for voltage graph-based LDPC tailbiting codes with large girth
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 58:4, s. 2265-2279
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Tidskriftsartikel (refereegranskat)abstract
- The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact representations of bipartite graphs based on convolutional codes can be found. Bounds on the girth and the minimum distance of LDPC block codes constructed in such a way are discussed. Algorithms for searching iteratively for LDPC block codes with large girth and for determining their minimum distance are presented. Constructions based on all-one matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.
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| 7. |
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| 8. |
- Bordenave, Charles, et al.
(författare)
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Asymptotic Stability Region of Slotted Aloha
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 58:9, s. 5841-5855
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of users, each equipped with an infinite buffer. Packets arrive into user i's buffer according to some stationary ergodic Markovian process of intensity lambda(i). At the beginning of each slot, if user i has packets in its buffer, it attempts to transmit a packet with fixed probability p(i) over a shared resource/channel. The transmission is successful only when no other user attempts to use the channel. The stability of such systems has been open since their very first analysis in 1979 by Tsybakov and Mikhailov. In this paper, we propose an approximate stability condition that is provably exact when the number of users grows large. We provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users (even two or three).
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| 9. |
- Bouyukliev, I. G., et al.
(författare)
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Results on Binary Linear Codes With Minimum Distance 8 and 10
- 2011
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 57:9, s. 6089-6093
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Tidskriftsartikel (refereegranskat)abstract
- All linear binary codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33, 18, 8] and [33, 14, 10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.
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| 10. |
- Cho, Jeong-woo, 1978-, et al.
(författare)
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On the Asymptotic Validity of the Decoupling Assumption for Analyzing 802.11 MAC Protocol
- 2012
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Ingår i: IEEE Transactions on Information Theory. - : IEEE Press. - 0018-9448 .- 1557-9654. ; 58:11, s. 6879-6893
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Tidskriftsartikel (refereegranskat)abstract
- Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. This decoupling assumption results from mean field convergence and is generally true in transient regime in the asymptotic sense (when the number of wireless nodes tends to infinity), but, contrary to widespread belief, may not necessarily hold in stationary regime. The issue is often related with the existence and uniqueness of a solution to a fixed point equation; however, it was also recently shown that this condition is not sufficient; in contrast, a sufficient condition is a global stability property of the associated ordinary differential equation. In this paper, we give a simple condition that establishes the asymptotic validity of the decoupling assumption for the homogeneous case (all nodes have the same parameters). We also discuss the heterogeneous and the differentiated service cases and formulate a new ordinary differential equation. We show that the uniqueness of a solution to the associated fixed point equation is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid in the asymptotic sense in stationary regime.
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