Symmetric Capacity Research Articles

Polar Codes for $q$-Ary Channels, $q=2^{r}$

We study polarization for nonbinary channels with input alphabet of size <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> =2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> =2,3,.... Using Arıkan's polarizing kernel <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , we prove that the virtual channels that arise in the process of channel evolution converge to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -ary channels with capacity 0,1,2,..., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> bits. As a result of this analysis, we show that polar codes support reliable transmission over discrete memoryless channels with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -ary input for all rates below the symmetric capacity of the channel. This leads to an explicit transmission scheme for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -ary channels. The block error probability of decoding using successive cancellation behaves as exp(- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the code length and α is any constant less than 0.5.

New encoding scheme of polar codes

The ‘polar coding’ proposed by Dr. Arıkan can achieve the symmetric capacity of binary-input discrete memoryless channels (B-DMC). The generator matrix of polar codes is GN = BNF⊗n for N=2n, BN was a permutation matrix. In the article it was realized with an interleaver, so the matrix production of GN was avoided; then the generator matrix was just determined by the matrix F⊗n which was constructed with three sub-matrixes of F⊗n−1 and one 2N−1 order zero matrix, it was deal with fast Hadamard transform (FHT) algorithm. The complexity of the new scheme was reduced sharply, and an iterative algorithm also can be used. The example showed that when N=8, complexity of the encoding scheme was just 16 which is obviously less than that of original encoding scheme 36.

Single fiber colorless symmetric WDM-PON architecture using time interleaved remodulation technique for mitigating Rayleigh backscattering resilience

A time interleaved differential phase shift keying (DPSK) remodulation technique is proposed to mitigate the effect of Rayleigh backscattering (RBS)-induced noise in a single fiber colorless wavelength-division-multiplexing passive optical network (WDM-PON). In order to achieve a cost effective optical network unit (ONU) solution without dedicated laser sources for upstream signals to provide optimum symmetric capacity in a colorless WDM-PON, remodulation becomes the core attraction. Also as the performance of colorless WDM-PON systems suffers from the transmission impairments due to RBS, it is mitigated by using this remodulation scheme. Simulation results show that downstream and upstream signals achieve the error-free performance at 10 Gbit/s with negligible penalty, and enhance the tolerance to RBS-induced noise over a 25 km single-mode fiber.

On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

This paper studies the capacity region of a K-user cyclic Gaussian interference channel, where the kth user interferes with only the (k-1)th user (mod K ) in the network. Inspired by the work of Etkin, Tse, and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han-Kobayashi power-splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region of the K-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the K-user cyclic Gaussian interference channel, a compact representation of the Han-Kobayashi achievable rate region using Fourier-Motzkin elimination is first derived; a capacity region outer bound is then established. It is shown that the Etkin-Tse-Wang power-splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special three-user case, this gap can be sharpened to 1 ½ bits by time-sharing of several different strategies. The capacity result of the K-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference channel. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.

Joint signal‐labeling optimization under peak power constraint

SUMMARYIn this paper, we introduce a variation of simulated annealing algorithm for optimizing two‐dimensional constellations with finite number of signals by maximizing the symmetric and pragmatic capacity. Our method also allows the joint optimization of constellation and binary labeling when the objective function is the pragmatic capacity. The algorithm can be applied with constraints on both the peak power and the average and peak power of the constellation. The proposed algorithm does not impose any a priori geometrical structure on the constellation and labeling. Here, we provide results only for the peak power constraints and constellations with up to 32 signals. For the symmetric capacity, optimal constellations depend on the signal to noise ratio and match in several cases the amplitude phase shift keying (APSK). On the other hand, for the pragmatic capacity several novel labeling constellation schemes are introduced, showing interesting differences between the two approaches. For modulation schemes with 32 signals, our optimized constellations perform up to 0.6 dB better than the optimized 4+12+16‐APSK used as the digital video broadcasting (DVB‐S2) standard. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Polar quantum channel coding with optical multi-qubit entangling gates for capacity-achieving channels

We demonstrate a fashion of quantum channel combining and splitting, called polar quantum channel coding, to generate a quantum bit (qubit) sequence that achieves the symmetric capacity for any given binary input discrete quantum channels. The present capacity is achievable subject to input of arbitrary qubits with equal probability. The polarizing quantum channels can be well-conditioned for quantum error-correction coding, which transmits partially quantum data through some channels at rate one with the symmetric capacity near one but at rate zero through others.

Symmetric Capacity of the Gaussian Interference Channel With an Out-of-Band Relay to Within 1.15 Bits

This paper studies the Gaussian interference channel (IC) with a relay, which transmits and receives in a band that is orthogonal to the IC. The channel associated with the relay is thus an out-of-band relay channel (OBRC). The focus is on a symmetric channel model, in order to assess the fundamental impact of the OBRC on the signal interaction of the IC, in the simplest possible setting. First, the linear deterministic model is investigated and the sum capacity of this channel is established for all possible channel parameters. In particular, it is observed that the impact of OBRC, as its links get stronger, is similar to that of output feedback for the IC. The insights obtained from the deterministic model are then used to design achievable schemes for the Gaussian model. The interference links are classified as extremely strong, very strong, strong, moderate, weak, and very weak. For strong and moderate interference, separate encoding is near optimal. For very strong and extremely strong interference, the interference links provide side information to the destinations, which can help the transmission through the OBRC. For weak or very weak interference, an extension of the Han-Kobayashi scheme for the IC is utilized, where the messages are split into common and private. To achieve higher rates, it is beneficial to further split the common message into two parts, and the OBRC plays an important role in decoding the common message. It is shown that our strategy achieves the symmetric capacity to within 1.14625 bits per channel use with duplexing factor 0.5, and 1.27125 bits per channel use for arbitrary duplexing factors, for all channel parameters. An important observation from the constant gap result is that strong interference can be beneficial with the presence of an OBR.

Coding for High-Density Recording on a 1-D Granular Magnetic Medium

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple one-dimensional combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.

Feedback Capacity of the Gaussian Interference Channel to Within 2 Bits

We characterize the capacity region to within 2 bits/s/Hz and the symmetric capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel (IC) with feedback. We develop achievable schemes and derive a new outer bound to arrive at this conclusion. One consequence of the result is that feedback provides multiplicative gain at high signal-to-noise ratio: the gain becomes arbitrarily large for certain channel parameters. This finding is in contrast to point-to-point and multiple-access channels where feedback provides no gain and only bounded additive gain respectively. The result makes use of a linear deterministic model to provide insights into the Gaussian channel. This deterministic model is a special case of the El Gamal-Costa deterministic model and as a side-generalization, we establish the exact feedback capacity region of this general class of deterministic ICs.

The Ordered Modular Averages

Ordered modular averages (OMAs) generalize ordered weighted averages operators, with the replacement of the additivity property by the modularity. OMAs can be seen as a symmetrized idempotent modular aggregation functions, characterized by comonotone modularity. Each OMA can be seen also as a copula-based integral with respect to a symmetric capacity. Special OMAs are characterized, such as associative operators, operators with neutral element, or operators with an annihilator. Some construction methods for OMAs are also discussed.

New Approach to Reliable Multipath Provisioning

We study the problem of reliably provisioning traffic in high-capacity backbone mesh networks supporting virtual concatenation (VCAT). Traditional approaches handled reliability requirements using full protection, which offers high assurance but can be costly. We take a less expensive approach by offering an expected bandwidth, rather than an absolute amount, but at lower costs than full-protection approaches. We propose a new routing algorithm that uses minimum-cost flow to find efficient collections of paths that satisfy traffic requests for expected bandwidth. We find that in most realistic network settings, paths are reliable enough so that only few additional network resources are required to compensate for the bandwidth loss incurred from possible network failures. We compared our approach to a previous algorithm under both a uniform setting, with symmetric traffic distribution and equal edge capacities, and in a more realistic setting with asymmetric traffic and differing edge capacities. Results show that our algorithm is an attractive approach in both settings, and much more effective than the previous scheme. We also compare our approach to a full-protection approach. Results show that by using fewer network resources, our algorithm is able to satisfy significantly more traffic requests than full protection. Thus, when full protection is not crucial, using our routing approach should be beneficial.

Quantum Polarization Codes for Capacity-Achieving in Discrete Memoryless Quantum Channel

Quantum channel combining and splitting, called quantum channel polarization, is suggested to design qubit sequences that achieve the symmetric capacity for any given discrete memoryless quantum channels. The polarized quantum channels can be well-conditioned for quantum channel codes, through which one need to send data at rate 1 by employing quantum channels with capacity near 1 and at rate 0 by employing the remaining quantum channels.

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Polar codes were recently introduced by Arikan. They achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancellation decoding scheme. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the 2 × 2 matrix [1 0 : 1 1]. It was shown by Arikan Telatar that this construction achieves an error exponent of 1/2, i.e., that for sufficiently large blocklengths the error probability decays exponentially in the square root of the blocklength. It was already mentioned by Arikan that in principle larger matrices can be used to construct polar codes. In this paper, it is first shown that any ℓ × ℓ matrix none of whose column permutations is upper triangular polarizes binary-input memoryless channels. The exponent of a given square matrix is characterized, upper and lower bounds on achievable exponents are given. Using these bounds it is shown that there are no matrices of size smaller than 15×15 with exponents exceeding 1/2. Further, a general construction based on BCH codes which for large I achieves exponents arbitrarily close to 1 is given. At size 16 × 16, this construction yields an exponent greater than 1/2.

Special fuzzy measures on infinite countable sets and related aggregation functions

While both additive and symmetric fuzzy measures on a finite universe are completely described by a probability distribution vector, this is no more the case of a countably infinite universe. After a brief discussion of additive fuzzy measures on positive integers, we characterize all symmetric fuzzy measures on integers by means of three constants and of two probability distribution vectors. OWA operators for n arguments were introduced by Yager in 1988. Grabisch in 1995 has shown representation of OWA operators by means of Choquet integral with respect to symmetric normed capacities. Based on symmetric capacities on positive integers, we extend the concept of OWA operators to infinitary sequences and thus we develop the concept of infinitary OWA operators.

A Wavelength-Division-Multiplexed Passive Optical Network With Simultaneous Centralized Light Source and Broadcast Capability

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We propose and experimentally demonstrate a wavelength-division-multiplexed (WDM) passive optical network (PON) architecture with simultaneous centralized light source and broadcast capability. The proposed WDM-PON supports simultaneous delivery of 10-Gb/s broadcast on–off-keying (OOK) signals and 10-Gb/s point-to-point (P2P) differential-phase-shift-keying (DPSK) signals. The broadcast OOK signals are obtained by modulating a part of the P2P DPSK signals to enhance the wavelength utilization efficiency. Then, the two kinds of signals are transmitted to the optical network unit (ONU) through different fiber links, and this configuration guarantees the good transmission performance. At each ONU, a portion of the P2P DPSK signal provides the seeding source for remodulating the upstream 10-Gb/s OOK signal, which avoids the cost of a wavelength-specific laser at each ONU. The performance of the proposed WDM-PON with a symmetrical capacity is comprehensively investigated through both simulation and experiment. The results verify that the proposed WDM-PON scheme is a good candidate to provide broadcast service through the WDM-PON infrastructure. </para>

Martingale Property and Capacity under G-Framework

The main purpose of this article is to study the symmetric martingale property and capacity defined by G-expectation introduced by Peng (cf. http://arxiv.org/PS_cache/math/pdf/0601/0601035v2.pdf ) in 2006. We show that the G-capacity can not be dynamic, and also demonstrate the relationship between symmetric G-martingale and the martingale under linear expectation. Based on these results and path-wise analysis, we obtain the martingale characterization theorem for G Brownian motion without Markovian assumption. This theorem covers the Levy's martingale characterization theorem for Brownian motion, and it also gives a different method to prove Levy's theorem.

Sourcing for Supplier Effort and Competition: Design of the Supply Base and Pricing Mechanism

We study a buyer's sourcing strategy along two dimensions: the supply base design and the pricing mechanism, considering supplier competition and cost-reduction e ffort. The supply base design concerns the number of suppliers (one or two) included in the supply base, and the capacity to be invested in each supplier. The pricing mechanism determines the timing of the price decisions, with the buyer making price commitments before suppliers exert cost-reduction eff orts that may be renegotiated afterwards. We fi nd that symmetric capacity investment in suppliers and low price commitments (more likely to be renegotiated) are eff ective at fostering supplier competition, while asymmetric investment and high price commitments (less likely to be renegotiated) are better at motivating supplier e ffort. A complementary relationship exists between the supply base design and pricing mechanism: A more symmetric supply base should be combined with lower price commitments leading to more renegotiation opportunities. This results in three possible sourcing structures: sole sourcing (investing capacity in a single supplier and forming price with ex ante commitments), symmetric dual sourcing (investing equal capacity in both suppliers and forming price with ex post negotiations), and asymmetric dual sourcing (investing positive but unequal capacities in two (ex ante identical) suppliers and forming price using both ex ante commitments and ex post (re)negotiations). We characterize the conditions for each structure, and identify a strategic role of capacity investment.

Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$I(W)$</tex></formula></emphasis> of any given binary-input discrete memoryless channel (B-DMC) <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$W$</tex></formula></emphasis>. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$N$</tex></formula></emphasis> independent copies of a given B-DMC <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$W$</tex></formula></emphasis>, a second set of <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$N$</tex> </formula></emphasis> binary-input channels <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\{W_N^{(i)}:1\le i\le N\}$</tex> </formula></emphasis> such that, as <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$N$</tex></formula></emphasis> becomes large, the fraction of indices <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$i$</tex></formula></emphasis> for which <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$I(W_N^{(i)})$</tex></formula></emphasis> is near <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$1$</tex> </formula></emphasis> approaches <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$I(W)$</tex></formula></emphasis> and the fraction for which <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$I(W_N^{(i)})$</tex></formula></emphasis> is near <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$0$</tex> </formula></emphasis> approaches <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$1-I(W)$</tex></formula></emphasis>. The polarized channels <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$\{W_N^{(i)}\}$</tex></formula></emphasis> are well-conditioned for channel coding: one need only send data at rate <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$1$</tex></formula></emphasis> through those with capacity near <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$1$</tex></formula></emphasis> and at rate <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$0$</tex></formula></emphasis> through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$W$</tex></formula></emphasis> with <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$I(W)&gt; 0$</tex></formula></emphasis> and any target rate <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$R ≪ I(W)$</tex></formula></emphasis>, there exists a sequence of polar codes <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$\{{\Fraktur {C}}_n;n\ge 1\}$</tex> </formula></emphasis> such that <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">${\Fraktur {C}}_n$</tex></formula></emphasis> has block-length <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$N=2^n$</tex> </formula></emphasis>, rate <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$\ge R$</tex></formula></emphasis>, and probability of block error under successive cancellation decoding bounded as <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$P_{e}(N,R) \le O(N^{-{1\over 4}})$</tex> </formula></emphasis> independently of the code rate. This performance is achievable by encoders and decoders with complexity <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$O(N\log N)$</tex></formula></emphasis> for each. </para>

Optimal Successive Group Decoders for MIMO Multiple-Access Channels

We consider a slow-fading narrowband multiple-input multiple-output (MIMO) multiple-access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) that simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the error exponent of the decodable set of users. An adaptive SGD is derived which not only retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight (in the limit of high signal-to-noise ratio (SNR)) affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacity yielded by the OSGD. Limiting expressions for the relevant capacities as the number of users and the number of receive antennas approach infinity are also obtained and it is shown that the OSGD yields symmetric capacity gains commensurate with the decoding complexity allowed. Simulation results with practical low-density parity-check (LDPC) outer codes show that the OSGD offers significantly improved performance at low decoding complexity.

Teaching &amp; Learning Guide for: The Ins and Outs of Introspection

Author's IntroductionPhilosophical interest in introspection has a long and storied history, but only recently – with the ‘scientific turn’ in philosophy of mind – have philosophers sought to ground their accounts of introspection in psychological data. In particular, there is growing awareness of how evidence from clinical and developmental psychology might be brought to bear on long‐standing debates about the architecture of introspection, especially in the form of apparent dissociations between introspection and third‐person mental‐state attribution. It is less often noticed that this evidence needs to be interpreted with due sensitivity to distinctions between different types of introspection, for example, introspection of propositional attitudes (beliefs, desires) vs. introspection of phenomenally conscious states (pains, emotional feelings). As contemporary debates about the machinery of introspection – and debates about mindreading in general – move forward, these distinctions are likely to figure more prominently.Author Recommends:Peter Carruthers, ‘Simulation and Self‐Knowledge: A Defense of Theory‐Theory’, in Theories of Theories of Mind, eds. P. Carruthers and P. K. Smith (Cambridge: Cambridge University Press, 1996), 22–38.Defends a sophisticated form of the theory‐theory of introspection, according to which we come to know at least some of our mental states (e.g., propositional attitudes) by reasoning from an innate folk‐psychological theory.Fred Dretske, ‘Introspection’, in Naturalizing the Mind (Cambridge, MA: MIT Press, 1995), 39–63.Introduces and defends the idea of introspection as ‘displaced perception’.Alvin Goldman, ‘Self‐Attribution’, in Simulating Minds: The Philosophy, Psychology, and Neuroscience of Mindreading (Oxford: Oxford University Press, 2006), 223–57.Defends a version of the ‘inner sense’ view of introspection in which mental state types are classified via their neural properties, and mental contents are classified via ‘redeployment’.Alison Gopnik, ‘How We Read Our Own Minds: The Illusion of First‐Person Knowledge of Intentionality’, Behavioral and Brain Sciences 16 (1993): 1–14.A noted psychologist defends a version of the theory‐theory of introspection, citing evidence of developmental symmetries between first‐person and third‐person mental‐state attribution.Robert Gordon, ‘Simulation without Introspection or Inference from Me to You’, in Mental Simulation: Evaluations and Applications, eds. T. Stone and M. Davies (Oxford: Blackwell, 1995), 53–67.Develops the idea of ascent routines – the rough analog of ‘displaced perception’ for the introspection of propositional attitudes.Uta Frith and Francesca Happé, ‘Theory of Mind and Self‐Consciousness: What Is It Like to Be Autistic?’Mind and Language 14 (1999): 1–14.Appeals to evidence from autism to motivate the idea that first‐person and third‐person mental‐state attribution have a common basis.Shaun Nichols and Stephen Stich, ‘Reading One's Own Mind’, in Mindreading: An Integrated Account of Pretence, Self‐awareness, and Understanding other Minds (Oxford: Oxford University Press, 2003), 150–99.Presents a comprehensive critique of leading theories of introspection (especially the theory‐theory), then introduces and defends the authors’ preferred alternative, the ‘monitoring mechanism’ account.Jesse Prinz, ‘The Fractionation of Introspection’, Journal of Consciousness Studies 11 (2004): 40–57.Develops the idea that introspection admits of several varieties.Philip Robbins, ‘Knowing Me, Knowing You: Theory of Mind and the Machinery of Introspection’, Journal of Consciousness Studies 11 (2004): 129–43.Defends a hybrid view of introspection for propositional attitudes, according to which both theoretic inference and monitoring play a role.Sample Syllabus: Week 1: Theory‐theory Alison Gopnik, ‘How We Read Our Own Minds: The Illusion of First‐Person Knowledge of Intentionality’, Behavioral and Brain Sciences 16 (1993): 1–14.Peter Carruthers, ‘Simulation and Self‐Knowledge: A Defense of Theory‐Theory’, in Theories of Theories of Mind, eds. P. Carruthers and P. K. Smith (Cambridge: Cambridge University Press, 1996), 22–38. Week 2: Displaced perception and semantic ascent Fred Dretske, ‘Introspection’, in Naturalizing the Mind (Cambridge, MA: MIT Press, 1995), 39–63.Robert Gordon, ‘Simulation without Introspection or Inference from Me to You’, in Mental Simulation: Evaluations and Applications, eds. T. Stone and M. Davies (Oxford: Blackwell, 1995), 53–67. Week 3: Monitoring theory Shaun Nichols and Stephen Stich, ‘Reading One's Own Mind’, in Mindreading: An Integrated Account of Pretence, Self‐awareness, and Understanding Other Minds (Oxford: Oxford University Press, 2003), 150–99. Week 4: Hybrid approaches Alvin Goldman, ‘Self‐Attribution’, in Simulating Minds: The Philosophy, Psychology, and Neuroscience of Mindreading (Oxford: Oxford University Press, 2006), 223–57.Philip Robbins, ‘Knowing Me, Knowing You: Theory of Mind and the Machinery of Introspection’, Journal of Consciousness Studies 11 (2004): 129–43.Focus Questions: What distinguishes ‘inside access’ from ‘outside access’ views of introspection? To what extent is the theory‐theoretic approach to introspection wedded to the idea that first‐person and third‐person mindreading are mechanistically symmetric capacities? What reasons are there for distinguishing between different types of introspection, and why might those taxonomic distinctions matter for theory construction in this area? In what sense, if any, are personality traits introspectible? Debates about third‐person mindreading have revolved around the relative merits of theory‐theory and simulation theory, whereas debates about introspection have taken a slightly different focus. For example, no one has defended a simulation‐theoretic account of introspection. Why might that be?