Frisch Demand Functions and Intertemporal Behaviour in Consumption: The Turkish Case

This paper examines the intertemporal behaviour in consumption for Turkey which has been experiencing high and chronic inflation since the late 1970s. The Frisch demand system is used to estimate three separate but inextricably intertemporal elasticities: intertemporal price elasticities of demand, commodity-specific intertemporal elasticities, and the intertemporal substitution elasticity of consumption. Our main result is that the Turkish households are reluctant to move their expenditures on non-durable goods from the current period to the next period, regardless of how high nominal interest rates are. This interesting result shows that the consumption behaviour in Turkey has been mainly shaped by uncertainty created by inflationary process and the tendency towards hedging against inflation.

Polarization as a novel architecture to boost the classical mismatched capacity of B-DMCs

We show that the mismatched capacity of binary discrete memoryless channels can be improved by channel combining and splitting via Ar{\i}kan's polar transformations. We also show that the improvement is possible even if the transformed channels are decoded with a mismatched polar decoder.Comment: Submitted to ISIT 201

Status Updates in a multi-stream M/G/1/1 preemptive queue

We consider a source that collects a multiplicity of streams of updates and sends them through a network to a monitor. However, only a single update can be in the system at a time. Therefore, the transmitter always preempts the packet being served when a new update is generated. We consider Poisson arrivals for each stream and a common general service time, and refer to this system as the multi-stream M/G/1/1 queue with preemption. Using the detour flow graph method, we compute a closed form expression for the average age and the average peak age of each stream. Moreover, we deduce that although all streams are treated equally from a transmission point of view (they all preempt each other), one can still prioritize a stream from an age point of view by simply increasing its generation rate. However, this will increase the sum of the ages which is minimized when all streams have the same update rate

Polar Codes for Arbitrary DMCs and Arbitrary MACs

Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is $o(2^{-N^{1/2-\epsilon}})$, where $N$ is the block length. Encoding and decoding for these codes can be implemented with a complexity of $O(N\log N)$. It is shown that the same technique can be used to construct polar codes for arbitrary multiple access channels (MAC) by using an appropriate Abelian group structure. Although the symmetric sum capacity is achieved by this coding scheme, some points in the symmetric capacity region may not be achieved. In the case where the channel is a combination of linear channels, we provide a necessary and sufficient condition characterizing the channels whose symmetric capacity region is preserved by the polarization process. We also provide a sufficient condition for having a maximal loss in the dominant face.Comment: 32 pages, 1 figure. arXiv admin note: text overlap with arXiv:1112.177

Polar Codes for the m-User MAC

In this paper, polar codes for the $m$-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Ar{\i}kan's polarization technique applied individually to each user transforms independent uses of a $m$-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: (i) the `uniform sum rate' of the original MAC is preserved, (ii) the extremal MACs have uniform rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits; in this sense they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of $O(n \log n)$ (where $n$ is the block length), a block error probability of o(\exp(- n^{1/2 - \e})), and capable of achieving the uniform sum rate of any binary input MAC with arbitrary many users. An application of this polar code construction to communicating on the AWGN channel is also discussed

On Channel Resolvability in Presence of Feedback

We study the problem of generating an approximately i.i.d. string at the output of a discrete memoryless channel using a limited amount of randomness at its input in presence of causal noiseless feedback. Feedback does not decrease the channel resolution, the minimum entropy rate required to achieve an accurate approximation of an i.i.d. output string. However, we show that, at least over a binary symmetric channel, a significantly larger resolvability exponent (the exponential decay rate of the divergence between the output distribution and product measure), compared to the best known achievable resolvability exponent in a system without feedback, is possible. We show that by employing a variable-length resolvability scheme and using an average number of coin-flips per channel use, the average divergence between the distribution of the output sequence and product measure decays exponentially fast in the average length of output sequence with an exponent equal to $[R-I(U;V)]^+$ where $I(U;V)$ is the mutual information developed across the channel.Comment: 8 pages, 4 figures; to be presented at the 54th Annual Allerton Conference on Communication, Control, and Computin

On the Correlation Between Polarized BECs

We consider the $2^n$ channels synthesized by the $n$-fold application of Ar\i{}kan's polar transform to a binary erasure channel (BEC). The synthetic channels are BECs themselves, and we show that, asymptotically for almost all these channels, the pairwise correlations between their erasure events are extremely small: the correlation coefficients vanish faster than any exponential in $n$. Such a fast decay of correlations allows us to conclude that the union bound on the block error probability of polar codes is very tight.Comment: 9 pages, Extended version of a paper submitted to ISIT 201

Purchasing Power Parity Revisited: A Time-Varying Parameter Approach

We re-examine the validity of Purchasing Power Parity (PPP) proposition using Taylor's (2002) data set. Applying the Kalman filter process, our findings not only demonstrate the strong instability in the relationship between the dollar denominated foreign price levels and the US price level, but also rule out the empirical validity of the PPP hypothesis. Thus, we argue that the inference based on the Fisher-Seater methodology cannot account for the Lucas critique in the PPP testing procedure.Purchasing power parity, Fisher-Seater, time-varying parameter, Kalman filter

Content Based Status Updates

Consider a stream of status updates generated by a source, where each update is of one of two types: high priority or ordinary (low priority). These updates are to be transmitted through a network to a monitor. However, the transmission policy of each packet depends on the type of stream it belongs to. For the low priority stream, we analyze and compare the performances of two transmission schemes: (i) Ordinary updates are served in a First-Come-First-Served (FCFS) fashion, whereas, in (ii), the ordinary updates are transmitted according to an M/G/1/1 with preemption policy. In both schemes, high priority updates are transmitted according to an M/G/1/1 with preemption policy and receive preferential treatment. An arriving priority update discards and replaces any currently-in-service high priority update, and preempts (with eventual resume for scheme (i)) any ordinary update. We model the arrival processes of the two kinds of updates, in both schemes, as independent Poisson processes. For scheme (i), we find the arrival and service rates under which the system is stable and give closed-form expressions for average peak age and a lower bound on the average age of the ordinary stream. For scheme (ii), we derive closed-form expressions for the average age and average peak age of the high priority and low priority streams. We finally show that, if the service time is exponentially distributed, the M/M/1/1 with preemption policy leads to an average age of the low priority stream higher than the one achieved using the FCFS scheme. Therefore, the M/M//1/1 with preemption policy, when applied on the low priority stream of updates and in the presence of a higher priority scheme, is not anymore the optimal transmission policy from an age point of view

Polar codes for the two-user multiple-access channel

Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of which uncoded transmission is optimal. The sum rate achieved by this coding technique is the one that correponds to uniform input distributions. The encoding and decoding complexities and the error performance of these codes are as in the single-user case: $O(n\log n)$ for encoding and decoding, and $o(\exp(-n^{1/2-\epsilon}))$ for block error probability, where $n$ is the block length.Comment: 12 pages. Submitted to the IEEE Transactions on Information Theor