How to Quantize nn Outputs of a Binary Symmetric Channel to n−1n-1 Bits?

Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The "most informative Boolean function" conjecture postulates that the maximal mutual information between $Y^n$ and any Boolean function $\mathrm{b}(X^n)$ is attained by a dictator function. In this paper, we consider the "complementary" case in which the Boolean function is replaced by $f:\left\{0,1\right\}^n\to\left\{0,1\right\}^{n-1}$, namely, an $n-1$ bit quantizer, and show that $I(f(X^n);Y^n)\leq (n-1)\cdot\left(1-h(\alpha)\right)$ for any such $f$. Thus, in this case, the optimal function is of the form $f(x^n)=(x_1,\ldots,x_{n-1})$.Comment: 5 pages, accepted ISIT 201

Random Coding Error Exponents for the Two-User Interference Channel

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.Comment: accepted IEEE Transactions on Information Theor

Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions

We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the mismatched MSE of a codeword (from a randomly selected code), corrupted by a Gaussian vector channel. In the second part, we provide several examples to demonstrate phase transitions in the behavior of the MSE. These examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions.Comment: 58 pages;Submitted to IEEE Trans. on Information Theor

Channels with Cooperation Links that May Be Absent

It is well known that cooperation between users in a communication network can lead to significant performance gains. A common assumption in past works is that all the users are aware of the resources available for cooperation, and know exactly to what extent these resources can be used. Unfortunately, in many modern communication networks the availability of cooperation links cannot be guaranteed a priori, due to the dynamic nature of the network. In this work a family of models is suggested where the cooperation links may or may not be present. Coding schemes are devised that exploit the cooperation links if they are present, and can still operate (although at reduced rates) if cooperation is not possible.Comment: Accepted for publication in the IEEE transaction on Information Theory, June 201

Monetary Policy Objectives in Pakistan : An Empirical Investigation

The Taylor rule (1993) focuses only on two objectives : output and inflation. In practice, the central banks loss function (especially in developing countries) contains objectives other than these two, like the interest rate smoothing, exchange rate stabilisation, etc. In this study, the monetary policy reaction function has been estimated, including five objectives for monetary policy as well as controlling for the effect of three other factors. Whereas the results confirm the counter-cyclical response of monetary policy to the factors in the loss function, the response of interest rate to changes in the foreign exchange reserves and the government borrowing has been negative. Variance decomposition shows that most of the variation in the interest rate is explained by its own lagged values. Other variables, in explaining variation in the interest rate, can be ranked as inflation, government borrowing, exchange rate, output gap, trade deficit, and, finally, the foreign exchange reserves.Monetary Policy Objectives, Variance Decomposition, Call Money Rate

Contribution of High-Yield Varieties Seeds to Major Food Crops Production, Yield and Area in Punjab - Pakistan

The present study is undertaken to measure the contribution of HYVs to major food crops (Wheat, rice, bajra, jowar and maize) production, yield and area in Pakistan Punjab. The study is based on secondary data for the last 44 years, i.e., from 1951-52 to 1994-95. For this purpose, a comparison of growth rates for production, yield and area is made (1) between period I (1951 to 1964) and period II 1965 to 1978). (2) between period II and period III (1979 to 1994) and (3) between period I and period IV (1951 to 1994). The study shows that the influence of HYV seed on production, yield and area for major food crops in Punjab is mixed. The contribution of HYVs to production, area and yield growth for wheat is remarkable. The adoption of HYVs has helped to accelerate the growth rate for production and yield for rice and maize in period II. In case of Jowar despite the fact that its area and production decreased its yield increased in period II, which may be due to the adoption of HYV seeds.Growth, Comparison, Periods, Time-series, Semi-log, HYV seed, Food crops, Area, Yield.

Monetary Policy Objectives in Pakistan: An Empirical Investigation

The Taylor rule (1993) focuses only on two objectives: output and inflation. In practice, the central bank’s loss function (especially in developing countries) contains objectives other than these two, like the interest rate smoothing, exchange rate stabilisation, etc. In this study, the monetary policy reaction function has been estimated, including five objectives for monetary policy as well as controlling for the effect of three other factors. Whereas the results confirm the counter-cyclical response of monetary policy to the factors in the loss function, the response of interest rate to changes in the foreign exchange reserves and the government borrowing has been negative. Variance decomposition shows that most of the variation in the interest rate is explained by its own lagged values. Other variables, in explaining variation in the interest rate, can be ranked as inflation, government borrowing, exchange rate, output gap, trade deficit, and, finally, the foreign exchange reserves.Monetary Policy Objectives, Variance Decomposition, Call Money Rate

Trends and Growth in Livestock Population in Sindh: A Comparison of Different Censuses

Livestock represents an important component of the agricultural sector in Pakistan especially Sindh. Indeed, crop and livestock activities are, to a great extent, interdependent upon each other, for their functioning within the farm sector. The latter provides inputs like farm yard manure (FYM) and draught power for the crop sector and, in turn uses fodder, crop products and residues. The present study has, therefore been undertaken to see the trend and growth rates of cattle, buffaloes, sheep, goats, and camels in Sindh during 1955 to 1996 livestock censuses. The study uses the livestock census data for 1955, 1960, 1972, 1976, 1986, and 1996. The study reveals that the population of cattle, buffaloes, sheep, goats, and camels has become steadily more important in the livestock economy of Sindh during the last two livestock census as compared to other provinces. The two types of livestock that showed relatively high growth rates over the four decades (1955-1996) are goats and sheep; the cattle, camels and buffaloes recorded relatively low growth rates. The highest number of cattle, sheep, goats and camels in Tharparkar are mainly glaring because the valley of Nagarparkar is richer in vegetable growth, which supports these types of livestock. A large number of buffaloes in Hyderabad and Nawabshah are mainly found, because in these two districts there are a large number of big farmers who can afford their farming in order to sell their milk.Livestock, Trends, Comparison, Historical, Compound, Growth-rate, Semi-log exponential, Sindh