Proof of Convergence for Correct-Decoding Exponent Computation

For a discrete memoryless channel with finite input and output alphabets, we prove convergence of a parametric family of iterative computations of the optimal correct-decoding exponent. The exponent, as a function of communication rate, is computed for a fixed rate and for a fixed slope

Channel Input Adaptation via Natural Type Selection

For the model of communication through a discrete memoryless channel using i.i.d. random block codes, where the channel is changing slowly from block to block, we propose a stochastic algorithm for adaptation of the generating distribution of the code in the process of continuous reliable communication. The purpose of the algorithm is to match the generating distribution $Q(x)$ to the changing channel $P(y\,|\,x)$, so that reliable communication is maintained at some constant rate $R$. This is achieved by a feedback of one bit per transmitted block. The feedback bit is determined by the joint type of the last transmitted codeword and the received block, a constant threshold $T>R$, and some conditional distribution $\Phi(x\,|\,y)$. Depending on the value of the feedback bit, the system parameters $Q(x)$ and $\Phi(x\,|\,y)$ are both updated according to the joint type of the last transmitted and received blocks, or remain unchanged. We show that, under certain technical conditions, the iterations of the algorithm lead to a distribution $Q(x)$, which guarantees reliable communication for all rates below the threshold $T$, provided that the discrete memoryless channel capacity of $P(y\,|\,x)$ stays above $T$.Comment: 5 pages, 1 figure, submitted to ISIT-201

Channel input adaptation via natural type selection

We consider a channel-independent decoder which is for i.i.d. random codes what the maximum mutual-information decoder is for constant composition codes. We show that this decoder results in exactly the same i.i.d. random coding error exponent and almost the same correct-decoding exponent for a given codebook distribution as the maximum-likelihood decoder. We propose an algorithm for computation of the optimal correct-decoding exponent which operates on the corresponding expression for the channel-independent decoder. The proposed algorithm comes in two versions: computation at a fixed rate and for a fixed slope. The fixed-slope version of the algorithm presents an alternative to the Arimoto algorithm for computation of the random coding exponent function in the correct-decoding regime. The fixed-rate version of the computation algorithm translates into a stochastic iterative algorithm for adaptation of the i.i.d. codebook distribution to a discrete memoryless channel in the limit of large block length. The adaptation scheme uses i.i.d. random codes with the channel-independent decoder and relies on one bit of feedback per transmitted block. The communication itself is assumed reliable at a constant rate $R$. In the end of the iterations the resulting codebook distribution guarantees reliable communication for all rates below $R + \Delta$ for some predetermined parameter of decoding confidence $\Delta > 0$, provided that $R + \Delta$ is less than the channel capacity