In a network application, channel coding alone is not sufficient to reliably transmit a message of finite length K from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. In this scenario RLNC has been shown to have a throughput advantage over TDMA schemes as K→∞ and q→∞. In this paper we focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel code rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small message lengths K and small q.

Channel coding alone is not sufficient to reliably transmit a message of finite length from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. We focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel coding rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small K and small q.

It has been widely observed that there exists a fundamental tradeoff between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity-achieving code ensembles typically are asymptotically bad in the sense that their minimum distance does not grow linearly with block length, and they therefore exhibit an error floor at moderate-to-high signal-to-noise ratios, asymptotically good codes usually converge further away from channel capacity. In this paper, we introduce the concept of tuned turbo codes, a family of asymptotically good hybrid concatenated code ensembles, where asymptotic minimum distance growth rates, convergence thresholds, and code rates can be tradedoff using two tuning parameters:$\lambda $and$\mu $. By decreasing$\lambda $, the asymptotic minimum distance growth rate is reduced in exchange for improved iterative decoding convergence behavior, while increasing$\lambda $raises the asymptotic minimum distance growth rate at the expense of worse convergence behavior, and thus, the code performance can be tuned to fit the desired application. By decreasing$\mu $, a similar tuning behavior can be achieved for higher rate code ensembles.

Channel coding alone is not sufficient to reliably transmit a message of finite length from a source to one or more destinations. To ensure that no data is lost, channel coding on the physical layer needs to be combined with rateless erasure correcting schemes such as automatic repeat request (ARQ) or random linear network coding (RLNC) on a higher layer. In this paper we consider channel coding on a binary symmetric channel and random linear network coding for erasure correction. Given a message of length K and network coding over a finite Galois field of size q, we obtain the optimal number of blocks for network coding that minimizes the expected number of transmissions. We consider both a single link and broadcast to n destinations. As the field size of network coding gets large and the expected coding overhead in blocks becomes small, we show that, given our assumptions, the benefit of using a larger channel coded block outweighs the advantage of employing network coding over many blocks and the optimal number of number of blocks tends to one, making RLNC equivalent to simple ARQ.

The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with block length. However, in practice these codes cannot be decoded by a maximum likelihood decoder, and iterative decoding schemes must be employed. For low-density parity-check codes, the notion of trapping sets has been introduced to estimate the performance of these codes under iterative message passing decoding. In this paper, we present a closed form finite length ensemble trapping set enumerator for repeat multiple accumulate codes by creating a trellis representation of trapping sets. We also obtain the asymptotic expressions when the block length tends to infinity and evaluate them numerically.

It has recently been shown that the minimum distance of the ensemble of repeat multiple accumulate codes grows linearly with block length. In this paper, we present a method to obtain the distance growth rate coefficient of multiple-serially concatenated code ensembles and determine the growth rate coefficient of the rate 1/2 double-serially concatenated code consisting of an outer memory one convolutional code followed by two accumulators. We compare both the growth rate of the minimum distance, as well as the convergence behavior, of this code with rate 1/2 repeat multiple accumulate codes, and we show that repeat multiple accumulate codes have better minimum distance growth but worse performance in terms of convergence.

This paper proposes iterative estimation and decoding techniques for memoryless channels with a bounded number of abrupt changes in channel statistics. Specifically, the channel under consideration is a binary symmetric channel with a crossover probability that changes a bounded number of times during the transmission of a codeword; the channel state information to be estimated consists of the crossover probabilities of the different segments and the location(s) of the transition point(s). To estimate the transition points, a technique developed for source coding of piecewise-stationary memoryless sources is adapted; then the expectation-maximization algorithm is used to estimate the crossover probabilities. This segmentation/estimation is carried out on the error sequence of the currently hypothesized frame. Simulation results using turbo codes indicate that the proposed receiver performs almost as well as a receiver that has perfect knowledge of the channel.