. • They are called fair since it is constructed by an equal number of all possible such columns (the number is called L). • Each fair code can be constructed by duplicating C (M,L) fair many times. • The fair weak flip codes have a maximum minimum Hamming distance and achieve the Plotkin bound. • These codes are not optimal in the sense of average error probability over the binary symmetric ch...

In this study, a periodic zigzag channel with rectangular cross-section has been used in order to obtain a high-efficiency system for cooling a polymer electrolyte fuel cell. An appropriate function of fuel cells and enhancement of their lifetime require uniform temperature conditions of around 80°C. On the other hand, due to volume and weight constraints, a low-density compact heat exchanger i...

We establish an information theoretic inequality concerning the binary skew-symmetric broadcast channel that was conjectured by one of the authors. This inequality helps to quantify the gap between the sum rate obtained by the inner bound and outer bound for the binary skew-symmetric broadcast channel.

This paper calculates new bounds on the size of the performance gap between random codes and the best possible codes. The first result shows that, for large block sizes, the ratio of the error probability of a random code to the sphere-packing lower bound on the error probability of every code on the binary symmetric channel (BSC) is small for a wide range of useful crossover probabilities. Thu...

We consider LDPC codes, transmission over the binary symmetric channel (BSC), and decoding using Gallager’s algorithm A. For those ensembles whose threshold is determined by the behavior of the algorithm at the beginning of the decoding process we derive a scaling law. This scaling law has the same form as the scaling law which was established for the the case of transmission over the binary er...

We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117–122], we derive an asymptotic formula (when the noise parameter is small) for the ent...

Time-domain equalization is crucial in reducing inter-carrier and inter-symbol interference in multicarrier systems. A channel shortening time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter, placed in cascade with the channel produces an effective impulse response that is shorter than the channel impulse response. We show that finite length minimum mean squared error (M...

We consider bounded distance list decoding, such that the decoder calculates the list of all codewords within a sphere around the received vector. We analyze the performance and the complexity of this suboptimum list decoding scheme for the binary symmetric channel. The reliability function of the list decoding scheme is equivalent to the sphere-packing bound, where the decoding complexity is a...

Though the schemes are different, both Horstein’s and Kudryashov’s non-block strategies for communication with feedback over the binary-symmetric channel asymptotically achieve the identical reliability function (error exponent); a function that displays some curious features. For positive rates their reliability function is strictly larger than Burnashev’s and transitions discontinuously at th...

A procedure for suboptimizing the choice of convolution codes is described. It is known that random convolution codes that have been passed through a binary symmetric channel, or a binary erasure channel, have a low probability of error and are easily decoded, but no practical procedure for finding the optimum convolution code for long code lengths is known. A convolution code is defined by its...