Binary Discrete Memoryless Channels Research Articles

Belief Propagation Decoding of Polar Codes Using Intelligent Post-Processing

Polar code is a channel coding method that has been proved to be able to reach Shannon capacity in the binary discrete memoryless channel. Because of the superior performance and low encoding and decoding complexity, polar code has attracted extensive attention in the industry and been chosen as the channel coding scheme for the control channel in the scenario of EMBB in 5G mobile communication. In this work, we propose an intelligent BP decoding algorithm of polar code based on smart post-processing. We employ the neural network to classify the output data of regular BP decoding into “good-bit” and “bad-bit” categories. We also design a strategy to search the bits, which are most probably incorrect from the “bad-bit” group for post-processing. Then, we can invert the “bad-bit” to correct the residual error in the Belief Propagation (BP) iterative process. Simulation results prove that the proposed algorithm can achieve at least 0.5dB error correction performance enhancement compared with the regular BP decoding with slight computation complexity and energy consumption increase.

Polar codes for non-identically distributed channels

We introduce new polar coding schemes for independent non-identically distributed parallel binary discrete memoryless channels. The first scheme is developed for the case where underlying channels are time invariant (the case of a deterministic channel parameters), while the other schemes deal with a scenario where underlying channels change based on a distribution (the case of random channel parameters). For the former case, we also discuss the importance of the usage of an interleaver Q to enhance system reliability, and for the latter case, we model the channel behavior of binary erasure channels. It is shown that the proposed polar coding schemes achieve a symmetric capacity.

Implementation of Polar Codes over AWGN and Binary Symmetric Channel

Objectives: Forward Error Correction (FEC) is a mechanism that has been used for years to improve the reliability of digital communications over wireless channels as they are subjected to interference, fading and noise. The goal of FEC is to add some redundant data to the input stream which facilitates the receiver to recognize and correct the errors with no need of sender to transmit the data again. In this paper we have computed bit error rate using polar codes in an Additive White Gaussian Noise Channel (AWGN) and Binary Symmetric Channel (BSC) at different block lengths. Methods/Analysis: Shannon limit states that it is the maximum amount of information that any given channel can carry. Latterly, there have been inventions in Forward Error Correction (FEC) area that allows today's systems to approach the Shannon limit. One such advancement in FEC is Polar Codes which has mathematically proved to attain the Shannon capacity for Binary Discrete Memoryless Channels using the phenomenon of channel polarization which states that by recursively combining and splitting N individual channels, some channels will become completely noiseless and some become noisy. These noiseless channels are then chosen to send information bits. Findings: We have implemented polar codes over BIAWGN and BSC and have calculated their bit error rate's at different channel ranges. The decoder used for decoding polar codes is successive cancellation decoder and it's seen that the performance is not that good at small block lengths but as the block length increases the performance improves when compared with the un-coded data stream. Applications: As polar codes are the first codes that achieve the Shannon capacity, so they seem to be the best solution for discrete memoryless channels which encounter packet failures and other noisy disturbances. Also, apart from channel encoding, polar codes found its applications in lossy and lossless source coding, coding for secrecy, communication over multiple access channels.

Extremal Channels of Gallager's $E_{0}$ Under the Basic Polarization Transformations

We study the extremality of the binary erasure channel and the binary symmetric channel for Gallager's reliability function E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarization. In particular, we show that amongst all binary discrete memoryless channels of a given E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (ρ) value, for a fixed ρ ≥ 0, the binary erasure channel and the binary symmetric channel are extremal in the evolution of E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> under the one-step polarization transformations.

Power Efficient Design of Polar Code

Polar codes are the family of the codes which are first ones to achieve channel capacity of any binary discrete memory less channel (B-DMC) with an explicit construction. The method relates with polar codes, channel polarization and encoding & decoding of polar code is considered that in the live structure of polar code when BER gets increase, channel capacity is satisfied but overall power of data transmition in channel gets increase. So here in this analysis the main issue is related with the power consumption. Encoding & decoding construction of polar codes is based on XOR-XNOR gates. The XOR-XNOR circuits’ design which uses 6 transistors instead of conventional structure is designed and it is suitable for lowvoltage and low-power application by achieving lower delay, power consumption and power-delay product (PDP).So by using this design phenomenon of XOR-XNOR gate it is possible to construct power efficient encoding and decoding of polar codes.

Optimal Ultrasmall Block-Codes for Binary Discrete Memoryless Channels

Optimal block-codes (in the sense of minimum average error probability, using maximum likelihood decoding) with a small number of codewords are investigated for the binary asymmetric channel (BAC), including the two special cases of the binary symmetric channel (BSC) and the Z-channel (ZC), both with arbitrary cross-over probabilities. For the ZC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two, three, and four codewords and conjectured in the case of five codewords. For the BSC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two and three codewords and conjectured in the case of four codewords. For a general BAC, the best codebooks under the assumption of a threshold decoder are derived for the case of two codewords. The derivation of these optimal codes relies on a new approach of constructing and analyzing the codebook matrix not rowwise (codewords), but columnwise. This new tool leads to an elegant definition of interesting code families that is recursive in the blocklength n and admits their exact analysis of error performance. This allows for a comparison of the average error probability between all possible codebooks.

Bounds on algebraic code capacities for noisy channels. I

This paper continues the study of algebraic code capacities, which were introduced by Ahlswede (1971) . He states an upper bound for the rates of codes which have the property that the code words form a linear space and the decoding procedure is arbitrary. It was asked (problem 5) whether this upper bound is actually the capacity if we deal with average errors. We answer this question in the affirmative for binary discrete memoryless channels. For nonbinary discrete memoryless channels we obtain slightly weaker result: If we allow those codes which have as code words a coset of a group which is a linear space, then the upper bound is again the capacity. An example shows that the result is not true for maximal error. In paragraph 3 we prove that the linear code capacity for compound channels with invariant transition probabilities equals the capacity for compound channels as given by Wolfowitz (1960) .