3 research outputs found
Bhattacharyya parameter of monomials codes for the Binary Erasure Channel: from pointwise to average reliability
Monomial codes were recently equipped with partial order relations, fact that
allowed researchers to discover structural properties and efficient algorithm
for constructing polar codes. Here, we refine the existing order relations in
the particular case of Binary Erasure Channel. The new order relation takes us
closer to the ultimate order relation induced by the pointwise evaluation of
the Bhattacharyya parameter of the synthetic channels. The best we can hope for
is still a partial order relation. To overcome this issue we appeal to related
technique from network theory. Reliability network theory was recently used in
the context of polar coding and more generally in connection with decreasing
monomial codes. In this article, we investigate how the concept of average
reliability is applied for polar codes designed for the binary erasure channel.
Instead of minimizing the error probability of the synthetic channels, for a
particular value of the erasure parameter p, our codes minimize the average
error probability of the synthetic channels. By means of basic network theory
results we determine a closed formula for the average reliability of a
particular synthetic channel, that recently gain the attention of researchers.Comment: 21 pages, 5 figures, 3 tables. Submitted for possible publicatio
Weight Structure of Low/High-Rate Polar Codes and Its Applications
The structure of a linear block code is pivotal in defining fundamental
properties, particularly weight distribution, and code design. In this study,
we characterize the Type II structure of polar codewords with weights less than
twice the minimum weight , utilizing the lower triangular affine (LTA)
transform. We present a closed-form formula for their enumeration. Leveraging
this structure and additionally characterizing the structure of weight
, we ascertain the complete weight distribution of low-rate and,
through the utilization of dual codes properties, high-rate polar codes,
subcodes of Reed--Muller (RM) codes, and RMxPolar codes. Furthermore, we
introduce a partial order based on the weight distribution and briefly explore
its properties and applications in code construction and analysis.Comment: 15 pages, 5 tables, 3 figure
Partially Coupled Codes for TB-based Transmission
In this thesis, we mainly investigate the design of partially coupled codes for transport block (TB) based transmission protocol adopted in 4G/5G mobile network standards. In this protocol, an information sequence in a TB is segmented into multiple code blocks (CBs) and each CB is protected by a channel codeword independently. It is inefficient in terms of transmit power and spectrum efficiency because any erroneous CB in a TB leads to the retransmission of the whole TB. An important research problem related to this TB-based transmission is how to improve the TB error rate (TBER) performance so that the number of retransmissions reduces.
To tackle this challenge, we present a class of spatial coupling techniques called partial coupling in the TB encoding operation, which has two subclasses: partial information coupled (PIC) and partial parity coupling (PPC). To be specific, the coupling is performed such that a fraction of the information/parity sequence of one component code at the current CB is used as the input of the component encoder at the next CB, leading to improved TBER performance. One of the appealing features of partial coupling (both PIC and PPC) is that the coupling can be applied to any component codes without changing their encoding and decoding architectures, making them compatible with the TB-based transmission protocol.
The main body of this thesis consists of two parts. In the first part, we apply both PIC and PPC to turbo codes. We investigate various coupling designs and analysis the performance of the partially coupled turbo codes over the binary erasure channel via density evolution (DE). Both simulation results and DE analysis show that such a class of codes can approach channel capacity with a large blocklength. In the second part, we construct PIC-polar codes. We show that PIC can effectively improve the error performance of finite-length polar codes by utilizing the channel polarization phenomenon. The DE-based performance analysis is also conducted. For both turbo codes and polar codes, we have shown that the partially coupled codes have significant performance gain over their uncoupled counterpart, demonstrating the effectiveness of the partial coupling