Lyons Zhang Blog on DSPRelated.com
https://www.dsprelated.com/blogs-1/nf/Lyons_Zhang.php
Lyons Zhang Blog on DSPRelated.com
https://www.dsprelated.com/blogs-1/nf/Lyons_Zhang.php
https://d23s79tivgl8me.cloudfront.net/user/profilepictures/55346.jpgen-USThu, 08 Dec 2022 08:42:26 +000016704889465G NR QC-LDPC Encoding Algorithm
https://www.dsprelated.com/showarticle/1297.php
3GPP 5G has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes, which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding using simple shift registers and logic circuits. 5G NR QC-LDPC Circulant Permutation Matrix

A circular permutation matrix ${\bf...]]>
Tue, 10 Sep 2019 10:13:29 +0000Lyons ZhangPolar Coding Notes: A Simple Proof
https://www.dsprelated.com/showarticle/1203.php
For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.

Mrs. Gerber’s Lemma

Mrs. Gerber’s Lemma...]]>
Thu, 08 Nov 2018 14:13:15 +0000Lyons ZhangPolar Coding Notes: Channel Combining and Channel Splitting
https://www.dsprelated.com/showarticle/1201.php
Channel Combining

Channel combining is a step that combines copies of a given B-DMC $W$ in a recursive manner to produce a vector channel $W_N : {\cal X}^N \to {\cal Y}^N$, where $N$ can be any power of two, $N=2^n, n\le0^{[1]}$.

The notation $u_1^N$ as shorthand for denoting a row vector $(u_1, \dots , u_N)$.

The vector channel $W_N$ is the virtual...]]>
Fri, 19 Oct 2018 09:35:34 +0000Lyons ZhangHalf-band filter on Xilinx FPGA
https://www.dsprelated.com/showarticle/124.php
There are many DSP48 Slices in most Xilinx® FPGAs, one DSP48 slice in Spartan6® FPGA is shown in Figure 1, the structure may different depending on the device, but broadly similar.

Figure 1: A whole DSP48A1 Slice in Spartan6 (www.xilinx.com)

2. Symmetric Systolic Half-band FIR

Figure 2: Symmetric Systolic Half-band FIR Filter

3....]]>Tue, 30 Nov 2010 12:58:29 +0000Lyons Zhang