Lyons Zhang (@fpgaplayer)

Digital signal process, digital communication, FPGA engineer. He has been worked at Tieto company since 2011. He is a fan of Rick Lyons.

5G NR QC-LDPC Encoding Algorithm

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 ${\bf I}(P_{i,j})$ of size $Z_c \times Z_c$ is obtained by circularly shifting the identity matrix $\bf I$ of...

Polar Coding Notes: A Simple Proof

November 8, 2018

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 provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...

Polar Coding Notes: Channel Combining and Channel Splitting

October 19, 2018

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 channel between the input sequence $u_1^N$ to a linear encoder and the output sequence $y^N_1$ of $N$...

Half-band filter on Xilinx FPGA

1. DSP48 Slice in Xilinx FPGA

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. Two-channel Symmetric Systolic Half-band FIR

Figure 3: 2-Channel...

Hello Pro. Rick Lyons，Thank you for your magnificent fascinating blog https://www.dsprelated.com/showarticle/143.phpYes, you are right. The system function...

Hello Pro. Rick Lyons,Thank you very much for your incredibly fast replay.It seems that R in Eq.(3) indicates there is a downsampling R, for the Hc(z)=1-z^(-RM).I...

Re: Digital signal processing

Dear Prof. Rick Lyons,Hope you are a handsome gentleman and happy everyday!I confused by Hogenauer's paper, could you help me?Question about Hogenauer's Paper (dsprelated.com)Thank...

Before I have not read Hogenauer's paper, but when I read I am confused about the paper. Could somebody help me?The denominator of (A2)，Here |z| = 1, why the second...

Re: Off Topic: Binary Numbers

At least 2000 years ago, the primordial "Bagua" appeared. Don't know what's this? Haha...In China, crystal ball was useless, the wizard can predict everything...

The MathJax CDN is shutting down on April 30, 2017!

https://www.mathjax.org/I don't believe April Fool joke.  :)

Re: Source coding in WiFi or LTE

speech code : e.g. : AMR for 2G, 3G , 4G; AMR-WB for 4G(VoLTE)

Re: Interpolate complement value

Thank you very much @drmike and @Tim Wescott, I am sorry I didn't say clearly, I mainly care about the Mix-Mode in the doc.complement.pngIn short, what are the...

Interpolate complement value

I read a doc http://www.analog.com/media/en/technical-documenta... , page 49 AD9119_9129_page49.pdf , found an interesting implementation. I greatly appreciate If...

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